JPRS ID: 10015 TRANSLATION WORKS OF THE 10TH ALL-UNION SEMINAR ON STATISTICAL HYDROACOUSTICS ED. BY V.V. OL'SHEVSKIY, ET AL.

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- JPRS L/ 10015
25 September 1981
Translation
WORKS. OF THE 10TH ALL-UNION SCHOOL-SEMINAR
ON STATISTICAL HYDRC)ACOUSTICS
Ed. by
V.V. OI'shevskiy, et al.
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JPRS L/10015
25 September 1981
WORKS OF THE IOTH ALL-UNION SCHOOL-SEMINAR
ON STATISTICAL HYDROACOUSTICS
Novosibirsk TRUDY DESYATOY VSESOYUZNOY SHKOLY-SEMINARA PO STATISTI-
CHESKOY GIDROAKUSTIKE in Russian 1980 (signed to press 23 Oct 80)
pp 2-144
[Complete contents of collection of works "Works of the lOth All-Union
School-Seminar on Statistical Hydroacoustics", edited by
V.V. Ol'shevskiy, N.G. Zagoruyko, S.V. Pasechnyy and L.Ya. Taradanov,
Institute of Mathematics, Siberian Department, USSR Academy of
Sciences, 400 copies, 144 pages]
CONTENTS
Annotation 1
Statistical Hydroacoustics and Oceanography: Review of Models and
Operators and Classification of Problems
(V. V. 01'shevskiy) 2
Applied Aspects of the Theory of Linear Random Processes
(B. G. Marchenko) 16
Synthesis of Determinative Systems in Problems Involving Investigation
of the World Ocean
(Yu. Ye. Sidorov) 19
A Linguistic-Ir.formation Model of Statistica.l Hydroacoustics
(V. P. Sochivko) 27
- Stochastic Algorithms for Investigating Nonconvex Fimctions With Many
Variab les
(V. I. Alekseye v) 29
Simulation Computer Nbdeling _in Acoustico-Oceanographic Research:
Purposes, Special Features, Scientific Pmblems
(V. V. 01'shevskiy) 31
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Volumetric Noise Spatial Correlation Function for Surface Antennas
(Yu. B. Goncharov and I. L. Oboznenko) 50
Low-Frequency Reverberation Caused by the Scatterirtg of Sound on the
Foamy Surface of the Ocean
(V. P. Glotov) 53
Information Characteri.stics of Reverberation Caused by Wide-Band
Sources in a Shallow Sea
(T. V. Polyanskaya) 57
Statistical Analysis of Acoustic Signals Scattered by a Sea Surface
(Ya. P. Dragan and I. N. Yaw rskiy) 59
_ Investigation of the Interference Structure of the Acoustic Field of a
Nbdel Waveguide
(G. K. Ivanovz, V. N. Il � ina, Ye. F. Orlov and G. A. Sharonov) 61
Multidimensional Modeling in Statistical Hydmacoustics

~ (V. V. O1'shevskiy) 64
Spatial Covariation Fimction of a Sonic Field
(V. M. Kudryashov) 67
, On the Question of Anisotropy of the Ocean's Noise Field
(B. I. Klyachin)....................................................... 71
\
A Method of Itodeling a Robot With an Echo-Locator
(D. Ye. Okho ts imskiy, A. K. Platonov and V. Ye. Pryanichnikov) 74
Characteristic Differences in Arrival Angles and Times of Signals in
Separate Beams Under Conditions of a Clearly Expressed Zonal Structure
of a Sonic Field
(V. P. Akulicheva) 76
Spatial Filtration of a Signal in a Field of Feverberation and Noise
Interference During Scattered Emission and Reception
(V. V. Krizhanovskiy and S. V. Pasechnyy) 78
Detecting Noise Signals in a Layered, Heterogeneous Medium With
Dispersed ReceiverE
(V. G. Berkuta' and V. S. Pasechnyy) 84
Cactrolling the Positions of Radiation Patterr! Zeroes in Antenna Arrays
With Digital Signal Processing
- (L. N. Danilevskiy, Yu. A. Domanov, 0. V. Korobko and
B. I. Tauroginskiy) 88
Concentration Factor of a Horiwntal, Linear Antenna During Multibeam
Propagation of a Noise Signal in the Sea
(V. I. Bardyshev and V. A. Yeliseyevnin) 91
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Passive and Active Inverse Synthesis of the Aperture in Dispersed Systems
(V. V. Karavayev and V. V. Sazonov)............................ 94
Relationship Between Results of Optimal and Nonoptimal Processing of Broad-
Band Signals Received by a Scanning Antenna
(B. M. Salin) 97
On Adaptive Optimization of the Detection Algorithm in a Spatiotemporal
Information Processing System
(V. G. Gusev and Ye. V. Cherenkova) 99
On the Structure of an Adaptive Goniometer
(Yu. K. Vyboldin and L. A. Reshetov) 103
Holographic Methods for Spectral Analysis of Random Sonic Fields
(B. I. Mel'treger and Ye. I. K.heyfets) 106
On the Effect of Large-Scale Nonuniformities in the Refractive Index on
Shifts in Evaluations of Optimum Goniometric Systems
(M. I. Levin, L. A. Reshetov and G. Kh. Takidi) 108
Processing Hydroacoustic Images on a Real-Time Scale
' (V. N. Mikhaylovskiy, V. V. Gritsky, B. V. Kisil' and A. Yu. Lutsky)... 111
, Ttie Method of Correlated Holograms in Acoustic Investigations of the Ocean
(Ye. F. Orlov) 113
Pal'm's Rando m Field
(A. G. Buymov and M. T. Resnetnikov) 117
Combining tlie Principles of Invariance and Nondisplaceability With
Other Solving Rules Synthesis Methods Under Conditions of Prior
Inde terminacy
(Yu. Ye. Sidorov) 120
Basic Concepts of the Stability of Statistical Procedures
(F. P. Tarasenko and V. P. Shulerin) 128
Adaptive Processing of Ztao-Companent Noise Signals
(V. P. Peshkov) 134
Effect of Concentrated Reflectors on the Effectiveness of Hydroacoustic
Infirmation Processing
_ (A. P. Trifonov and Yu. S. Radchenko) 136
On the Quality of Some Evaluations of Maximum Likelihood
(V. V. Borodin) 140
Gaussian Signal Detection With a Lang Observation Time
(K. B. Krukovskiy-Sinevich) 143
On Selecting the Interference Classifier for Signal Detector Systems
(A. M. Zil'Lershteyn and Yu. S. Natkovich) 145
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Noise Signal Identification Under Conditions of Interference and
- Fre quency-Indep en dent Ilistortions
(V. V. Geppener, V. B. Nazarov.and M. A. Senilov)................ 147
Methods for Discovering the Properties of Objects on the Basis of the
Analysis of a Set of Return Signals
(I, 0. Arro, T. Yu. Sullakatko and V. R. Kheynrikhsen) 148
On an Algorithm for the Remote Determination of Pararaeters of Shells
(Ya. A. 14etsaveer) 152
Measuring the Quality Factor of the Primary Fil�ei's of a Human Being's
I7irectional Auditory System
(L. A. Zliestyannikov, V. A. Zverev and V. A. Chaplygin) 156
Principles of the Design of an Operational System for Predicting the
Acoustical Situation in the Ocean
,
(V. V. Ol'shevskiy, V. S. Timerkayev and Z. D. Usmanov) 158
On Selecting the Minim:is Distance Between 7.tao Antennas When Determining
the Correlation Function's Dependence on the Space Angle
(V. V. Buryachenko, V. S. Gorbenko and L. Ya. Taradanov) 162
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ANNO TA TION
/Text/ This collection contains materials from the lOth anniversary All-Uihion
School-Seminar on Statistical Hydroacoustics, which was organized by the Scientific
Council on Hydrop,:ysics of the USSR Academy of Sciences' Presidium, the 1JSSR
Academy of Sciences' Acoustics Institute, the Mathematics Institute of the USSR
Academy of Sciences' Siberian Department and the Kiev Polytechnic Institute.
- The seminar was held in Sukhumi, from 17 to 21 October 1978.
This collection's subject matter includes methodological questions on modern sta-
tistical acoustics; questions on the study of a hydroacoustic channEl and its char-
acteristics; questions on the processing of signals against a background of noise
and the transmission and processing of inf ormation on biological objects.
- The materials in this work will be of interest to scientific wor kers and special-
, ists in the field of hydrophysical research and information processing, as well as
graduate stiidents, engineers and senior students.
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STATISTICAL HYDROACOUSTICS AND OCEANOGRAPHY: REVIEW OF MODELS AND OPERATORS AND
CLASSIFICATION OF PROBLEMS
[Article by V. V. 01'shevskiy pp 3-15]
/Text/ 1. Introduction. The development of the theory and methods of statistical.
hydroacoustics, particularly in the last 10-15 years (see, for example, /1-6, 12,
13/), made it possible, on the one hand, to solve a whole series of scientific
problems related to the development of statistical models, the anal"sis and synthe-
sis of algorithms for the processing of hydroacoustic information, Lhe formulation
and conduct of simulated computer experiments and so on; on the other hand, the de-
velopment of statistical hydroacoustics engendered new problems directed at a more
thorough examination of various hydrophysical phenomena and the mechanis:n-s of their
funetioning, as well as the study of the interaction of hydroacoustic information
systems with the ocean. Primarily, these types of problems have to do with inves-
tigations of acoustico-oceanographic models--namely, the determination of the spe-
cial features of their formation, the analysis of the interrelationships of special
and general models, and the solution of different statistical problems emanating
from the need for a more thorough linderstanding of the acoustical situation, the
acoustic weather and tl-e acoustic climate in the ocean /137.
Generally speaking, acnustico-oceanographic research as a scientific field apPeared
quite long ago. It is sufficient to point out the fundamental works /1, 7-10/ to
make clear the definite direction of different investigators: for more than 30
years now, steps have been taken toward a joint (integrated) examination of oceano-
graphic and acoustic phenomena. In the 10 yeurs since 1969, the annual All-Union
School-Senainars on Statistical Hydroacoustics have been playing a significant role
in the formation of these outlooks / 67, along with the First Congress of Soviet
OceaYographers /117, which was held in 1977, the annual regional,seminar on
"Acoustical Methods of Investigating the Ocean" /12/, which has been held since
1976, and the First Semina.r on "Acoustic Statistic Models of the Ocean" /13/, which
was conducted in 1976. Alot-tcy with development in this direction, the last 10-15
years have also seen the development of a general methodology and constructive com-
puter programs for image i.dentification (see, in particular, /14-177 and others).
In these methods we have synthesized many heuristic ideas about searching for and
2
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making quantitative descriptions of regularities and ideas about classifying ob-
jects of various types and identifying them, in connection with wY:ich statistical
analysis was improved, procedures and programs for computer modeling were developed
and so on. At the same time, ideas about computer data banks have also been devel-
oped intensively in recent years: methods for forming them have been created,
along with information retrieval programs, interpreting programs, operational con-
~ trol systems fQr computers and so forth. All of this--the development of
acoustico-oceanographic statistical models, the accumulation of experimental data
about r_he ocean, the development oi image identification methods and the theory of
data banks, as well as methods for creating and using them--makes it possible, from
a rather general viewpoint, to form an opinion about contemporary stati.stical
acoustico-oceanographic problems, to review the models and operators that have been
created up until now and, finally, to formulate several problems on the formal lev-
el. On the whole, this worlc is of a systems (ir.tegraled) nature: essenJtially, it
seems to us, it is onl.y such an approach that can make i.t possible to tie special
and general models togetlier into a unified whole, indicate ttie positicn af individ-
ual problems in the general problem of investigating ttie ocean and, finally, deter-
mine the current level of development of the problem, while noting the near anrl re-
mote prospects in connection with this.
2. Formal Description. Let us introduce the following sets: OZ = the set of
oceanographic characteristics; OY = the set of the ocean's acoustic characterist-
ics; ClX = the set of characteristics of the acoustic fields in the ocean; Or~ _
= the set of output data of a hydroacoustic information system. The elements of
these sets are the vector functions
Z(Y) E OZ, Y~a) E OY, X~a) GX, R(n) C ()R,
it being the case
T
jec�-s: 2(Y) = oc
the ocean; X(a) _
output data. Let
vector functions,
that each of these vector functio
~ 4.
2anographic characteristics; Y(S)
the acoustic fields in the ocean;
us further introduce the transfer
so that
ns describes the following ob-
= acoustical characteristics of
K(n) = the information syetem's
statements between pairs of
--Y } = QYZ{ -?7 ~Y)}, X~~) = QXY{Y(R)}, -l R(n-)) = Q. {X~-Y a-T)}. (2)
Y
In a more compact form, systrm of equati.ons (2) can be written as the following se-
quence:
W0 = QyZ{Z(Y)}, '
~
X((X') = QXYZ{Z(Y)} = QXYQyZ{Z(Y)}, ~ (3)
R01) = QRXYZ{Z(Y)} = QRX14XY4YZ{Z(Y)},}
in connection with which ttie introduced operators correspond to the following coup-
lings: operator QyZ couples the oceanographic characteristics with the ocean's
acoustic characterislics; operator QXy couples the ocean's acoustic characteristics
with the characteristics of the aco.ustic fields in it; operator QRX couples the
hydroacoustic information systcm's output data with the acoustic fields; in addi-
- tion, from (3) it follows that QXYZ - QXYQYZ and QRXYZ - 4RXQXYQYZ� Let us mention
here tllat since, in the general case, operators QRX, QXY and QYZ are a combination
' of li_;iear (smoothing) and nonlinear (modulating) operators, their rearrangement
3
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when determining the combined operators QXYZ and QRXyZ is not permissible. Furthcr,
in the space of the vector functions (1) under discussion, it is necessary to in-
roduce distance ar the degree of proximity. Let us write the distance functionals
as follows:
dZ(k,k) = d[Zk(Y)'ZQ(Y)], dY(k,Q) = d[Yk~6),YQM]
- dX(k,Q) = d[Xk(a),XQ~a)], dR(k,Q) = d[ Rk~n),R(4)
. where k, k= numbers of the vector functions, the distances between which are being
determined. Let us now discuss the form of the description of the vector functions.
When investigating acoustic phenomena and information systems in the ocean accord-
~
ing to model (2) and (3), the original vector function is the random one (Y),
which characterizes the oceanographic situati'on. A completely probable description
of the vector functi.ons in the group of sets OZ, OY, OX and OR is given by the com-
bined probability distribution law .
Pr(Z,Y,X,R/X) (5)
of the vector functions under discussion, as well as by the distribution law
PrM,
(6)

it being the case that in the general case, the multidimensional value a character-
izes the complete set of acoustico-oceanographic conditions: in this sense, proba-
bility distribution (5) is provisional. It is obvious that the construction of the
complete acoustico-oceanographic probability model (5) and (6) is a practically un-
realizable task at the present time. Therefore, the first constructive step in
this direction is the construction of parrial probability models of the qpe:
Pr(Z/aZ), PrWaY), Pr(X/aX), Pr(R/aR)
together with the probability models of the operators
(7)
Pr(QYZ/'Y)'Z)j Pr(QXY/AX)aY), Pr(QRX/aR,aX), (8)
where aZ, aY, aX and ,}1R characterize the corresponding oceanographic and acoustic
conditions, the probability distributions of which must also be determined:
Pr(aZ), Pr(aY), Pr(~X), Pr(XR).
(9)
A second approximation to a full probability description of acoustico-oceanographic
conditions (5) and (6) is the assignment of the first joint distribution laws of
the type
+ -r -r + -r + +
Pr(Z,Y/aZ,aY), Pr(Y,X/XY,aX), Pr(X,R%aX)x R), (10)
which are possibly the probability distributions of operators (8), as well as the
conditions
PrOZ,aY), Pr(X Y, x X), Pr(axI aR). ~11)
This, as is the case with approximation (7)-(9), is an incomplete (partial) proba-
bility description of the acoustico-oceanographic models, although it is much more
difficult to realize it than description (7)-(9). Among the other approximations
to a complete probability model it is necessary to mention the correlational level
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of the description of the acoustico-oceanographic phenomena. In connection with
this, of course, an estimate of the degree of completeness of the description is
not guaranteed in the general case, although in a number of cases correlational
models prove to be quite effective. This type of correlational model of the vector
functions under discussion is presented in the form
K[I~ lZ] = KZ(Y',Y" IaZ) , K[V~)IaY) = KY6R' ~ Iay) ~ (lZ)

-'l i -T -Y -Y .

K[X(ic()/->aX] = KX(a~ ~a/xX~ ~ K[R(naR] _ K R(n' ,n"/aR)
together with the correlational models of the corresponding paired operators
- K(QYZ/aY'~Z), K(4XY/XX'~Y)' M4RX/XR,~X(1_3)
it being the case tllat as in ttie other cases under discussion, correlationa1 models
are provisional in the sense of the acoustico-oceanographic situation aZ, XY, AX

and aR, for which its own probability description must be given at (for example
- the level of (9).
3. Interpretation. Let us now discuss and give an acoustico-oceanographic inter-
pretation of the formal concepts of vector functions that were introducecl in
Section 2.
3A. Vector function
~(y) _ 1zl(Y1),z2(Y2),...,zq(Yq)l (14)
*
is understood to mean the set ot scalar functions zi(yi), i= l,q, of vector argu-
ments yi that describe the oceanographic--in the broad sense (atmospheric, aqueous
and geological)--phenomena affecting the ocean's acoustic characteristics. Primar-
ily, this means:
thc characteristics of the layer of atmosphere adjacent to the ocean's sLlface: in
connection with this, zl(_Y,1) describes the depen
the characteristics of the mixing of water masses and currents: in connection with
this, z9(Y9) describes the rate of motion as a function oL the spatial coordinates
/sic/> Yg - (A,t);
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_ the ocean's temperature characteristics, including both its surface and subsurface
~
waves: in connection with this, z10(Y10) describes the temperature's dependence on

the spatial and temporal coordinates, YlU -(p,t);
the ocean's salinity characteristics: in connection with this, z11(Y11),
z12(y12),...,zZ(YZ) describe the concentrations of different salts in the ocean as
a function of the spatial and temporal coordinates, Y11,Y12, �'�)yz -(P)t);
the characteristics of biological objects: in connection with this, zZ+1(YZ+1
-*zz+2(YZ+Z),...,zP~yp) describe the species composition of biological objects as a
_ function of the spatial and temporal coordinates, YZ+1,YZ+2,�.�,Yp _(P,t);
-r
the characteristics of the ocean's bottom: in connection with this, zp+1(Yp+1),
z+2(yp+2),...)z (Y ) describe the relationships of ttie different components of tne
P q Q
bottom, including ita surface, as a function of the spatial coordinates, Yp+l'
Yp+2,...,yq = ~P~�
All of these functions zi(yi) are random in nature, so their description is given
with the help of probability laws or their parameters.
3B. Vector function
Y(Q) _ [Yl(sl)IY2(62),...,yp0D)J (15)
is understood to mean the set of scalar functions yj(sj), j= l,p, of vector argu-

menrs Rj that describe the acoustic characteristics of the ocean rhat aFfect the
formation of acoustic fields in it. Primarily, this means:
the scattering characteristics, also including coherenr scattering, on irregulari-
~
ties in the water surface: in connection with this, yl(R1) describes the depend-
ence of the undulating surface's scattering function on the spatial and temporal
coordinates and the acoustic signal's frequency, a1 =(p,t,w);
the water surface's reflection characteristics: in connection with this, y202)
describes the dependence of the surface's scattering function on the spatial and
-r
temporal coordinates and the signal's frequency, S2 =(p,t,w);
the scattering characteristics, also including coherent scattering, on air bubbles
in the layer near the surface: in connection with this, Y3(S3) describes the de-
pendence of the layer's scattering function on the spatial and temporal coordinates
and the signal's frequency, R3 =(p,t,w);
the characteristics of scattering on the solid particles in the ocean layer: in
~
connection with this, y4(W describes the dependence of the particles' scattering
-r
function on the spatial ar.d temporal coordinates and the frequency, R4 =(p,t,(a);
the characteristics of scattering on temperature irregularities in the ocean: in
connection with this, y50 5) describes the dependence of the ir.regularities'
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scattering function on the spatial and temporal coordinates and the frequency, ~5 =

- the scattering characteristics, also including coherent scattering, on biological
objects in the ocean: in connection with this, y06)' y7(~7)-�,yz(sz) describe
the dependences of the scattering functions of different types of biological ob-
jects on the spatial and temporal coordinates and the frequency, R6,j,s8,�..,OZ =
-r
(P,t,W);
the refraction characteristics related to the nonuniformity of the ocean's tempera�-
}
ture and salinity: in connection with this, y+1( z+l)' yz+2~~z+2)' "''ym(~ m) de-
scribe the dependences of the acoustic wave re~fraction parameters (during their
-
propagation) on the spatial and temporal coordinates and the frequency, SZ+1'
(P)t,w);
- t~ie2absorpTion characteristics related to the effect of the ocean's temperature and
salinity, irregularities in its boundaries, air bubbles, biological objects and the
structure of the bottom: in connection with this, Ym+16sm+1)'ym+~(sm2)' "''y1~sX)
describe the dependence of the absorption functions on the spatia an tempora co-
~
ordinatPS and the frequency, S ,S ,R =(p,t,w);
the scattering characteristicsm+also+i,.ncl..uding coherent scattering, on irregulari-
ties on the bottom and nonuniformities in its structure: in connection with this,
ya+l(satl)'ya+2(~a+2)' "',y ) describe the dependences of the indicated objects'
11
scaftering f.unctions on the1Jtem
poral and spatial coordinates and the frequency,
-4.
S lR (P,t,w);
- t~elre~~ection ~haracteristics of the ocean bottom and its different structural
~
formations: in connection with this, yu+l0 +1)'y t2~su+ )'"''yv~sv) describe the
dependences of the reflection functions on t~ie spa~ial an9 temporal characteristics
- and the frequency, S tl,s +2,...3 _(P,t,w);
the characteristics ~t th~ sources of underwater nozses in the ocean, including
wave action from the water's surface, cavitation phenomena in the ocean, sources of
biological origin, manmade underwater equipment and seismic sources related to the
+
_ dynamics of the water masses: in connection with this, YV+10 v+l)'yv+20 v+2~'
i describe
...,yp(~P) the dependences af the sources' functions on the spatial and
- temporal coordinates and the frequency, Rv+14 v+2' p (p'tm'
The functions y�(~�) under discussion--as was the case with zi(yi)--are random, so
' their description is given with the help of probability laws and their parameters.
3C. The vector function
~ X(a) _ 1xl(al)1x2(a2),...,xm(am)1 (16)
is undgrstood to mean the set of scalar functions xk(ak), k= l,m, of vector argu-
ments ak that describe the acoustic fields in the ocean that affect hydroacoustic
information systems. Primarily, this means:
the field of direct signals: in connection with this, xl(a*l) describes these
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fields as a function of the spatial coordinates of the observation point, time and
-r
the frequency, a.l = (p,t,w);
the field cf reverberation signals: in connection with this, x2(a2) describes
these fielas as a function of the spatial coordinates of the observation point,

time and frequency, a2 = (p,t,w);
- the field of return signals: in connection with this, x3(a3) describes these
tields as a function of the spatial coordinates of the observation point, time and

frequency, a3 = (p,t,w);
~
_ the field of underwater noises: in connection with this, x4(a4) describes these
fields as a function of the spatial coordinates of the observation point, time and
frequency, 0.4 = (p,t,(A)).
3D. The vector function
. R(n) _ ~rl(nl),r2~n2),...,rn~nn)] (17)
is understood to mean the set of scalar functions rk(rjk), k= l,n, of vector argu-
- ~
ments nk that describe the processes at the hydroacoustic information systems' out-
puts. Since these systems are oF a measuring type, R~(~r1) usually means a set oF
statistical evaluations of different probability characteristics of the acoustic
fields for which one or more features are being studied. These can be evaluations
of mathematical expectations, moment functions of different orders, probability
densities, characteristic functions, correlation functions and others.
4. Data Banks. The basis of the solution of many informational acoustico-
oceanographic problems is data banks. Information on the sets OZ, Oy, OX and OR is
_ stored in them. In connection with this, the information is represented by tYie
subsets .
OZC OZ, OY C OY, OXC OX, ORc OR, (18)
since the sets themselves are ideal (complete) models, while the actual information
in them (indicated by the sign above) essentially corresponds to the working
models; that is, models obtained on the basis of experimental investigations, con-
structive theories and modeling. Along with these data banks (18), there are also
other banks in which information on the operators QYZ, QXY, 4RX, 4XYZ and QRXYZ is
stored. In a manner analogous to (18), the banks of operators naturally contain
information on the working operators, which are subsets of the ideal ones; that is,
QYZ c QYZ' 4XY C 4XY' 4RX c 4RX' QXY7, c 4XYZ' QRXYZ c 4RXYZ' (19)
since we do not know the ideal operators.
Acoustico-oceanographic information of the following types is stored in tlle data
banks:
1. The results of experimental investigations, including:
samples of random values, processes, fields and vector functions characterizing the
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phenomena observed in the ocean;
statistical estimates of the probability characteristics, as obtained by processing
the samples.
2. Empirical regularities about the acoustico-oceanographic situation.
3. Equations (and their solutions) describing acoustico-oceanographic pnenomena, as
= well as the characteristics of the hydroacoiistic information systems. .
5. Statistical Methods. The development of mathematical statistics methods, which
took place intens'ively over the course of many decades, resulted in the emergence
of a powerful (and one that has already become the classical) apparatus.for pro-
cessing the results of observations and testing hypotheses. However, two fundamen-
tal questions concerning the use of statistical methods have still not received
full and constructive answers. The first question concerns the use of statistical
procedures under dynamic conditions of observation of investigated phenomena and
objects: these are problems of the statistical analysis of heterogeneous samples,
nonstationary processes, nonisotropic and nonstationary fields and so on. The sec-
ond question concerns multidimensional statistical procedures. These two fields
are being developed at the present time, primarilY within the framework of the
overall problem of an artificial intellect /14-17/. Despite the fact that in con-
nection with this many methods are heuristic and in a number of cases even non-
rigorous, the successes and constructive results of the area of statistical analy-
sis are obvious.
6. Formulations of Several Typical Problems. As follows from what was. explained
above, most problems in the field of the investigation of acoustico-oceanographic
models include the following main aspects: first, each problem must be given a
clear acoustico-oceanographic interpretation; second, it is necessary to forrnulate
a groblem on the basis of clearcut formal definitions and concepts; third, it is
not mandatory to look for the solution of a problem with the help of analytical
methods, since image identification and similar methods are more appropriate here;
fourth, the solution of a problem will most likely be obtained with the help of a
computer (that is, with the help of numerical methods, modeling and computer simu-
lation methods. Below we will discuss several typical acoustico-oceancgraphic
problems, following the concepts explained in Sections 2-5 and keeping in mind the
methods from identification theory developed in the works of N.G. Zagoruyko and his
colleagues (see /15,16,18.197 and others).
6A. Filling Spaces in a Data Bank and Editing Its Elements. A data bank--particu-
larly a set of acoustico-oceanographic situation banks that are in accordance with
- "(1$) and (19)--cannot, of course, be full. The reasons for this lack of fullness
are, in the first place, the practac:il impossibility of obtaining exhaustive exper-
imental data on an entire set of acoustico-oceanographic conditions; in the second
place, the presence of errors when conducting experimental research; in the third
place, incomplete monitoring of the acoustico-oceanographic situation during exper-
iments; finally, in the fourth place, the lack of general acoustico-oceanographic
models at the present time. All of this results in a situation where a bank of
acoustico-oceanographic conditions is a set of tables (files) containing spaces in
the elements, the lines and the columns. The primary processing assignments of
- such a bank are /15,16,18,197:
filling the available spaces with the "most probable," "most nearly correct" image;
detecting errors in the data bank's tables; that is, "editing" it.
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Both these problems are solved by image identification methods that have now been
developed, in connection with which the objective redundancy of the information in
the data bank is used and the information content of the effect of some parts of
the tables (lines, columns) on the different elements 43-s investigated beforehand.
Thus, according to (18) and (19), a bank of acoustico-oceanographic conditions con-
sists of sets (see Sections 3 and 4) characterizing the properties of the four vec-
tor functions
J 0 = OZ[-)OYUOXUOR,
as well as the bank of operators of their interaction
(20)
Q= QYZ U4XY UQRX UQXYZ UQRXYZ` (21)
After the solution of the problems under discussion by image identification methods,
we obtain the improved banks 0* and Qwhich satisfy the conditions
(22)
0D pp, Q:) QQ,
where 0 and Q are ideal (complete) models of the sets of vector functions and oper-
_ ators, which, of course, are not known precisely.
6B. Determination of Classes of Oceanographic Characteristics According to Acoustic
Features. One o� the problems in image identification theorY is the determination
of classes (groups, taxons or clasters that are equivalent /15-17,197) into which
several objects in a space of features can be divided. For a whole series of prop-
ositions it is necessary to divide oceanographic characteristics into classes. The
main problem in connection with this is selecting the features in the space of
which the classification will be made. Keeping in mind the hydroacoustic aspects
and the final purpose of the solution of such a problem, as the features it is ne-
cessary to take acov.stical ones; that is, according to (1)-(3) and Section 3(see
3C and 3D) they can be vector functions
g(a) E OX (23)
or
4.
x (n)EoR' (24)
which are available in the data bank (see above, problem 6a).
With the help of taxonomic methods /15-17,197, by introducing distance dX(k,Q�),
dR(k,Z) in the spaces of vector functions (23) or (24) in accordance with (4), the
set OZ of oceanographic characteristics can be divided inEo the following subsets:
(25)
iOZ;�~Zi(l~Zj=$~ i#.l~
where 4Zi, i= 1,NZ, will also be the unknown, nonintersecting classes of oceano-
graphic characteristics. Let us mention here that when solving this problem, it is
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necessary to give either the allowable values of distance dXp, dR0 corresponding to
any of the classes ri or the desirable number of classes NZ into which set OZ is
- divided.
Thus, the division of set OZ into classes 4Zi according to acoustic features (for
}
example, according to vector functions RW) is done according to the following al-
gorithm: into class iZi enter all the vector functions .
k,k = var, ~26)
~k,lt,i(Y)E ~'Zi)
for which the condition
sup dR(k,k) : dR0 (27)
k,k
occurs. It goes without saying that in connection with this, one keeps in mind the
maximally complete utilization of information about the coupling operators (19) of
the vector functions under discussion.
6C. Determination of Classes of Acoustic Characteristics According to Oceanographic
Features. By its nature, this problem is similar (symmetrical) to problem 6B, the
only difference being that the space of the features is the set of vector functions
describing the oceanographic characteristics (see Sections 3 and 3A):
Z*(Y) E OZ, (28)
while set (23) or (24) corroborates the division into classes.

In connection.with this, the division of (for example) set OR into classes ,`~Rj ac-

faatiires (that iS, vector functions Z~('~()) 1S done accord-
ing to the following algorithm: into class -3'Rj enter all vector functions
Rk, Q,iE9Ri, k,Q = var, (29)
for which the condition.
sup dZ(k,k) < dZ0 (30)
k,Q
- occurs.
For class ~Ri there must occur conditions of the type of (25):
U4Ri - OR' jRi $RJ # J , (31)
i
where -3'R i= 1,NR, are the unknown, nonintersecting classes; NR = the total num-
ber of tAese classes.
6D. IdentificaLion of the Acoustic Situation. Problems af this type are formulated
in the fallowing manner: the classes of objects to be identified are given (in
this case, the classes,~'Ri of the hydroacoustic systems' output effects, L)4Ri
i
i= 1,NR, or the classes O'Xj of the acoustic fields,~j,9'X~ = OX, j= 1,NX); also
i
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given is the space of identification features (in this case, the vector functions
Z"(y)E OZ of the oceanological characteristics). When solving this problem, for
the given realizations ZZ(y), Q= 1,L, it is necessary to establish the classes 9RQ
n ~ J' }
y or~'XQto which ZQ(y) belong; that is, to determine the correspondence
ZQ(Y) RQ (32)
or
ZR(Y) (33)
_ Such a problem is solved by standard image identification methods /14-187, and its
specific nature in the acoustico-oceanographic interpretation under discussion is
ortly that it is necessary to allow correctly for the following operator couplings:.
R~~n) = QJRXYZ{Z"(y)}
or
(34)
X`(a) = QXYZ{Z~(Y) ~ (35)
keeping in mind the fact that Q~XYZ and QiyZ are of a stochastic nature.
6E. Identification of the Oceanographic Situation. This problem is similar (sym-
metrical) to problem 6D, the only difference being that what is given is the class-
es of oceanolo ical characteristics U~'~~ = 0~
Zi g ~ Zi Z, while the features are the
^ i
space R''~r1)E OR of the hydroacoustic information system's output effects or the

space a4 of the acoustic fields. The solution here is the determination of
the affiliation of realizations Rp(n), p= 1,P, or Xq(a)) q= to one of the
classes 3-ZP or ~Zq; that is, determination of the correspondence
RP01) ~ZP (36)
or
Xq~a) -i ~Zq. (37)
6F. Hierarchy of Classes: Acoustical Situation, Acoustic Weather and Climate.
Above (see problems 6B-6E) classes of acoustico-oceanographic models with some
boundary distances do given in the space of the selected features, such as dR0 (ac-
cording to (27)) or dZo (according to (30)) and so on. In connection with this
analysis, however, the spatiotemporal coordinates (tllat is, the different regions
of tte world ocean) were not figured in explicit form. We will assume that the
acoustic characteristics that are of interest to us are described by the vector
:inction R(r1although the entire discussion can also be applied, in full measure,
- -r
- to the acoustic fields' vector function X}*(a). Let us introduce the concept of
spatiotemporal limitations
V = (P E (Ry�AR,V); t E (TV�ATV)), (38)
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U.,
where I2v determines the spatial coordinates of the center of the selected region;
ARV--its area; TV--tI1e initial moment of time; ATV--the observational Cicne interval.
We will call the acoustic situation that set of realizations of the vector func-
tions iv06n) that is defined for the limitations ~0:
Vo _ (p E(Rv�ARvO); t E(Tv�ATvo){Rvp(n)(39)
where pRvp and pTvo are selected on the basis of the statistical uniformity of the

ensemble of realizations {Rv0(n)}. In .c.onnection with this,
Rvp(n)E $RvO(Rv,Tv); (40)
that is, the vector functions under discussion form a set depending on the initial
coordinates ~v and the current time TV. The determination of classes (40) must be

made in the space of oceanographic features Z"~(y) according to the technique de-
scribed in problem 6C, using taxonomic methods. Let us mention here that the
choice of limitations Vo according to (39) can be made on the basis of the intro-

duction of a boundary value of distance dZ00 in the space Z"(y), which essentially
also determines class (40) as a function of the spatiotemporal coordinates. We
will consider the term "acoustic weather in the ocean" to mean seasonal changes in
the acoustic situation in some region of the ocean. This means that, according to
(40), acoustic weather corresponds tc the set
(41)
I ~i~T ~RvO(Rv'Tv~ - ~Rvw~RVw~ ~
i
j where IZvw definPs a region with homogeneous (in the statistical sense) acoustic
i weather satisfying the condition
i
' = arg [sup dRO (k, Q) : dRw] , Tv E (0,��) ~
(42)
i k,R
where dRp(k,Q) = distance between corresponding vector functions (40) with numbers
(k,Q); dRW = permissible level of the difference in these vector functions within
~
the limits of a single weather region Ryw. Thus, set (41) determines the weather
changes in the given region. "Acoustic climate in the ocean" means durable changes
in the acoustic weather in some region of the ocean. This means that, according to
(41), acoustic climate corresponds to the set
R~~~Rvw(Rvw) -'~Rvk(Rvk)j (43)
vw

where Ryk determines a zone in the ocean with homogeneous (in the statistical
sense) acoustic climate satisfying the condition
i
Rvk = arg [sup dRp(k,k) : dRk], (44)
k,Q
where (in addition to the definitions used above) dRk = permissible level of dif-
ference in vector functions (40) within the limits of a single climatic zone P-vk.
Thus, according to (40), (41) and (43), the hierarchy of acoustico-oceanographic
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classes has the following form:
Rvk{Rvw~~,i~Tv~~n) E ~RvO(Rv,Tv) -'gRvw(Rvw)~ - Rvk~Rvk) } = OR. (45)
`
7. Resume. In this article we have discussed some contemporary statistical aspects
of the investigation of acoustico-oceanographic models, using image identification
methods and methods from adjacent fields as tools to solve the corresponding prob-
- lems. The problems formulated above naturally require additional specific defini-
tion and the development of constructive methods for their computer realization.
In this area there are, of course, certain difficulties that, it is to be hoped,
will be overcome.
BIBLIOGRAPHY
l, Chernov, L.A., "Rasprostraneniye voln v srede so sluchay_nym neodnorodnostyami"
/Wave ProPagation in a Med ium With Random Irregularities%, Moscow, Izdatel'stvo
AN SSSR /USSR Academy of Sciences/, 1958.
2. 01'shevskiy, V.V., "Statis ticheskiye svoystva morskoy reverberatsii" fStatisti-
cal Properties of Marine Reverberation/, Moscow, Izdatel'stvo "Nauka", 1966.
3. Middleton, D., "A Statistical Theory of Reverberation and Similar First-Order
Scattered Fields," IEEE TRANS. INF. THEORY, IT-13, 1967, pp 372-392, 394-414
(Parts I and II), IEEE TRANS. INF. TH., IT-18, 1972, pp 35-67, 68-90 (Parts III
and IV). 4. 01'shevskiy, V.V., "Statis ticheskiye metody v gidrolokatsii" /Statistical Meth-
ods in Hydrolocation/, Len ingrad, Izdatel'stvo "Sudostroyeniye", 1973.
5. Middleton, D., "Characterization of Active Underwater Acoustic Channels," TECH.
REP. ARL-TR-74-61, Applied Research Labs, University of Texas at Austin, 1974.
6. "Trudy Vsesoyuznykh shkol-seminarov po sCatisticheskoy gidroakustike" /Works of
the All-Union School-Seminars on Statistical Hydroacoustics/, Novosibirsk,
Institute of Mathematics, Siberian Department, AN SSSR, 1969-1978.
7. Mleshchev, V.I., editor, "Fizicheskiye osnovy podvodnoy akustiki" /Physical
Principles of Underwater Acoustics7, Moscow, Izdatel'stvo "Sovetskoye radio",
_ 1955 (translated from English).
8. Shuleykin, V.V., "Ocherki po fizike morya" /Essays on the Physics of the Sea/,
Moscow-Leningrad, Izdatel'stvo AN SSSR, 1949.
9. Tolstoy, N., and Kley, K., "Akustika okeana" /Ocean Acoustics/, Moscow, Izda-
tel'stvo "Mir", 1969 (translated from English).
10. Brekhovskiy, L.M., editor, "Akustika okeana" /Oceua Acoustics/, Moscow, Izda-
tel'stvo "Nauka", 1974.
11. "I s"yezd sovetsicikh okeanologov. Referaty dokladov" /First Congress of Soviet
Oceanographers: Abstracts of Reports/, Moscow, 1977.
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12. "Akusticheskiye metody issledovaniya okeana" /Acoustic Methods of Investigating
the Ocean, collection of works7, Leningrad, Izdatel'stvo "Sudostroyeniye", No
237, 1976; No 255, 1977 (materials on exchange of experiences).
13. "Trudy per.vogo seminara 'Akusticheskiye statisticheskiye modeli okeana /Works
of the First Seminar on "Acoustic Statistical Models of the Ocean"/, Moscow,
Acoustics Institute, AN SSSR, 1977.
14. Sebestian, G.S., "Protsessy prinyatiya resheniya pri raspoznavanii obrazov"
/Decision-Making Processes in Image Identification/, Kiev, Izdatel'stvo
"Tekhnika", 1965 (translated from English).
15. Zagoruyko, N.G., "Metody raspoznavaniya i ikh primeneniye" /Identification
Methods and Their Use/, Moscow, Izdatel'stvo "Sovetskoye radio", 1972. .
16. Zagoruyko, N.G., "Iskusstvennyy intelekt i empiricheskoye predskazaniye"
/Artificial Intellect and Empirical Prediction/, Novosibirsk, Novosibirsk State
! University, 1975.
17. Dyuran, B., Odell, P., "Klasternyy analiz" /Claster Analysis/, Moscow, Izda-
tel'stvo "Statistika", 1977.
18. Zagoruyko, N.G., Yelkin, V.N., and Timerkayev, V.S., "Ttie '75' Algorithm for
Filling_Spaces in Empirical Tables," in "Vychislitel'nyye sistemy" /Computer
Systems/, Novosibirsk, No 67, 1975, pp 3-28.
19. Yelkin, V.N., and Zagoruyko, N.G., "Quantitative Quality Criteria From Taxonomy
and Their Utilization in the Decision-Making Process," in "Vychislitel'nyye
sistemy", Novosibirsk, No 61, 1975, pp 3-27.
Q. " . .
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APPLIED ASPECTS OF THE THEDRY OF LINEAR RANDOM PROCESSES
[Article by B. G. Marchenko pp 16-181
/Text/ Introduction. An orderly and compact statement of many questions in the
theory of stochastic integrals can be obtained within the framework of the class of
linear random processes. In the extensive propagation of linear random processes
for the solution of applied problems, an essential role is played by the fact that
for linear random processes presented in an integral form, the general form of the
characteristic functional is known and the p~ysical meaning of the parameters and
functions that are part of it is described /1,27, which in a number of cases makes
it possible to obtain the moments and semi-invariants of such processes compara-
tively simply or, speaking in the language of physics, for such processes there is
a generalized theorem on the imposition of random disturbances.
2. Linear Random Processes: Definition. An actual, random, separable process
Cw(t) in a probability space {St,B,PT}, where T is a unidimensional set with separa-
bility set To _{tj, j= 1,2,...,tj e T}, is called linear if it can be represented
as a limit in the sense of weak convergence of the distributions in the for
n
Qt) = lim E nni (t,w), ~1)
n4co j=1
, where {nnj(t,w), j= l,n, n= 1,2,...} is an infinite sequence of processes that
are independent for each fixing of n, the sequential sums of which satisfy the con-
dition of uniform infinite smallness; that is,
lim max P1Innj(t,w)1 : e} = 0 (2)
n-~�� j
for each e> 0 and tE To.
2. Processes With Independent Increments. We will define them in terms of n(t) and
give them on the semiaxis or the entire number-scale axis. These processes' incre-
ments are independent in nonintersecting time intervals and ehe general form of
their characteristic function's logarithm is
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ln f(u,t) = ln M exp{iu[q(t2) - n(tl)]
2 ~ 2 (3)
= iu[U(t2) - u(tl)] - 2 [D(t2) - D(tl)] + _j (eiux _ 1 - i)1+X G(dx x [tl,t2]),
where u(t), D(t) ; 0= some numerical functions determined unambiguously by n(t),
while G(dx xltl,t2]) = Poisson measure of the discontinuities. It can be said
that separable random processes with independent increments satisfy the definition
of linear rar_dom processes formulated above.
4. Integral Representations of Linear Random Processes. The linear processes that
have been most tl:oroughly studied are (Gil'bert) linear processes represented by a
stochastic integral in the form
_ Eft) _ _I ~(T,t)dq(-O, t F T,
(4)
where ~(T,t) is a nonrandom numerical function satisfying Che condition
_I ~2(T,C)dT for all tE T; {rj(t),n(0) = 0, t E(-~,~) Gil'bert process with
independent increments; T= an arbitrary set of real numbers;including the multi-
dimensional spaces Rn. The logarithm of the characteristic function of process (4)
is determined by the expression
ln f(u,t) = ln Meiu~(t) = iu_~ 2_z ~;2'(T,t)dD(T) +
(5)
iux~(T,t) iux~(T,t) 1+x2 F
+_~f _ I[e - 1- 1+---1 X~(dx x dT) ~
~
where }i(T), D(T) and G(dx Y dT) are defined as in formula (3) and characterize a
process with independent increments r1(t).
The general form of the characteristic function (5) of process (4) makes it possi-
ble to conduct a complete analysis of the responses of linear systems: find the
semi-invariants and density of the probability distribution or the response distri-
bution function, and study the distributi.on of discontinuities in its realizations.
5. Connecting Linear Random Processes With Other Processes. The convenience of the
_ utilization of a model of a linear random process consists not only of the fact
that practically all the characteristicscan be obtained for such processes, but al-
so in its close relationship with other, no less important models such as--for ex-
ample--harmonizable and periodically correlational random processes (PKSP).
If, in representation (4), the nucleus satisfies.the condition
C(T,t) _ ~(T + T,t + T), t E (O,W), (6)
for all T and tc- process (4) will be a PKSP; that is, its correlation func-
tion will also satisfy a condition analogous to (6). Such processes are encounter-
ed quite frequ.ently in practice and are used to describe rhythmic phenomena.
As is known, a process permitting a representation in the fci�i
_4 '0 ei27ratdz(A),
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where z(a) = some random process, the correlation function of which has limited
variation, is said to be (Loev) harmonizable.
Tf we assume'~that z(a) in (7) is some process with independent increments (not ne-
cessarily uniform ones), (7) will then be a harmonizable, linear random process
with complex signs.
5. Physical Processes Described With the Help of Linear Random Processes. Along
with the solution of the problems mentioned above, which are related to linear and
nonlinear transformations of random processes, linear random processes also prove
to be extremely useful when creating primary, original models of different real
physical processes, which models can be constructed starting with an elenentary
pulse structure and the physics of the formation of such processes.
In conclusion let us note that a model of linear random processes can be used to
obtain series of pseudorandom numbers, cvith previously assigned characteristics
and interconnections, with the help of a computer. Such series can be used in the
so.lution of problems by the statistical modeling method.
BIBLIOGRAPHY
1. Marchenko, B.G., "Metod stokhasticheskikh integral'nykh predstavleniy i yego
primeneniye v radiotekhnike" /The Method of Stochastic Integral Representations
and Its Use in Radio Engineering/, Kiev, Izdatel'stvo "Naukova dumka", 1973.
2. Marchenko, B.G., and Shcherbak, L.N., "Lineynyye sluchaynyye protsessy i ikh
prilozheniya" /Linear Random Processes and Their Applications/, Kiev, Izdatel'-
stvo "Naukova dumka", 1975.
3. 01'shevskiy, V.V., "Statisticheskiye svoystva morskoy reverberatsii" /Statisti-
cal Properties of Marine Reverberation/, Moscow, Izdatel'stvo "Nauka", 1966.
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SYNTHESIS OF DETERMINATIVE SYSTEMS IN PROBLEMS INVOLVING INVESTIGATION OF THE WORLD
OCEAN
[Article by Yu. Ye. Sidorov pp 18-26
/Text/ 1. Introduction. Every year there is more interest in problems concerning
the investigation and mastery of the world ocean, which--as far as its importance
and the extent to which it is being studied--has become a"second space." In the
opinion of both Soviet and foreign scientists, in the next few years the ocean will
become an object for which it will be profitable to direct maximum efforts in order
to investigate it and utilize its resources.
In connection with this, the question of equipment and methods for investigating
the hydrosphere is an extremely urgent one. The basic facilities for collecting
oceanographic information are: 1) buoy stations (sea buoys); 2) ships; 3) aviation
(airplanes, helicopters); 4) artiticial Earth satellites and other flying space-
craft (KLA). The information obtained with the help of buoy stations, ships and
' aviation is of a regional nature, while that obtained with the help of KLA is of
tlie global type. Other facilities for gathering regional information are balloons
(controlled and uncontrolled), dirigibles (automatic) and sounding balloons and
rockets. Different equipment for remote investigation of the ocean (by, for exam-
ple, photography) can be placed in the cars of balloons and sounding balloons and
the bodies of rockets. The basic methods for obtaining oceanographic information
are contact and remote (noncontact) methods; the latter include: 1) visual obser-
vations; 2) photographic and television surveying of the surface of a water area;
3) infrared aud multispectral surveying (in the wave band X= 0.3 Um to 1 mm); 4)
radiophysical methods (radiothermal location, radar) with a= 1 mm to 1 m; 5)
acoustic location; 6) optical (laser) location. Remote sounding methods can also
be divided into two groups: active and passive. The active methods include radar
and acoustic and optical location, while the passive ones include visual observa-
tions, photographic and television surveying, radiometric measurements and images
obtained with the help of scanning radiometers in the visible light, near infrared
and microwave bands, and acoustic methods.
Each of the methods listed above can be used to obtain some bit or another of
oceanographic information that is of interest to us. The most promising and
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� 2/
informative methods are the remcte methods for sounding the ocean, which are based
on the emission and reflection of electromagnetic and/or acoustic waves by the
aqueous medium.
A special place is occupied by radioliydroacoustic: methuds of investigating the
world ocean in combination with aviation and KLA, whicti proauce the basic flow oF
information about the ocean's depths (see Figure 3.1 in / 17).
zl
1 6
S a 7n. L
Ef'
I
i �
a~
ZP.I
~ ro > 2c .j
P . ~ 15
/Q rP +
rr J ~3 ~
Figure 1. Illustration of problems and methods of investigating the world
ocean: 1. world ocean; 2. investigations of the surface and the surface
layer; 3. underwater hydroacoustic investigations; 4. hydrophysics prob-
lems; 5. temperature irregularities and layers; 6. dangerous phenomena;
7. underwater part of an iceberg; 8. reefs, shallows; 9. tsunamis; 10.
biological products from the ocean; 11. sea life; 12. fish; 13. plankton;
14. structure of the bottom; 15. global; 16. local (for engineering pur-
poses); 17. investigations of the nature of the Earth's surface beneath
the world ocean; 18. search for useful minerals (marine geology); 19.
special problems; 20. navigation problems; A. active methods; H. passive
methods; 21. development of optimum algorithms for classitying and evalu-
ating signal parameters (for different levels of prior information about
probability models and their characteristics).
The possibilities of solving various scientific and national economic problems con-
cerning the study and mastery of the world ocean's depths with the help of aero-
space radiohydroacoustic sounding methods in active and passive hydrolocation modes
are illustrated in the block diagram shown in Figure 1. As an example, Block 2 is
concerned with the study of the water's surface (determining temperature, boundar-
ies and types of ice covers, degree of wave action and pollution and so on) by the
different methods listed above as Nos 1-4 and 6. The necessity of obtaining ocean-
ographic information that is as nearly complete as possible (which is achieved by
the integrated utilization of various sounding facilities and methods), its opera-
tional and objective processing (including the finding and supplying to the consum-
er of certain solutions), and the multibranch nature of the data supplied to the
consumer all require an examination of the problems involved in creatina an ASOAOI
/automated system for processing asynchronous oceanographic information/.
2. Some Propositions of the Theory Df Complex Hierarchical Systems. The need for a
systems approach to the synthesis of an ASOAOI is dictated by the direction oi the
development of automated control systems toward the study of objects and processes
of ever-increasing complexity. A clear example of this is the investigation of the
ocean. The desire for an accurate and as nearly complete as possible accounting of
the variegated phenomena and processes taking place in the ocean and the set of
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factors affecting these phenomena and processes cannot be satisfied without con-
structing ati appropriately complex automated system. This means that the research-
ers and developers a.re faced with new scientific and technical problems. These
problems are thc substance of a new scientific and technical Lield: systems analy-
sis. The mathematical basis of systems analysis is the theory uf complex (or
large) systems
At the present time there is no clearcut (from the viewpoint of constructing a rig-
orous theory) definition of a complex system.
One spec:al class of complex systems is information systems, the structure of which
is adaptable to the implementation of special functions (such as receiving, stor-
ing, processing and publishing large masses of information) and which are intended
for operc;tion on especially large information flows /2/. In addition to this, an
information system satisfies the following requirements /5/: 1) the nature of the
input signals is random and is formalized within the framework of a theoretical-
probability apparatus; 2) the system can be part of a larger system, but its func-
tion criterion can be formulated autonomously, to some degree; 3) the system oper-
ates according to an algorithm emanating from the function criterion that includes
the extension of several statistical decisions.
The questioci of the presence or absence of a hierarchical organization in the sys-
~ tems is of extreme importance.
If we consider that the essential characteristics inherent in all hierarchical sys-
= tems are /3/: a) sequential, vertical arrangement of the subsystems constituting
the given systezn (vertical decomposition); b) priority of action or the right of
interference by subsystems on a higher level; c) dependence of the higher-level
subsystems' actions on the actual_performance of their own functions by the lower
levels, then any ergaticheskaya /translation unknown/ system is hierarchical, so
that man--an upper level of hierarchy--can interfere in the operation of the system
and monitor it, and his activities naturally depend on the results of the lower-
" level subsystems' operations. Here the concept "system" or "subsystem" (module)
has the additional meaning of realizing the process of transforming input data into
output.
Three levels of hierarchy are recognized: 1) the description or abstraction level
(stratum); 2) ttie level of complexity of an accepted decision (layer); 3) the or-
ganizational level (echelon). The echelon concept refers tu interlinking between
_ the decision-making elements that form the system. It implies that 1) the system
consists of a group of clearly defined interacting subsystems; 2) some of these
_ subsystems are decision-making (determinative) elements; 3) the determinative ele-
ments are arranged hierarchically in the sense that some of them are affected or
controlled by other determinative el.ements /3/. Such systems are called multi-
echelon, multilevel or multipurpose.
The basic stages in the synthesis of determinative systems (in the methodology of
systems analysis) can be defined as follows /3/: 1) description on the verbal
level; 2) conceptualization and representation in the form of a bloctc diagram; 3)
formalization and formulation of problems (within the framework of the systems'
_ general theory); 4) analysis (with the enlistment of additional mathematical con-
structs) and investigation of properties. The verbal (word) description of the
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system makes it possible to construct a block diagram of
action of the subsystems and the connections among them.
ization'nE,the block diagram's description and thc� obtai
of an abstract system. For this model it is possible to
description and study the system's behavior analytically
puter.
it that shows the inter-
The next stage is formal-
zing of a model in t}ie Lorm
construct a mathematical
or with the help of a com-
3. Global Structure of the ASOAOI. This system is used to obtain information on
the status, development and quantitative evaluation o.E various oceanographic pro-
cesses and objects (such as water temperature, salinity and chemical composition,
the location and direction of migration of biological objects, bottom relief,
underwater storms, icebergs, tsunamis and many other things). The basic problems
~ that the system must solve are: collection of primary information; classification
and evaluation of the parameters of the processes and objects ttiat are of interest
to the consumer; presentation of solutions to the consumer. An ASOAOI has the fol-
lowing requirements: operativeness and accuracy of data processing and publication
(in different fortns); formulation of solutions with the fewest possible errors and
maximum efficiency (probability that the solution is correct); the system must be
of a minimum size and economically justified.
An ASOAOI's structural diagram must contain the following subsystems (modules): a
measurement complex; an information reception, storage and processing system; an
information transmission system; an information display system; a monitoring and
coordination system; a system for detecting and eliminating malfunctions.
The equipment and methods for obtaining oceanographic information must be deter-
mined for the measurement complex (this was discussed in Section 1). The measure-
ment complex naturally contains the appropriate surveying and measuring equipment.
The information reception, storage and processing system must include: 1) a recep-
tion center; Z) storage devices; 3) a primary (preliminary) processing system; 4) a
system for sorting information and tieing it in wi*h some geographic region or
another, transforming the scales and standardizing and interpreting the data; S) a
system for making decisions.
Figure 2. Block diagram of ASOAOI: 1. external environment
(world ocean); 2. measurement complex; 3. information reception,
storage and processing system; 4. information transmission sys-
tem; 5. information display system; 6. information consumer; 7.
monitoring-coordinating center; 8. repair and operating center.
On the basis of the verbal description it is possible to draw up a block diagram of
- the ASOAOI that reflects the system's global structure (Figure 2). From a prelim-
inary familiarity with the basic problems solved in this system and its block
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- diagram, the diversity of the functions performed by the system--the main ones of
which are related to the stage-by-stage processing of large flows of information--
is quite clear. Moreover, an ASOAOI satisfies requirements (1-3) for information
systems that were formulated in Section 2; for instance, it can be part of a larger
system (a system for remote sounding of th e Earth). Therefore, our system can un-
doubtedly be assigned to the class of comp lex, cybernetic information systems; its
special feature must be a high degree of automation based on the use of high-spe~-:d
computers that are functionally joined int o large computer complexes.
4. Formalization of the Description of the System. For purposes of description and
analysis of its operation, a complex system must first be broken down into separate
elements, caith their functioning being studied first, it being the case that this
division is not always carried out unambiguously and is largely determined by the
specific purpose of the system. Our system can be assigned to the class of hierar-
chical, multilevel, multipurpose systems. This assignment agrees completely with
the definition of siich systems given in Section 2. For example, the purpose of the
reception, storage and processing system is to distinguish useful information with
the maximum probability, while the transmission system's function is to transmit
this information undistortedly and witr minimum error. It is also obvious that the
ASOAOI's other subsystems have distinctive (local) purposes, it being the case that
each of these subsystems has its own function criteria and criteria for evaluating
the quality of its own actions. T'hus, an ASOAOI is fundamentally a multicriterion
system. A formalized mathematical representation of an ASOAOI is possible in terms
of a relationship between sets X and Y:
S S X " Y, ~1)
where X= the input set; Y= the output se t, while elements xE X and y E Y are in-
puts and outPuts, respectively. If S is the function S:X-+Y, the system is called
functional / 3/. Thus, the representation of the system in the form of a relation-
sliip is a representation in the "input-output" form. It is possible to discuss the
0
spacc of input signals (states) X= X1 x X2 x,,,x Xn of the system; here Xi,
i= l,n are the elementary axes (subspacesl and an input signal x is a point in the
0
0
space X described by the coordinates xl,x2,...3xn (in the general case, X X).
Anal'ogously, the space of the system's output signals is the direct product
_ o 0
y- yl x y2 x,,, x yni, y c Y. Such operations are, naturally, also correct for each
of the subsystems, so that Y is the space of the output signals for a higher-level
- (such as the r-th level) subsystem and the space of the input signals for a lower-
level ((r-1)-th) subsystem. It is particu larly convenient to define the system in
terms of a decision-making problem. The system S!E X x Y is called determinant if
the family of problems DX, x E X is given, along with the set of solutions Z and the
mapping T:Z`iY, dx 4X and Hy e y of the pair .(x,y) E S only if there exists an ele-
z Z such that it is the solution of the p r oblem DX and T(z) = y. In most cases
the output is the solution of the formulated problem and Z= Y; that is, T is an
identity mapping / 37.
Any system formalized in the form of an "input-output" model can be represented in
the form of a determinant system, and vice versa. Systems possessing a hierarchi-
cal structure are distinguished by the fact that their subsystems' functions can be
interpreted easily as the search for and making of decisions / 37. If the decision
(operation) algorithm is determined Eor each of an ASOAOI's subsystems, the entire
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system's algorithm can be represented in the form of a combination of separate al-
gorithms. This is possible because of the fact that an ASOAOI (as is the case with
all technical hierarchical systems) belongs to the class of reflex systems, the re-
action of which to a disturbance is completely unambiguous.
5. On Optimality and Evaluating a System's Efficiency. The concept of "optimality"
of a hierarchical system is extremely diffuse, since there exists the possibility
that each subsystem can independently make a decision; this applied, in particular,
to maximizing its own functional. As we know, a hierarchical multipurpose system
is a multicriterial system (an ASOAOI, for example). Therefore, here we need to
find rational mathematical formulatior..s of problems and give a reasonable meaning
to the concept of optimality.
There are several possible ways to optimize such systems.
A. The problem of searching for satisfactory solutions. Let g:X x St-+V and T:S2-+V,
where X= the set of all solutions; 0 = the set of indeterminacies; V= the set of
payoffs; g= the object function; T= the permissibility function. The problem
J. ~ J.
/ 3 / : given subset X"S X, it is necessary to find x in X" such that Vw ES2 and
g(x,w) , T(w).
(2)
Criterion (2) is the satisfiability criterion. The quartet (g, T, X*, S2) defines
the problem of finding satisfactory solutions, while any x from X" for which (2)
realizes Vw E 2 is a solutior: to this problem.
2. The matched optimum principle ((Pareto's) principle). This principle appeared
- in the theory of nonantagonistic analystical games, which solves the problem of
finding points that maximize several functions at the same time. An analytical
, game is understood to mean the following mathematical setup / 67. 1) In the game
there are n players (subsystems, in our terminology) S1,...,Sn. The situation is
described by n analytical gain functions I1 = fl(x),...,In = fn(x), where Ii = gain
of the i-th subsystem, while x is the vector of the control parameters. 2) the
space of control parameters x X is continuous. The set of functions {fi} deter-
mines the "metrics" of this space. 3) The set of control parameters x is divided
into n sets x = (xl,...,xn), where xi is the set of parameters monitored by the
i-th subsystem. 4) Each subsystem, by selecting the set of parameters monitored by
it, strives to maximize its gain Ii.
Matched optimum means the conversion of a conflicting situation into one in which
none of the subsystems can improve its status without causing "harm" to the others
' by its actions. Therefore, the matched optimum status is the best for all the sub-
systems; that is, it is optimal / 67. The ma*ched optimum point is determined by
the equation
Df/Dx = 0, (3)
where f=(fl,...,fn) = a vector composed of gain functions fi, while D/Dx = the
Jacobian of vector transformation I= f(x).
It is sufficiently optimal in the sense that any player (any subsystem) withdrawing
from it can increase its own gain (improve its own quality functional) without
thereby reducing the gain (without causing the quality functional to deteriorate)
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of the other participants (subsystems). Therefore, the disruption by any partici-
pant in the game of the matched optimum conditions is "punished" by all the other
participants by measures directed against the "disrupter" (for example, by increas-
ing the penalty function. This gives stability to the matched optimum point (pro-
viding, of course, that all the participants know each other's object functions,
which are assumed to be stable).
3. Stage-by-stage synthesis of hierarchical systems, using different optimication
methods. There is more information on methods for optimizing a system for making
statistical decisions in / 1
Since the ASOAOI's functioning (as is the case with any complex system) takes place
under conditions where a significant effect is exerted by random external factors,
the system's achievement of its final goal will be subject to the influence of
these factors. Therefore, it is advisable to evaluate the system's efficiency with
the help of various probability characteristics. In practice, the efficiency indi-
cator /7 / is the probability characteristic that'is frequently used as the quanti=
tative measure for expressing a system's efficiency.
Any efficiency indicator is
y = nl1n2-.,n�)1 (4)
where E1,E2,...,Cn = the system's parameters; nl,n2,...,nn = parameters character-
izing the effect of the external environment.
- Along with its dependence on the system's parameters and the external environment,
which figure clearly in expression (4), the efficiency indicator also depends on
the system's structure, the nature of the connections between elements, the form of
the control actions and the functioning rules; that is, on factors that do not
yield to description with the help of parameters. These factors are taken into
consideration both by the form of the function `Y (or the form of the algorithm that
makes it possible to compute the values of `Y if there is no exElicit expression for
it) and the introduction of additional structural parameters / 27. As a rule, ex-
pression (4) is awkward to derive, and the task of calculating it frequently re-
quirEs the realization of a rather complex algorithm and the handling of a large
amount of information, which can be done only with a modern, highly productive com-
puter. Maximally simple models that take into consideration only those factors and
connections of substantial significance are used in the experimental-theoretical
calculation method 077.
Let us mention here that in this article we have made an attempt to take a broader
look at the problem of studying the hydrosphere, both from the viewpoint of solva-
ble problems and investigative methods and facilities and from the viewpoint of
methods for describing and formalizing the proposed global structure of a system
for processing asynchronous oceanographic information. It seems that this approach
to synthesizing an ASOAOI from the standpoint of the theory of complex hierarchical
systems is quite convenient and effective and demonstrates graphically the utility
of theoretical-set structures for the formalization of such systems.
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BIBLIOGRAPHY
_ 1. Sidorov, Yu.Ye., "Metody statisticheskogo sinteza algoritmov obrabotki aero-
- kosmicheskoy informatsii." /Methods for the Statistical Synthesis of Aerospace
Information Processing Algorithms/, Leningrad, Izdatel'stvo Leningrad Polytech-
nic Information imeni M.I. Kalinin, 1977.
2. Buslenko, N.P., Kalashnikov, V.V., and Kovalenko, I.N., "Lektsii po teorii
slozhnykh sistem" /Lectures on the Theory of Complex Systems/, Moscow, Izdatel'-
stvo "Sovetskoye radio", 1973.
3. Mesarovich, M., Mako, D., and Takakhar,, I., "Teoriya iyerarkhicheskikh mnogo-
urovnevykh sistem" /Theory of Hierarchical Multilevel Systems/, Moscow, Izda-
tel'stvo "Mir", 1973.
4. Moiseyev, N.N., "Elementy teorii optimal'nykh sistem" /Elements of the Theory of
Optimal Systems/, Moscow, Izdatel'stvo "Nauka", 1975.
5. Levin, B.P., introductory article to thematic issue of the magazine TIIER /ex-
pansion unknown/, Dlo 5, 1970, pp 3-5.
6. Volgin, L.N., "Printsip soglasovannogo optimuma" /Principle of the Matched
Optimum/, Moscow, Izdatel'stvo "Sovetskoye radio", 1977,
7. Sharakshane, A.S., and Zheleznov, I.G., "Ispytaniya slozhnykh sistem" /Tests of
Complex Systems/, Moscow, Izdatel'stvo "Vysshaya -shkola", 1974.
r~
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A LINGUISTIC-INFORMATION MODEL OF STATISTICAL HYDROACOUSTICS
[Areicle by V. P. Sochivko pp 26-281
/Text/ 1. An analysis of the texts in a set of 103 publications on statistical
hydroacoustics shows: a significant part of the texts consists of verbal (word),
mathematically unexpressable elements; the linguistic structures of the titles,
annotations, essays and conclusions inform the reader quite accurately of the basic
results represented in the text; the final results of the symbolic (mathematical)
transformations of the physical processes and structures of statistical hydro-
acoustics permit a verbal representation (although some part of--mainly--the phys-
ically unrealizable transformation operators "escape" an unambiguous verbal furmu-
lation).
2. The problem of constructing a l.inguistic-information model of statistical hydro-
accu;,'~_;,~ was formulaCed. The model must satisfy the following requirements: ex-
plain the basic concepts and categories of statistical hydroacoustics with an un-
ambiguous interpretation of the professional terminology; present the terminology
of statistical hydroacoustics in the form of a unified, correlated system; describe
the structure of the semantic field that has been built up in this field of knowl-
- edge; facilitate the accumulation of new knowledge and data on statistical hydro-
acoustics; create a foundation for standardizing the descriptions of prototypes of
- documents; assist in the formalization of information inquiries when searching for
needed data; support the information search for needed documents and specific
factographic data; support the information-logic processing of available data;
unite the aggregate information on statistical hydroacoustics with the other,parts
of the entire spectrum of knowledge.
3. The following formalization is possible: there is a set of events SZ that can be
discussed within the framework of statistical hydroacoustics. Set S of observa-
tions on the results of experiments A:Q S gives a verbal-symbolic representation
of texts B:S T that are registered in documents (articles, reports and so on).
It is necessary to construct a model
L-IM = {C,/I,B x A:S2 T},
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where C= signature of the basic concepts of statistical hydroacoustics; /l = the
language of the theory; A, B= basic representations (an experiment and the symbol--
sign formulat:ion of the results).
4. It can be said that a linguistic-information model of statistical hydroacoustics
is a specialized microthesaurus (a standardized reference dictionary in which all
the descriptors and keywords that are synonymous with them are listed in general
alphabetical order and in which there is also an explicit expression of the'most
important paradigmatic relationships among the basic concepts) that is linked with
the general thesaurus "Hydroacoustics."
5. The first version of the "Hydroacoustics" thesaurus was worked out by the author
in 1971. The most recent edition, published in 1977, contains more than 1,800 key-
words, of which 1,400 are descriptors. The "Statistical Hydroacoustics" micro-
thesaurus, the first version of which is being presented for discussion by the par-
ticipants in this school-seminar, contains about 1,000 keywords, of which 900 are
descriptors.
6. The "Statistical Hydroacoustics" thesaurus is an information retrieval one; that
is, it makes it possible to index publications, formulate search samples of inquir-
ies and documents and support linguistically the procedures used in information re-
trieval.
7. The thesaurus is a linguistic-information model in the sense of all the other
requirements listed above. For example, its linguistic coupling with some other
thesauri produces intersections, the results of which admit of interesting inter-
pretations: in an intersection lie (Adamar's) and (Uyelsh's) transformations,
which have proven themselves in general identification theory, statistical radio
engineering and other fields. Within the framework of scientific organizational
activity it is necessary to call the attention of investigators to these transfor-
mations; an analogous conclusion can be reached for discrete (digital) algorithms
and other elements.
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STOCHASTIC ALGORITHMS FOR INVESTIGATING NONCONVEX FUNCTIONS WITH MANY VARIABLES
[Article by V. I. Alekseyev pp 25-29]
/Text/ The identification of the structure of an investigated f.unction with many
variables by the well-known methods of regression analysis and experiment planning
involves large material and computational outputs, particularly when planning
second- and higher-order experiments.
Let us discuss stochastic methods for localizing the extreme areas of a multi-
extreme function and identifying the structure of the extreme area. The method for
identifying the extreme area's structure is based on regression analysis. The re-
gression control factors are computed with the help of the nonlinear, nonparametric
averaging operators
_ ~ (X1 + SiuiQ) (e,Q(x + auQ
xi (1)
N , i)...)u,
-R=1 RE1B(e,Q(x + SuQ))
I with a random sampling of the experimental points. The following symbols are in-
i troduced in formula (1): x= vector of the parameters (factors) being evaluated;
R= vector of the averaging interval; u= vector of the uniformly distributed ran-
~ dom numbers from [-1,1]; Q(x + Su) = the function being investigated;
; B(e,Q(x + gu)) = a bell-shaped weight function; e= scalar parameter of the bell-
~ shaped function that gives its width, such as e= Q(x); N= number of experiments
, (computations) performed. When operator (1) is used, the greatest weight is given
~ to those values of the factor (x + su) for which Q(x + su) has the smallest (larg-
est) value.
In the most general case, k:1aeA--the investigation is carried out with incomplete
knowledge of the mechanism of the phenomena being studied, it is natural to assume
that the analytical expression of the function is unknown and is represented in the
form of a polynomial:
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n n
= b + E bixi + E b..X.X. + E b��x?
y (2)
o ixl ilCj 1J 1 J i=1 11 1
with the theoretical regression coefficients bo, bi, bii, biJ-. Estimates of the
regression control coefficients (2) are found by using operator (1); namely:
bi E uil3(e,Q(xo + RuQ))l[QE1 B(e,q(xo + Ru~"))]-1, i= 1,...,n,
X=1
N N
b�� E uQv~"B(e,Q(x +~uQ))][ ~ B(e,Q(x + SuQ)~~-1~ i= 1,...,n; j= i,...,n
1J Q=1 i ~ o R=1 0 (3)
N N
_ bi.k = [QE1 uiu~ukB~e,Q(xo + ~uQ))][ RE1 B(e,Q(xo + ~ue))l-I,
J
. i= 1.... ,n, j= i,...,n, k= j) ...,n,
and so on, where xo = value of the basic level's factor. An estimate of the free
term bo is found with the help of the linear smoothing operator / 17
N
bo = QX1 Q(xo + Ru~')h(Q),
where h(k) = a weight function.
The total number of coefficients in regression equation (2) is cn+d' where d= the
order of the polynomial. In the classical variant, in order to evaluate cn+d zt is
necessary to have N>, cn+d experiments. In the method under discussion, as is ob-
vious from expressions (3), the number of experiments N can also be less than cn+d'
Localization of the extreme areas of a multiextreme function is accomplished by
conducting experiments at randomly selected points in the factor space and keeping
in mind those values of the factor, with the help of operator (1), for which the
experiment's value is less than that of a fixed level.
BIBLIOGRAPHY
1. Katkovnik, Ya.V., "Lineynyye otsenki. i stokhasticheskiye_zadachi optimizatsii"
/Linear Evaluations and Stochastic Optimization Problems/, Izdatel'stvo "Nauka",
1976.
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- SIMULATION COMPUTER MODELING IN ACOUSTICO-OCEANOGRAPHIC RESEARCH: PURPOSES,
SPECIAL FEATURES, SCIENTIFIC PROBLEMS
[Article by V. V. 01'shevskiy Pp 29-49]
/Text/ 1. Introduction. In the field of acoustico-oceanographic research, in re-
cent decades we have seen the development of new areas related to the development
of probability models of random values, processes and fields, the study of the
methods and procedures of statistical measurements and quantitative experimental
acoustico-oceanographic research, machine modeling and, finally, the creation of
systems analysis methods for analyzing and synthesizing complex acoustico-
oceanographic information measuring systems. Modern camputers, which make it pos-
sible to solve multidimensional problems of vast complexity, have, in the last dec-
ade, created the structural basis for the development of the methods that combine
the entire range of acoustico-oceanographic research into a unified system. All of
this has resulted in the appearance of a new field of research that is called simu-
lation computer modeling. Simulation computer modeling in acoustico-oceanographic
research naturally did not appear out of the void. The basis of this approach lies
_ primarily in the following areas:
the theory and methods of investigating special and general acoustico-oceanographic
models /1-4,6,8,9,19,23-25,27-29,34,40,48-50,53,58,597;
the theory and methods of experiment plannin2, including statistical measurements,
as applied to different fields of research /7,10,13,24,32,41,43,54/;
the theory and methods of modeling in different branches of science and technology
/5,11,14,17,18,22,56%;
the theory and methods of image identification /16,35,46/.
Having been born within the framework of several previously developed areas of sci-
ence and technology, simulation computer modeling comparatively rapidly--basically
in the last 8-10 years./36,39,44,45,49,51,52,55,57/--took shape as an independent
research field, with a clearcut methodology, with the separation of heuristic and
formalized problem-solving procedures, and with--which is obviously the rnost basic
of all--a clearly expressed applied, constructive direction for the results that
are obtained. At the present time the situation relative to simulation computer
modeling is such that it has propagated as a fundamental research tool /36,45,55,
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577 in physics, economics, the social sciences, psychology, the solution of trans-
portation problems, personnel policies, the planning of experimental researcli in
the most diversified fields and so on. There is no doubt that simulation computer
modeling will make it possible to solve many problems in the field of acoustico-
oceanographic research, the moreso since, as has already become clear, with its
help it has become possible to formulate and solve problems that it was not possi-
ble to solve correctly with traditional approaches or could be solved only on an
intuitive level, which involves emotional judgments. The main thing here, perhaps,
is that simulation computer modeling made it possible, for the first time, to ap-
proach the solution of the problem of complexity from fully clear and constructive
viewpoints. Along with this, the development of simulation modeling natura11y also
gave birth to a whole series of new scientific problems that proved to be far from
trivial and that still have to be solved.
Below wP will discuss the special features of simulation modeling and some scien-
tific problems that arise in connection with this in the field of acoustico-
oceanographic research.
2. Spme Definitions and the Inevitability of Using Simulation Computer Modeling
/5-8,11-22,29-45,47-55,57-59/. Here we will give several definitions of the basic
concepts that we will use later. In general, it is a well-known fact that there
are few things that cause so much debate and pretentiousness (which is, by the way,
- most often correct) as definitions. Meanwhile, if anyone relies on concepts that
are not clearly defined and make it possible to give an ambiguous treatment to
questions under discussion, this creates an even more unsatisfactory position in
comparison with the situation where there are definitions, even if they are not un-
questionable from the viewpoints of various specialists. Therefore, some defini-
tions will be given here, even though the author is aware that, from the viewpoint
of the conjectural readers of this article, part of them may prove to be trivial,
while part of them may be debated. In any case, the definitions presented below
correspond to the author's convictions today and, it seems to him, do not contra-
dict the content of most of the works cited at the beginning of this section.
A system is a group (set) of objects that is united by some form on interaction and
that carry out certain functions in order to achieve a given goal. The greatest
interest is evoked by the so-called large or cumplex systems, for which the follow-
ing basic features are characteristic:
the system interacts with its environment, it being the case that some part of this
environment can, when necessary, be included in the discussion of a complex system;
the system has several "inputs" and "outputs," as well as a definite structure;
the system's structure and characteristics can change as the result of the action
of natural factors and as the result of purposeful activity;
on the whole, the system's properties are distinctive from the properties of the
objects of which it is comprised.
An acoustico-oceanographic system is a camplex system composed of water masses, in-
cluding the atmospheric and bottom layers adjacent to them, and facilities for
studying the oceanographic characteristics, the acoustic characteristics of the
ocean and the acoustic fields in it.
Measurement is the establishment of quantitative relationships between two objects,
one of which is the real object (of natural or artificial origin) that is being
investigated, while the other is taken to be the pattern (standard).
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Let us mention here that with such a generalized concept, measurements here, of
course, also apply to the problem of detecting signals against a background of
noise (binary measurement), problems of evaluating, recognizing and identifying
parameters and so on.
An information measurement system is the set of ineasurement facilities that is ne-
cessary and sufficient for the conduct of a given experiment, as the result of
whicli the measurement information on the quantitative values of the investigated
object's characteristics should be obtained.
Starting with these definitions and considering the requirements and trends of
acoustico-oceanographic research, let us mention here that values, functions, or
probability characteristics of investigated objects may be subjected to measurement.
A model is an idealized image of the real object (or system) that is being investi-
gated, in which image those properties of the object that are essential in the
problem being solved are reflected.
In the problem we are discussing, our greatest interest is in analytical, algorith-
mic, empirical and descriptive (evaluational) models.
An acoustico-oceanograpliic model is a description of oceanographic phenomena, the
acoustic characteristics oI the ocean, the acoustic fields in it and the inter-
related oceanographic and hydroacoustic information measurement systems that is ade-
quate For the solution of a formulated scientific and/or applied problem.
From this it follows that an acoustico-oceanographic model is a description of a
complex system consisting of hydrophysical and technical objects. Such an associa-
tiou is necessary for various reasons: first, no experimental investigation can be
conducted without a measurement system; second, if the information processing pro-
cedures are not optimized with due consideration for changing measurement r_ondi-
tions, the conduct of full-scale investigations in the ocean can entail significant
irrational expenditures of materials; third, to study the entire (or almost the en-
tire) set of acoustico-oceanographic conditions when makind direct measurements in
the occan is practically impossible, even in the distant Luture, as a result ot-
which clear planning of future experimental research is required; fourth, the lack
of acoustico-oceanographic models of this type makes it impossible to plan, at the
present level, the appropriate information systems and to make substantiated deci-
sions.
This is a far from complete list of reasons in accordance with which there has
arisen the necessity of deve.loping the acoustico-oceanographic models under discus-
sion as complex systems.
Systems analysis (or, which is almost equivalent, the systems approach and the in-
vestigation of operations) comes to this: the investigator studies the behavior of
- a complex system as a whole, without concentrating all his attention c:lly on some
single element of this system, although this element may also he (undei a more de-
tailed examination) a complex system and is extraordinarily interesting in the sci-
entifir sense.
In systems analysis we are, naturally, dealing not with real objects and complex
systems, but with models of them.
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Further, we will make a single prelininary remark on acoustico-oceanographic models
(later we will return again to a discussion of this extremely important question)
that c;oncerns several debatable aspects of this problem.
Hardly anyone would say that a satisfactory model of the ocean can be constructed
if sufficient thoroughly investigated separate acoustico-oceanographic objects are
not available. On the other hand, however, even having thoroughly studied special
acoustico-oceanographic phenomena at our disposal, we undoubtedly cannot assume
that a model of the ocean has already been constructed. The situation with the investigation of information measurement systems.is com-
pletely analogous: elements of these systems can each be studied separately in ex-
treme detail, from the viewpoint of specialists in these elements, but, meanwhile,
no one has yet succeeded in changing over to an examination of the functioning of
an information system as a complex system that is a unified whole with the ocean
and a mechanical association of the indicated elements.
An even more composite problem in connection with the systems approach is the com-
bined discussion of acoustico-oceanographic phenomena, acoustic fields in the ocean
and information measurement systems. Besides the complex structural interactions
of the large number of objects in such a system, we should also remember the fact
that these objects, in and of themselves, have been studied extremely inadequately:
the specialists who are doing research in specific narrow areas can confirm this
completely competently and convincingly.
In view of what has been said and possibly other subjective reasons, the impression
can appear that it is practically impossible to create a model with such a degree
of complexity and incompleteness of description. Moreover, since bad bricks cannot
be used to erect a good building, the following question also arises: should not
all the basic attention of investigators be concentrated exclusively on extending
our knowledge about the elements of a complex system; that is, on the "bricks"? In
connection with this, it is Pither explicitly or nonexplicitly assumed that it is
too early to construct a generalized acoustico-oceanographic model, since the time
for this has not yet arrived.
Without in any way disparaging this possible viewpoint that has been formulated,
which draws much from natural scientific skepticism, let us examine the question of
the creation and utilization of acoustico-oceanographic models (in our general for-
mulation) from other viewpoints.
Cognilive activity in the field of acoustico-oceanographic research (this situation
-is analogous to other fields, also) has traditionally taken place according to this
cycle: EXPERIMENT-ANALYSIS-MAKING OF DECISIONS-EXPERIMENT and so on.
In connection with this, between the analysis and decision-making stages the inves-
tigator studied possible variants, constructed hypotheses, examined the results
previously obtained and, finally, made decisions and formulated further problems.
This sequence fully satisfied scientific workers, in any case, until there appeared
three important elements, as the result of analysis, in the field of acoustico-
oceanographic research: multidimensionality of the results, their random nature
and an understanding of the presence of complex interrelationships among many
acoustico-oceanographic objects.
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The situation that has been created is, of course, characteristic not only of the
field of acoustico-oceanographic research. It arose in almost all the basic areas
of human activity, primarily as the result of the scientific and technical revolu-
tion, the accumulation of specific knowledge and the increased complexity of the
problems that the increasing practical requirements of people have placed before
science.
And so the following cycle of cognitive activity appeared: EXPERIMENT-ANALYSIS-
SIMLILATION COMPUTER MODELING-MAKING OF DECISIONS-EXPERIMENT and so on.
What is simulation computer modeling as applied to the field of acoustico-
~ oceanographic research?
- Before formulating an appropriate definition, let us list those problems that (in
the opinion of specialists in the field of computer simulation) can be solved by
means of simulation computer modeling):
a more thorough and intelligent undersi_anding of real activities;
- an improvement in intercourse among specialists, primarily those whose investigat-
- ive results are included in the simulation model;
training and practice on a large class of examples and simulated situations;
predicting the situation and behavior (evolution) of systems and their separate el-
ements;
, planning technical systems and their separate elements;
planning new experiments.
At the present time there are several definitions of simulation computer modeling
~ that differ primarily 'in the special features of their applications, thanks to
which formulated problems can be solved. As it applies to the field that we are
- discussing, this definition can be as follows.
Simulation computer modeling in acoustico-oceanographic research is the creation of
a model of a real, complex acoustico-oceanographic system and the conduct, with the
- help of a computer, of numerical experiments with this model for the purpose of
- learning the regularities inherent in the system for different input data, limita-
tions and criteria.
1fie following terms are synonyms here: simulation computer experiments, computer
simulation, computer experimentation.
Simulation computer modeling is distinguished, of course, from the previously gen-
erally accepted use of computer methods and from the so-called modeling that is
understood, in the normal narrow meaning, to be a numerical method for solving var-
ious analytical problems. In simulation modeling the model can contain both ana-
lytical and logical objects, and objects in the form of programs for computers, and
the results of expert evaluations, and empirical rules. It goes without saying
that such a model of a complex system can contain random values and field processes
that are formulated in accordance with given probability characteristics.
3. Basic Stages in the Organization and Conduct of Simulation Modeling /36,39,42,
44,45,49,51,52,55,577. Simulation computer modeling is a sequence of definite
stages, each of which is--even by itself--a quite complex scientific problem. In
this sense, the methodological principles of the organization and conduct of simu-
lation modeling acquire special importance.
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As in other fields of science and technology, when investigating acoustico-
oceanographic models computer simulation includes the following six basic stages:
Stage 1: formulating the problem, determining the goals of computer simulation,
introducing criteria.
Stage 2: developing mathematical models.
Stage 3: creating the software.
Stage 4: evaluating the quantitative degree of adequacy of the adopted modelfor
the actual objects of the investigation. '
Stage S: planning and conducting simulation computer.experiments. - Stage 6: processing and interpreting the results of the computer simulation.
= These stages, as applied to simulation computer experiments with acoustico-
- oceanografhic models, have different degrees of r_omplexity and problematicness.
= Below we will discuss each of these stages briefly and formulate those scientific
tasks that simulation modeling is capable of performing at the present time as far
= as acoustico-oceanographic research is concerned.
- 4. Formulating tlle Problem /24,30,36,45,51,55,57/. Computer simulation, as in any
- scientific investigation, begins with the formulation of the problem; that is, with
the compilation of a list of problems that it is necessary to solve as the result
of simulation experiments. It should not be assumed that this stage is quite sim-
ple in the substantive and quantitative sense, although it sometimes seems that the
purposes of an investigation are, it goes without saying, clear, otherwise the ac-
tual formulation of the problem and the performance of the investigation would not
malce any particular sense; that is, there would be no need for it. In much re-
search of a physical nature--exploratory research, in particular--it is sufficient
to describe these purposes qualitatively, in the form of some scientific areas
trends and unformalized hypotheses. Such a descriptive formulation is frequently
sufficient for an investigator of a specific physical area (at any rate, many in-
vestigators are convinced of this).
When formulating simulation computer experiments, the situation is different.
= Since the investigator is dealing with a computer in this case, the problem and the
goals of the computer simulation must be formulated specifically and unambiguously,
in a quantitative form that is expressed in mathematical concepts. In connection
with this, the following scientific problems arise in the field of acoustico-
- oceanographic research.
1. Substantiation, selection and formalization of the hypotheses that it is neces-
sary to test during the conduct of simulation modeling.
2. Substantiation, selection and formalization of tlie quality criteria for the in-
- formation systems that give an adequate description of the requirements pla.:ed on
them from systems of a higher order (supersystems).
3. Determination of rhe special and general quality criteria for the systems that
reflect, respectively, the solution of individual special problems and sets of them
(solution of the criteria convolution problem).
4. Determination of limitations (individual and combined) that must be placed on
both the acoustico-oceanographic conditions that will later be simulated by the
computer and the systems characteristics of the information systems.
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5. Determination of the temporal evolution of the criteria and limitations: an
analysis of their dynamics in the past, present and future.
At first glance these problems can be solved quite simply by (for example) using
the method of expert evaluations by competent specialists in different areas. This
is partially so, however (let us emphasize again this important factor) it is ne-
cessary to represent the results of the solution of these problems in a quantita-
tive, mathematical form that is suitable for use in a computer.
Let us also mention that 11ere we are talking not about the solution of any specific
set of problems concerning systems and acoustico-oceanographic models, but about
general methods for solving such problems and their theoretical (systems, physical
and mathematical) interpretation.
5. Determining Simulation Models /1-597. In the next stage after the machine simu-
lation problem has been formulated and the purposes and goals of the investigation
have been determined, it is necessary to construct acoustico-oceanographic and sys-
tems mathematical models. To determine a mathematical model means to substantiate
and formulate the set of equations, relationships, algorithms and conditions with
the help of which the acoustico�-oceanographic conditions' quantitative character-
istics would be related to the information systems' quality indicators. Since the
overwhelming majority of acoustico-oceanographic problems permit a formal, paramet-
ric description (altllough, it is true, it may be an extremely multidimensional one),
_ the mathematical model must relate the following groups of parameters to each other
in spatial-frequen.cy-temporal coordinates: a. parameters characterizing oceano-
_ graphic characteristics; b. the ocean's acoustic parameters; c, the acoustic param-
eters of signal sources; d, the parameters of the acoustic fields in the ocean; e.
the information systems' parameters; f. the information systems' quality indicators.
From this list, as well as from an analysis of the state of acoustico-oceanograpliic
and systems research, it is clear that the models under disclission will be compos-
ite deterministic-s::atistical ones. It is also obvious-that these models will be
depressingly complex, particularly from the viewpoint of traditional analytical
methods of solving physical and systems problems. The construction of such a simu-
lation model is a task of exceptional complexity, since here it is necessary to
combine the most diversified viewpoints of specialists, analyze experience, make
use of expert estimates and so on. In the opinion of the author of /57/, such a
task is more an art than scientific research in the generally accepted meaning.
In any case, the heuristic beginnings during the construction of a model are clear-
ly expressed. It should be mentioned that far from all scientific workers regard
such problems as being worthy of serious attention. Moreover, both in the area of
acoustico-�oceanographic research and in other areas of science and technology, it
was not so long ago assumed that the only serious scientific research was, in some
classical sense, "pure"; that is, a correctly formulated and specific physical,
systems or technical investigation, but in no case a composite one. Many scientif-
ic workers regarded (and frequently still do) combined (complex) investigations as
some compilatioii that was of no particular scientific interest.
There is some common sense in this, since in the creation oi models of complex
systems their basis is always a set of results of special investigations. But how
is it in the case where these special investigations were conducted from different
viewpoints, their results explained in different forms and frequently with the use
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of different concepts, parameters and methods of description? In our opinion, the
combination of special models into a general one is undoubtedly a creative scien-
tific activity that does not contradict research in special areas. Essentially
this is the so-called systems analysis, theory of operar43ns and allied cybernetic
and information fields mentioned above.
In many respects, the mathematical model creation and formalization stage is the
key stage in this problem of computer simulation, since it is on to what degree
this model corresponds to the actual investigated objects (hydrophysical phenomena
and the characteristics of technically realized information systems) that the suc-
cess and scientific validity of simulation experiments as a whole depend. It is
completely obvious that computer experiments with a low-quality and inadequate mod-
el are not useful, even if they are realized on a computer at an extremely high
level with respect to the software used.
Everything is far from clear as far as the development of acoustico-oceanographic
mathematical models is concerned, although explicit progress has been made in this
area in recent years. Let us now formulate several more scientific problems that
still need to be solved in connection with this.
1. The creation of acoustico-oceanographic data banks into which the results of ex-
perimental research, empirical regularities and theoretical relationships for the
entire set of studied objects in the ocean must be entered.
2. The investigation of regularities in the progress of different phenomena in the
ocean, including combined, multidimensional deterministic and statistical regu?ari-
ties.
3. Classification of acoustico-oceanographic conditions and determination of the
acoustic situation and acoustic weather and climate.
4. The development of a mathematical model for predicting the ocean's acoustic
characteristics, including multidimensional modeling of acoustico-oceanographic
conditions.
5. The development of mathematical models for the spatial-frequency-temporal pro-
cessing of information with the tielp of an extensive set of algor.ithms, including
the determination of the quality indicators (special and general) of the systems
for all known models of the fields affecting the antenna systems.
6. The development of optimization models for multiparametric, multiextreme prob-
lems.
The question of the formulation of mathematical models, as has already been said,
is the key question,in the entire problem of computer simulation. Of course, the
problems related to the construction of such models require a maximum concentration
of efforts from investigators with the most diversified profiles and styles. True,
another opinion is sometimes expressed: since scientif.ic research was always di-
rected at the construction of some models or another of phenomena and elements of
systems when solving specific acoustico-oceanographic problems, here nothing new
appears i:n the scientific plan. Unfortunately, this is not the case. Moreover, in
the field of acoustico-oceanographic research we cannot complain about an excess of
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special models (mathematical models, in the strict meaning of systems analysis).
The construction of an acousticc-oceanographic model as a complex system (see Sec-
tion 2) is a task that is much more laborious and no less creative than the con-
struction of any special hydrophysical or systems model. Many specialists working
in other areas of science and technology became convinced of this as soon as they
started to consCruct models of camplex systems (see, for example, /36,45,55,57/).
It very quickly turned out to be the case that even with the presence of special
models--which, by the way, have been being developed for decades--at the stage of
the creation of a model of a complex system (on the basis of the indicated special
ones, of course), it is especially important to utilize the erudition and
physical-systems intellect and to realize the creative capabilities of many inves-
tigators. Generally, the creation of generalized (integratea) models on the basis
of special ones that are developed by individual investigators in their plan for
the solution of specific scientific problems proved to be a most interesting ,
_ scientific-heuristic problem in systems analysis. Here everything is in dialectic
interrelationship: the special models determir.L: the level of description of the
generalized ones, while the latter affect the examination of the former from the
viewpoint of the demands made on them. It frequently proves to be the case (such
experience is already available in other areas of research) that special models are
developed on different levels in the space of different, unmatched parameters, so
that in the generalized model they do not "adjoin." Such a matching of models is a
creative scientific problem in an of itself, without even mentioning the necessity
of reviewing the formulations of separate special problems and enlarging the
"spheres of influence" of different investigators.
The formulation of models is a unique creative process that, of course, neither now
nor in the foreseeable future can be performed by even the most productive comput-
ers, although the researcher will continue to become more and more free from having
to carry out many computational and logical procedures.
6. Creating the Software /5,11,14,17,18,22,36,45,55,577. The next stage in the or-
= ganization of computer simulation experiments (after the creation of the mathemati-
cal model) is Fhe compilation of computer programs; that is, the creation of the
appropriate software. At the present time many computer languages that are suita-
ble in different degrees for the solution of computer simulation problems have ap-
peared. They include FORTRAN, ALGOL, PL/I, KOBOL, AUTOCODERS of various types and
others.
The creation of software for simulation computer experiments goes beyond the frame-
work of compiling standard programs for the solution of individual mathematical
problems by numerical methods. Here we are talking about the creation of a system
of programs that are informationally interrelated with due consideration, of course,
for the real memory and high-speed operating capabilities of modern computers. Ac-
tually, the problem comes down to the so-called systems programming for a general,
integrated mathematical simulation model, allowing for the possible simplications
allowable errors and capabilities of modern computers.
The following scientific problems arise when creating the soft*�7are for simulation
modeling.
1. Development of machine methods for multidimensional modeling on a computer for
given probabilities or empirical joint /word illegible/ of the distribution of
probabilities or a set of random values.
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2. Creation af "fast" algorithms for solving problems during integral, differential
and mixed transformations for large masses of information.
3. Development of inethods for evaluating the errors in a computer's computational
procedures with respect to given mathematical models; that is, the creation of inet-
rological facilities for simulation computer experiments.
4. Development of systems programming ideas in the direction of creating complexes
of programs for the simulation modeling of acoustico-oceanographic processes and
information systems.
5. Creation of information retrieval programs and programs for controlling'computer
simulation experiments, with due consideration for the "man-computer" system, using
rational combinations of different programming languages and information display
forms.
The solution of these and several other software problems will make it possible to
create rational systems of programs, organize the entry of the necessary data in
computers and the output of results from them and, finally, conduct the experiments
themselves at the appropriate time. The latter question is an extremely important
one, since the requirements for machine time in multidimensional statistical model-
ing are frequently so great that complete computer experiments become unrealistic
(this problem of multidimensional investigations long ago received the title of
"the curse of dimensionality").
In concluding this section, let us emphasize one important fact that is not always
taken into consideration when conducting theoretical research by traditional ana-
lytical methods. The fact of the matter is that the compilation of programs for
computers places certain requirements on the methods used to develop models of phe-
nomena and systems: these models, no matter how much we talk about their pro-
grammed realization on a computer, must not be simplified formulated mathematically,
but must be created with consideration for their embodiment in the form of computer
programs. This is a far from simple question and possibly /words illegible/, in
the final account, will lead to a review of the original /;aord illegible/ during
the solution of many special acoustico-oceanographic and systems problems. There
is nothing surprising here, since the formulation and solution of scientific prob-
lems were always matched with the necessity of obtaining constructive results dur-
ing their solution. In the case under discussion, the constructive result of the
solution of the scientific problems is computer programs, and not just any programs,
but reliable, compact and high-speed ones.
7. Evaluating the Quantitative Degree of Adequacy of a Model for the Actual Objects
of the Investigation J20,24,26,32,33,36,39-45,49-52,54,55,57/. The problem of es-
tablishing the suitability of a simulation moGel and reducing to a quantitative
evaluation the degree of adequacy of the adopted model for the actual investigated
objects (phenomena and systems) is extremely complicated in general form: the so-
lution of this problem involves mathematical, hydrophysical, experimental, techni-
cal and even philosophical questions. As a matter of fact, how can the question of
the quantitative degree of difference between a mathematical model of an object and
the actual object be answered if a true (complete) description of the object is in
no way known to the investigator? Further: can we count on the adequacy.of a gen-
eralized integrated model of a complex system if the degree of adequacy of the
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special models is known? And yet one more question: is it possible to plan and
carry out in the ocean a statistical experiment that in structure and size is simi-
lar to a computer experiment? This list of questions could, oi course, be contin-
ued by building the appropriate analogies between the ocean and its mathematical
simulation model. It is clear that it is not so easy to answer such questions from either the general
or the practical (applied) viewpoint, the moreso since here we are not talking
about a qualitative discussion of the questions (even by extremely competent ex-
perts), but about the correct evaluation of adopted decisions in a quantitative
form and with a known degree of accuracy. Thus, obviously, this problem is a com-
plicated one. However, this indication of the complexity of its solution is, of
course, little comfort for researchers who are conducting simulation computer ex-
periments.
Actually, if the quantitative degree of adequacy has not been established, the
whole idea of conducting simulation computer experiments does not withstand the
most elementary criticism. As is correctly noted in /36/, in the first place,
"...it is necessary to determine whether or not a model describes the system's be-
havior correctly. Until this problem is solved the value of the model remains in-
significant and the simulation experiment is converted into a simple exercise in
the field of deductive logic." Later in this work: "...experimentation on a com-
puter with an inadequate model is of little use, since we will simply be simulating
our own ignorance."
Thus, what can be said about the possibilities of evaluating the adequacy of an
adopted model and the actual object of investigation?
Starting from the general concepts of the dialectic theory of knowledge, let us
mention that when evaluating the adequacy of a model we should start with the fact
that the model must the main property of enabling us to predict (forecast) real
facts. Here, of course, two variants of prediction are possible: predicting ex-
perimental facts that were previously obtained (retrospective prediction) and pre-
dicting future facts (prospective prediction). In view of the statistical nature
of a simulation model and in view of the fact that the ideally accurate monitoring
of acoustico-oceanographic conditions during the conduct of full-scale experiments
in the ocean is practically impossible, and also because of the finiteness of our
resources (a finite numbex of samples, a finite time for observing them), the com-
parison of experimental data with results obtained with the help of simulation mod-
els must be based on the use of statistical criteria. With retrospective predic-
tion according to a simulation model the question is more or less clear (in its
fundamental sense, of course): here it is necessary to organize the statistical
processing of the available experimental data correctly and reduce it to the level
of a measurement procedure. Less clear is the question of prospective prediction:
here, apparently, we cannot be satisfied with traditional methods of obtaining
acoustico-oceanographic experimental data, but must create a new foundation for ex-
- periments in the ocean, the basic purpose of which will be to confirm and correct
the model that has been developed. In general, quite a lot has already been done
in this field, although there is still a whole series of scientific problems that
require substantial development work. We will point out some of these problems.
Development of special and general criteria for matching a simulation model to
real acoustico-oceanographic and phenomena and hydrophysical signals (degrees of
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difference and convergence, the distance in the space of multidimensional functions
and other factors).
2. bevelopment of a theory and methods for determining the representativeness of
the final selections of multidimensional random values and multidimensional deter-
ministic series in connection with their nonlinear interaction in a simulation mod-
el.
3. Creation of a general theory and constructive methods for planning purposeful
full-scale experiments in the ocean that in nature and volume are sufficient to es-
tabKsh,the quantitative degree of accuracy of a simulation model.
_ It is obvious that each of these problems is actually a whole scientific field and
cannot be solved by researchers in any narrow field: here we need a concentration
of efforts by specialists in different areas and their close creative interaction
_ in discussions and matching of positions, which can sometimes prove to be mutually
exclusive propositions. 8. Planning Simulation Computer Experiments /7,13,36,45,55,577. Computer simula-
tion experiments must be planned just as physical experiments must. The basic rea-
son for this necessity is the practical impossibility of conducting computer simu-
lation for an entire set of acoustico-oceanographic conditions and systems parame-
ters; consequently, in the planning under discussion an effort is made to provide
the greatest information content for such experiments, with permissible expendi-
tures (of human, material, technical and temporal resources). While noting that
several quite effective methods (stochastic search methods with adaptation, gradi-
ent methods, nonlinear filtration and prediction methods, nonparametric statistical
procedures and other) have been developed in recent years in the area of planning
simulation computer experiments, we must nevertheless mention several problems that
still remain to be solved in this area.
1. A search for methods of solving extreMe multiparametric problems for randon
functionals (criteria) when the original functions are not given analytically but
are calculated on a computer, while in the area of optimizable parameters there ex-
ist common dynamic, nonlinear limitations.
2. The development of constructive computer methods for evaluating the stochastic
- convergence of the results of statistical experiments on a computer with finite vol-
umes of sampling data for multidimensional, modeled initial data.
In the solution of these problems, we must naturally use the powerful and well-
developed methods of the theory of statistical hypothesis testing and the theor.y of
experiment planning, which has already become a classical method.
9. Statistical Processing of the Results of Simulation Computer Experiments /10,13,
17,24,32,36,38-41,55,57/. The result of the conduct of a simulation computer ex-
periment is some set of values that it is necessary to process for the purpose of
reaching some conclusion or another and making the appropriate decisions. Let us
stress this important fact: the result of a computer simulation is some statisti-
cal regularity inherent in the simulation model, and the utilization of this regu-
larity is the proper business of the investigator or the people who are the consum-
ers of the results t:iat are obtained. In other words, making appropriate decisions
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on the basis of the results of simulation modeling goes beyond the framework of the
problem we are discussing.
Thus, the final stage in computer simulation is the processing of the results ob-
tained by the computer. Generally speaking, all the classicial statistical proce-
dures for analyzing random values, including multidimensional ones, are used to
process the results of computer experiments. Moreover, during computer modeling a
whole series of statistical methods of analysis can be realized substantially more
nearly correctly than under the conditions of a full-scale hydrophysical experi-
ment: by using a computer it is possible to obtain the necessary volumes of samp-
ling data, observe the conditions of statistical homogeneity of experiments and so
forth. Along with this, however, here there arise certain specific problems, some
of which we will list below.
1. A search for effective quantitative congruence criteria that are adequate for
the acoustico-oceanographic problems that are being solved and that should be used
in the statistical processing of the results of simulation computer experiments.
2. The creation of a theory and methods for evaluating errors in simulation comput-
er experiments, including the errors related to inadequacy of the adopted simula-
tion model and the closeness of the realization of the modeling algorithms (other
types of errors--finiteness of the samples, finiteness of the number of characters,
temporal discreteness of the readings and so on--are analyzed by the usual methods).
3. A search for stable (robust) statistical analysis procedures based, in particu-
lar, on the methods of nonparametric statistics.
10. Summary. As follows from this brief review of the content, special features
and scientific problems in simulation computer modeling, the problem under discus-
sion is quite complicated in the scientific sense and--which is an extremely impor-
tant factor--also an integrated one. Naturally, it cannot be solved without the
efforts of specialists in hydrophysics, acoustics, cybernetics, computer mathemat-
ics and programming. The development of this field, of course, requires signifi-
cant expenditures of creative and material resources for an extended period of time.
Specialists in the field of simulation modeling have already analyzed the available
exPerience in ttie conduct of research in this area (see, in particular, /36,45,55,
57/. At the present time it is considered that the creation of a single simulation
model--from its conception to its realization on a computer in a form suitable for
the conduct of simulation computer experiments--takes from 3 to 10 years, depending
on the complexity of the system being modeled and the degree of development of the
_ special models. In connection with this it is assumed that the number of special-
- ists--highly qualified, of course--working on such a problem is 8-10 people, not
counting approximately the same number of programmers with standard qualifications.
It is interesting to mention also the amount of computer time needed (based on the
most efficient computers in the early 1970's): the creation of a single simulation
model requires from 104 to 105 hours of computer time (including the debugging of
the special and general programs, the organization of computer data banks and ser-
vice systems, the making of calculations for a set of situations and so on). Since
the creation of acoustico-oceanographic simulation models is a problem of increased
complexity, it is obvious that it will require significant efforts on the part of
many researchers. However, such significant expenditures are justified by the
bright prospects for the solution of many interesting (in the scientific sense) and
important (in the applied sense) problems, the primary ones of which include:
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the creation of generalized acoustico-oceanographic simulation models, including
the corresponding computer data banks, and the determination of the regularities
inherent in these models;
' the planning of purposeful, full-scale experimental investigations in the ocean on
- the basis of the conduct of simulation computer experiments, including an evalua-
= tior. of the quantity and value of the information obtained during the conduct of
full-scale acoustico-oceanographic research;
systems-analysis planning of oceanographic and hydroacoustic inforniation systems;
the prediction of the acoustic situation in the ocean and the evaluation of the
quality of the functioning of inf.ormation systems under these conditions.
Naturally, these and many other interesting and important problems can be solved
only by using the most modern computers, providing that the appropriate software is
created for them. In this sense it is no accident that it is precisely the power-
ful and highly efficient computers that have stimulated the most extensive develop-
ment of simulation modeling projects abroad, where they have been going on for more
than 10 years on extremely large scales and in the most variegated fields of sci-
ence and technology. It should not, however, be thought (let us emphasize this one
more time) that the question of the development of simulation modeling boils down
only to tfi e use productive computers. It is important, every time, to emphasize
the attention that must be given to the necessity of conducting physical acoustico-
oceanographic research on the broadest possible scale and in the most purposeful
and thorough manner. In this respect, we cannot help but agree with the opinion of
USSR Academy of Sciences Corresponding Member N.N. Moiseyev, who, in his foreword
to the Russian edition of a book /367, remarked:
"It is necessary, with total clarity, to understand that the problem of construct-
ing a sirculation model--as is the case with any other model--is a problem of the
adequate description of the real world's objective laws. This problem has been be-
fore science for many centuries, and the appearance of the most powerful computer
technology has still not solved it. I am convinced that now and in 20 years, as it
was 20 years and 20 centuries ago, the discovery of new laws (that is, the con-
struction of new models oF the phenomena occurring in the world around us) will be
worth the tense creative activity, will be worth the inc�edible expenditures of hu-
man intellect and spirit. No amount of compucer time can replace them, since the
computer merely makes this process easier by taking over the performance of more
and more routine procedures."
What Moiseyev said needs no further comments.
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poley" /Ninth All-Union Symposium on "RePresentation Methods and Equipment
Analysis of Random Processes and Fields"/, Leningrad, VNIIEP, Section 4, 1976,
pp 3-6.
43. 01'shevskiy, V.V., "Statistical Measurements Under Conditions of Dynamic Acous-
tic Experiments," "Trudy Vtoroy nauchno-technicheskoy konferentsii po informa-
tsionnoy akustike" /Works of the Second Scientifi_c and Technical Conference on
Information Acoustics/, Moscow, Institute of Acoustics, USSR Academ,y of Sci-
_ ences, 1976, pp 67-71.
44. Ol'shevskiy, V.V., "Simulation Experiments in Statistical Hydroacoustics:
Selecting Models and Checking Their Adequacy for Real Phenomena," in "Akusti-
cheskiye metody issledovaniya okeana," Leningrad, Izdatel'stvo "Sudostroyeniye
1977, pp 6-17.
45. Buslenko, V.N., "Avtomatizatsiya imitatsionnogo modelirovaniya slozhnykh
sistem" /Automation of the Simulation Modeling of Complex Systems/, Moscow, Iz-
datel'stvo "Nauka", 1977.
46. Dyuran, B., and Odell, P., "Klasternyy analiz" /Claster Analysis/, Moscow, Iz-
datel'stvo "Statistika", 1977.
47. Grubnik, N.A., and 01'shevskiy, V.V., "An Acoustic Model of the Ocean," "Trudy
Pervogo seminara 'Akusticheskiye statisticheskiye modeli okeana /Works of the
First Seminar on "Acoustic Statistical Models of the Ocean"/, Moscow, Institute
of Acoustics, USSR Academy of Sciences, 1977, pp 3-11.
48. Middleton, D., "A Statistical Acoustic Model of the Ocean," "Trudy Pervogo se-
minara 'Akusticheskiye statisticheskiye modeli okeana Moscow, Institute of
Acoustics, USSR Academy of Sciences, 1977, pp 12-55.
49. 01'shevskiy, V.V., "Models and Simulation Computer Experiments in Statistical
Hydroacoustics," "Trudy Pervogo seminara 'Akusticheskiye statisticheskiye mode-
li okeana Moscow, Institute of Acoustics, USSR Academy of Sciences, 1977, pp
70-85.
50. Middleton, D., and 01'shevskiy, V.V., "Contemporary Problems in Constructing
Acoustic Statistical Models of the Ocean," "Trudy Pervogo seminara 'Akustiches-
kiye statisticheskiye modeli okeana Moscow, Institute of Acoustics, USSR
Academy of Sciences, 1977, pp 86-90.
- 51. 01'shevskiy, V.V., "Simulation Computer Experiments in Statistical Hydro-
acoustics: Models, Algorithms, Measurements," "Tru~y Vos'moy Vsesoyuznoy
shkoly-seminara po statisticheskoy gidroa~-ustike" /Works of the Eighth All-
Union School-Seminar on Statistical Hydroacoustics/, Novosibirsk, Institute of
Mathematics, Siberian Department, USSR Academy of Sciences, 1977, pp 138-154.
52. 01'shevskiy, V.V., "Vybor modeley pri imitatsionnykh mashinnykh eksperimentakh
v statisticheskoy gidroakustike" /Selecting Models for Simulation Computer Ex-
periments in Statisti.cal Hydroacoustics/, Moscow, Institute of Acoustics, USSR
Academy of Sciences, 1977, pp 23-32.
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53. Zavadskiy, V.Yu., "Akustika i EVM. Voprosy sudostroyeniya. Seriya: akustika"
/Acoustics and Computers: Questions in Shipbuilding. Acoustics Series/, Ts1vII
"Rumb" /expansion unknown/, No 10, 1978, pp 80-90.
54. 01'shevskiy, V.V., "Modeling in Statistical Measurements: Problems and Metro-
, logical Aspects," "X Vsesoyuznyy simpozium 'Metody predstavleniya i apparatur-
nyy analiz sluzhaynykh protsessov i poley" /lOth Al1-Union Symposium on "Repre-
- sentation Methods and Equipment Analysis of Random Processes and Fields"/,
Leningrad, VNIIEP, Section 4, 1978, pp 2-7.
55. Kleynen, Dzh., "Statisticheskiye metody v imitatsionnom modelirovanii" /Statis-
tical Methods in Simu]ation Modelinv~/, Moscow, Izdatel'stvo "Statistika", lst
and 2nd editions, 1978.
56. RaLiner, L., and Gould, B., "Teoriya i primeneniye tsifrovoy obrabotki signa-
lov" /Theory and Utilization of Digital Signal Processinj, Moscow, Izdatel'-
stvo "Mir", 1978.
57. Shcnnon, R., "Imitatsionnoye modelirovaniYe sistem---iskusstvo i nauka" /Simula-
tion Modeling of Systems--Art and Science/, Moscow, Izdatal'stvo "Mir", 1978.
58. Grubnik, N.A., and 01'shevskiy, V.V., "Methodological Questions on the Con-
struction of Acoustic Models of the Ocean," "Trudy Chetvertoy nauchno-
tekhnicheskoy konferentsii po informatsionnoy akustike" /Works of the Fourth
Scientific and Technical Conference on Information Acoustics/, Moscow, Insti-
tute of Acoustics, USSR Academy of Sciences, 1978, pp 3-10.
59. 01'shevskiy, V.V., "Principles of the Investigation of Acoustico-Oceanographic
Models," "Trudy Chetvertoy nauchno-tekhnicheskoy konferentsii po informatsion-
_ noy akustike", Moscow, Institute of Acoustics, USSR Academy of Sciences, 1978,
= pp 11-22.
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VOLUMETRIC NOISE SPATIAL CORRELATION FUNCTION FOR SURFACE ANTENNAS
[Article by Yu. B. Goncharov and I. L. Oboznenko pp 49-52]
- /Text/ In this article we discuss the effect of the reflecting surface on which
acoustic pressure receivers are located on the spatial correlation function of vol-
umetric, isotropic noise. The receivers' inherent diffraction effects are not tak-
en into consideration; that is, they are assumed to be point receivers.
Let us examine an unlimited space D that
. t contains an arbitrary body S(Figure 1),
c Q~ry~`~.) on the surface of which ar.e located point
A~ receivers Al(pl,01,~l) and A2(P2,02,W
R ,p R Qten (p,6,~ = spherical coordinates of the sur-
, e ( J
t 1 face points re lative to the center 0; �p =
o_ radius vector describing the surface of
� ~ S). Let space D- V0, where VD is the
. Q volume of the scattering body, be continu-
O ous and filled uniformly with point noise
~ s sources Q(ro), ro c(D - VO). Let us as-
Figure 1. sume that the noise field on the outer
surface of S is homogeneous and that the
voltage at the outpiits of point receivers A1 and A2, as well as that of an external
(relative to the surface of S) point receiver P(ro), rOc= (D - VD), is proportional
to the total pressure p at the indicated points. We will assume that each noise
source creates a pressure in space D- VD that is characterized by identical sta-
Listical properties and that the noise formation process itself is ergodic. We as-
snmr that the phases of noise sources Q(rO) are random for all roE (D - VO) and
~
tliat at a random irequency w the amplitudes of the total pressure p(r) are dis-
tributed relative to tlie averagc value and that the average for the ensemble equals
Clic average wilh respcct Lo time. I3y analogy with /1,27 let us determine the nor-
malized spatial corrclation function of the noise interference at the two points
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+.o R'R~---- -

4~ - ;
Qs - -

0'+ -
- ~Q-;--- -
Q2 - L
o - F
Figure 2.
FOR OFFiC1AL USF. ONLY
..o
.Q:
~o ---r~---,
i 1g , ope
\
04 - - - ~ .
~
07 - -
\
Figure 4.
A1(pi) and A2(p2) (Figurc 1) in the forn
- R(I1)1 - p2I~T) = R(d,O)cos G1T, d= Ipl - p2I1 ~1)
where
R(d,O) _ 2'12 - 1 = 1 = 1, u = ~P) (2)
2p 2p
T= time lag of the pr.ocess; sensitivity of t.he point receivers; 12 and
p = mean squares of the voltages at the output, respectively, of the two (at
points A] and A2) and one (reduced to a certain point on the surface of S) receiv-
. ers sensing noise from volume D- V0.
; As a reducti.on point, let us take one of the points on the surface (P,0,0). Let
� us represent the pressure waves falling from point Q(ro) and scattered at point
I }
i p(rp) in the form
I pi(r,t) = pi(r)e-lwt; ps(r,t) = ps(r)e-lwt, (3)
' where pi, ps = comples pr.essure amplitudes in the incident and scattered waves, re-
the total pressure amplitudes are
I spectively. At points A1 and A21
I' p1 ~P 1 ) = p i.l 1 ) + p sl (P 1 P Z (P 2) = pi2 (P Z ) + p S2 (P 2 ) . (4)
If we selecl- point !11 on the surface of S as the reduction point, in accordance
with the pr.ocedure / 2/ tor computing spatial correlation function (2), we obtai.n
1 !II ~P17IZ
dv - 1. (5)
' R(d,O) = Z'fYj p1~V
Here,
p1.2 P1( _P1) + P2(P2) - ~'i1(Pl) + ~'i2(P2) + Ps1(Pl.) + ~'s2(P2~ . (6)

Since the pressure in ttie i.ncident wave is assumed to be known for any source Q(ro),
roF- V, aC an arbitrary point P(r), r E V, including points on the surface of S, in
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order to determine spatial corr.elation function (5) it is necessary to find the
scattered field at point P(and, in particular, at tile points on the surface of S).
For a spherical, acoustically stiff surface the expression for the spatial correla-
tion factor of volumetric noise has the form
OR(d 0) = En + 1)Pn(cos 0) L(2n + 1) 1 , 2
Dn(ka) _ Ihn(ka)I . (7)
' n=0 D� ( ka ) n=0 D., ka I '
Figure 2 shows the dependences of the spatial correlation functions of isotropic,
volumetric noise for acoustically stiff [R(d,0)] and acoustically transparent
[RD(d,0)] spherical antennas on the spatial location of the two receivers A1 and AZ
for different values of the wave size ka. Figures 3 and 4 show the dependences of
functions R and Rp on wave size ka for fixed spatial positions of receivers A1 and
A2. As is obvious from these figures, for average values of the scattering sur-
face's wave sizes, functions R and Ro can differ substantially. For large surface
wave sizes, differences between functions R and Ro are observed only in the area of
weak currelation.
BIBLIOGRAPHY
1. Eckart, G., J. ACOUST. SOC. AM., Vol 25, 1953, p 195.
2. Kron, B., and S}ierman, I., "Spatial Correlation Functions for Different Models
of Noise," in "Nekotoryye problemy obnaruzheniya signala maskiruyemogo flyuktua-
- tsionnoy pomekhoy" /Some Problems in Detecting a Signal Masked by Fluctuating-
Interference/, Moscow, Izdatel'stvo "Sovetskoye radio", 1965.
;
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F()It ()F'FI('IAI, llfiEONI.Y
LOW-FREQUENCY REVERBERATION CAUSED BY THE SCATTERING OF SOUND ON THE FOAMY SURFACE
nF THE OCEAN
[Artic].e by V. P. Glotov pp 52-56]
/TexL/ It is a well-known fact /1,27 that resotiance scatterers i.n the form of
pulsing air bubbles form in a thin layer of water that is disturbed by wind-caused
waves. What is of interest is the low-frequency surface reverberation (back scat-
tering) that occurs under extreme meteorological conditions--a foamy, irregular
ocean surface (wind speed v> 6-8 m/s)--when the scattering is great not only at
high, but also at low frequencies ('u1 kHz). A characteristic feature of this st.a-
- tistical problem is accounting not only for the wave action, but also the acoustic
interaction of a bubble witt its mirror image. As the model of the scattering me-
dium 1et us talce a stociiastic complex consisting of a large-scale ir.regularity
(that is fluent and sloping) and an underlying layer of bubbles, the concentration
of wtiich is constant (throughout the layer) and the radii a of which are small in
comparison with the wavelength a= 27/k in the water and the distance between them.
We will separate a layer of bubbles of thickness H= 0.1A tliat is adjacent to the
surface and compute its contribution to the total scattering. The other part of
the layer 'is of no interest, since its effect on the reverberation has already bcen
studied in detail /3,47.
~ � �o n
. S
N 'L .
' � o ~ o o~^~ ~�~O?-~ ~~.f". .'peO11. a~r
cr o)
, ~ . . _ . _ . - ~
Figure 1,
Let a narrow-band pulse, the spatial length L oi which exceeds the irregularities'
correlation interval, strike an agitated surface at a glancing angle ~(to the
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plane z= 0, Figure 1). Now let us find the intensity of the reverberation from
layer H.
At low frequencies (1 kHz and lower), rrad = kZa2 rn (loss resistance) and thr
J scattering cross-section of a bubble in a limitless space can be represented ap-
proximately as
a = 4�Ra2/rrad = a2/7r. ( 1)
For the intensity of the reverberation from laye~.- H we have /3,4/:
rrev - (n6140, (2)
where n= average concentration of bubbles in the layer; T = disturbing sonic field
under the irregular surface (in the layer); G= Green function; u= volume of the
layer; = averaging with respect to the collective of irregularities.
In the propositions formulated above relative to the surface (soft, fluent and
sloping), the field beneath it can be represented in the following form / 67 (we
ignore the contribution of the bubbles):
I `Y(R) I = 2&(R) JRN)
~
(3)
where IV = unit normal vector to the irregular surface at the current point i;
F(~) = distance from volume du to the irregular surface along the normal to it; R=
= distance from du to the observation point.
Let us now determine the Green function. From the figure it is obvious that the
indicatrix of tlie dipole (the bubbles plus their mirror image) has the form:
4~2(X) = sin2 (k~�sin X), (4)
where X= the scattered wave's angle of yaw to the tangent plane.
From formula (4) it is obvious that the indicatrix has maximums in different direc-
tions. For k~ < 7/4 (that is, fmax H= 0.11) the indicatrix has a single maximum
in a direction close to the tangent plane's normal. In this direction the oscilla-
tions of a bubble and its image are almost opposite in phase (the intensity equals
the square of the sum of the pressures):
2 sin2(k ) (kF)Z WG
lmax = v WS 4~r m~ ~ 5)
where v= the number of oscillations (v = 2); WS = a bubble's scattering power in a
limitless space; m= a facL-or (0 , m4 1) allowing for the change in a bubble's re-
sistance in the presence of an absolutely soft interface (rrad = mk2a2).
Factor m can be related to the axial scatterinb concentration / 7/:
W/2
m= j sin2(kf;�sin X)cos XdX = 1-(sin 2k~/2k~). (6)
-1r/2
We see that for lc& , ir, m= 1(there is no interaction). On the contrary, however,
for Ic~ < u/4 the interaction is great, since m= 2/3(k~)2, which means a sharp
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intensification of a bubble's pulsations and, consequently, scattering. For a thin
layer kH < n/4, according tu (5) and (6) the intensity of the scattering at the in-
dicarrix's maximum will be
lmax = 6(WS/4nR2); (7)
that is, 7.8 dB more than in a limitless space under the same conditions. For the
intensity at angle X we obtairi (k~ w/4):
i(X) = imaxD2(x) _ (ws/4n)IGI2, (8)
where D(x) _(kF)-202(X; = k2(~ N)2 = normalized indicatrix;'k-* = wave vector of the
scattering of the wave; IGI = absolute value of the Green function:
I G~ = F6 [(xN)/kRl � (9)
Considering expressio.is (3) and (9) and integrating (2) with respect to the thick-
ness of the layer, we obtain
(rrev)~=k = 8n H3 > (10)
k4R4
- where so = the surface limiting the scattering volume (so = 2ffRL).
Further calculations of the reverberation level can be made only if the statistical
properties of the agitated surface are given. Assuming that the slopes of the
large-scale isotropic irregularities are distributed according to the normal law,
according to (10) we obtain
- rrev = 8H3sOR-4C(~,6), (11)
where C(~,d) = a function depending on the incident wave's &lancing angle and the
root-mean=square angle of the irregular surface's slope / 6/.
Let us calculate function C(~,d) for the reverberation aspect of the glancing an-
gles 0). We have:
C(~,d) ~ ~4[1 + 6(1)2(1 + a2 = 3d4. (12)
~,->0 $ 2$2
Substituting expression (12) into (13) and converting to the surface reverberation
factor mPM = 4TIrPR2/roso, where ro - RZ is the intensity of Lhe direct wave, for
0 we obtain
!I mPM = 96ffnH3~4. (13)
~
Thus, for small glancing angles the value of the factor mP($) does not depend on
~ the angle, but on the root-mean-square angle of the i.rregular surface's slope (a
I linear dependence on v /8 and the average concentration ot bubbles (an exponen-
; tiat dependence on v/1,2/). It is easy to see, however, that formula (13) gives
an exaggerated reverberation value, since part of the bubbles are "shaded" by the
~ irregularities in the surface when G~-> 0. Let us introduce the approQriate correc-
; tion factor. For the "shading" function at glancing angles we have / 57:
i
~
~
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Q(~,a) = S($,d)/so = 2.5�6-1, (14)
where S(~,d) = the effective area.
Allowing for (14), cve will finally have
mPW = 2407nH363~; (15)
that is, the reverberation's spatial subsidence follows the law R-4, since
zo/R, where zo is the depth of submergence of the hydrflacoustic system.
Let us evaluate the equivalent radius of the surface reverberation for an undirect-
ed hydroacoustic system. Assuming that f= 1 kHz, zo = 100 m, H= 15.cm, d= 0.17
(v = 15 m/s), n= 10-6-10-7 cm-3 (the extrapolation value of the concentration of
resonance bubbles according to the optical data in / 27 and L= 50 m, we obtain
~ aequ = 4-12 m(independent oF distance).
Thus, the contribution of a tliin layer of bubbles (foam) can be extremely signifi-
cant.
BIBLIOGRAPHY
1. Glotov, V.P., Kolobayev, P.A., and Nauyman, G.G., "Investigation of the Scatter-
ing of Sound by Bubbles Created in Seawater by an Artificial Wind and the Sta-
tistical Distribution of the Bubbles' Dimensions," AKUSTICHESKIY ZHURNAL, Vol 7,
No 4, 1961, pp 421-427.
2. Kolobayev, P.A., "Investigation of the Concentration and Statistical Distribu-
tion of the Sizes o� Bubbles Created in the Surface Layer of the Ocean by Wind,"
OKEANOLOGIYA, Vol 15, No 6, 1975, pp 1013-1017.
3. Glotov, V.P., and Lysanov, Yu.P., "On Surface Reverberation Caused by Resonance
Air Bubbles," TRUDY AKUSTICHESKOGO INSTITUTA, No 2, 1967, pp 26-32.
.
- 4. Glotov, V.P., and Lysanov, Yu.P., "On the Relative Role oF Air Bubbles and an
Agitated Sea Surface in the Formation of Reverberation," AKUSTICHESKIY ZHURNAL,
Vol 14, No 3, 1968, pp 371-375.
5. Bass, F.G., and Fuks, I.M., "Rasseyaniye voln na statisticheskoy_nerovnoy po-
ver.khnosti" /Wave Scattering on a Statistical, Irregular Surface/, Moscow, Izda-
tel'stvo "Nauka", 1972, pp 183, 351, 243.
fi. Kur'yanov, B.F., "Scattering of Sound on a Rough Surface With Two Types of Ir-
rebularities," AKUSTICHESKIY ZHURNAL, Vol 8, No 2, 1962, pp 325-333.
7. Skuchik, Ye., "Osnovy akustiki" /Principles of Acoustics/, Moscow, Izdatel'stvo
Inostrannoy literatury, 1958, Part 1, p 293.
8. Cox, C., and Munk, W., "Measurement of the Roughness of the Sea Surface From
Photographs of the Sun Glitter," J. OPT. SOC. AMER., Vol 44, 1954, pp 838-850.
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INFORMATION CHARACTERISTICS OF REVERBERATION CAUSED BY WIDE-BAND SOURCES IN A
SHALLOW SEA
[Article by T. V. Polyanskaya pp 56-571
/Text/ An analysis of works devoted to the study of the characteristics of rever-
beration in lakes and a shallow sea when wide-band sources are used showed that at
the present time insuffici.ent attention is being devoted to establishing a connec-
tion between the rzverbers.tion signal's characteristics and the spatial-structural
characteristics of the medium's boundaries, with the low-frequency area being the
least studied of all.
In this article we stsdy the information characteristics of low-frequency (f < 1
kHz) reverberation (which include duration, the shape of the signal's envelope and
its spectral characteristics) caused by an explosive source in lakes and a shallow
sea. In order to obtain the initial data, we nade experimental recordings of re-
verberation signals under diff erent conditions (in Lake Svityaz' in Volynskaya
_ Oblast and in Lake Ladoga, as well as shallow bays in the Barents Sea, with the av-
erage depths for all of this work being 10-130 m). Different geometric arrange-
ments of the monostatic and bistatic sound sources and receivers were used. As a
signal source we used explosive charges of various sizes, while the receivers wer.e
nondirectional hydrophones, the depth of submergence of which equaled the depth at
which the charges were detonated. The wide-band reverberation signals that were
received were recorded on a tape recorder. The characteristics that were analyzed
were duration, envelope shape and signal spectrum. The spectral characteristics
were obtained during the processing of the signals, using a BPF /expansion unknown/,
for frequency values of 0-5,000 Hz and a 2-Hz band, in connection with which the
realzzation was divided into sections lasting 0.5 s. The analysis that was made of
the experimental results showed that the geometric characterisrics of the body of
water can be determined from the duration of the reverberation. We constructed an
empirical law for the dependence of the duration of reverberation on the area of
- the sonicated water area (for those cases where the area of the basin was evaluated
preliminarily with certain reflectors) that showed that the duration of the rever-
beration is almost di.rectly proportional to the area of the basin. The experimen-
tally obtained reverberation duration values were compared witti theoretical ones
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calculaLed with Yu.M. Sukhrirevslciy's formula / 17 for boundary reverberation. The
besC correspondences wt-re obtained for the regions with the least broken land pro-
files, when small ctiarges were used, and for depths not exceeding 15-20 m. In the
general case the experimental values are always higher than the calculated ones,
which can be explained by the fact that the �ormula used does not allow for such
essent:ial (in this case) parameters as ttie size of the body of water, the land pro-
Lile and the simultaneous presence of both bottam and surface reverberation. Peri-
odic brokenness of the spectrum oi a reverberation signal with an amplitude of 8-10
dB and a frequency of 25-45 Hz is seen in the spectrograms of recordings made in
open areas and rather wide bays. This can be.explained by the effect of the pulsa-
tions of the gas bubble appearing in connection with the detonation of the explo-
sive charge, since the frequency of the pulsations diminishes with a decrease in
tlie depth at which the charge is detonated and in increase in the weight of the ex-
plosive used. This makes it possible to link a reverberation signal's character.-
islics with the working conditions and the depth of detonation of the charge. Ttie
statistical regularities of a reverberation signal were studied with the help of a
discrete, canonical model of reverberation for broad-band emissions / 27. V.V.
01'shevskiy showed that in such a case, the reverberation process is essentially
nonstationary, since the form of the correlation function (and not only its disper-
sion) depends on the current time. Research conducted by us and reported in detail
in / 3/ showed that reverberation from an explosive source in a shallow sea is a
process that leads to a stationary one, in connection with which the stationary
component of the reverberation signal is distributed according to the normal law.
Thus, our research demonstrated the promise of the study of the information charac-
teristics of reverberation caused by broad-band sources for the study of the spa-
tial and structural cltaracteristics of the boundaries of a medium. The development
of this area of research can move along the path of predicting marine reverberation,
as well as the study of the effect of the frequency characteristics of the scatter-
ers and the marine medium on the temporal and spatial correlation of reverberation.
BIBLIOGRAPHY
1. Sukharevskiy, Yu.M., "TYieory of Marine Reverberation Caused by the Scattering of
Sound," DOKLADY AN SSSR, Vol 55, No 9, 1947, pp 825-828.
2. 01'shevskiy, V.V., "Statisticheskiye metody v gidrolokatsii" /Statistical Meth-
ods in Hydrolocation/, Leningrad, Izdatel'stvo "Sudostroyeniye", 1973.
3. Gonopol.'skiy, A.L., Cronskiy, Ya.I., and Polyanskaya, T.V., "Some Results of
Experimental Investigations of Reverberation Caused Uy Broad-Band Sources in a
Shallow Sea," in "Trudy 9-oy Vsesoyuznoy shkoly-seminara po statisticheskoy
gidroakustiki" /Works of the Ninth All-Union School-Seminar on Statistical
Hydroacoustics/, Novosibirsk, 1978.
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STATISTICAI. ANALYSIS OF ACOUSTIC SIGNALS SCATTERED BY A SEA SURFACE
[Article by Ya. P. Dragan and I. N. Yavorskiy Pp 58-591
/Text/ Let us examine the methods for obtaining statistical evaluations of the
characteristics of biperiodically correlated random processes (BPKSP) and the algo-
rithms used to compute them. Algorithms for determining evaluations of the charac-
teristics of periodically correlated random processes (PKSP) are derived from them
- as special cases. A BPKSP is a random process, the mathematical expectation
m(t) = E~(t) and correlation function B(t,T) = E(&(t + T) - m~(t + T)]
- [~(t) - m~(t)) of which are almost peri~Sic functions of time with Fourier indica-
tors llnz = n(2w/T1) + Q(2ff/T2), where n and Q are whole numbers, so that they can
be represented in the form
co co
m~t) = m exp j11 t, B(t,T) = E B(T)exp jA t.
E n,~=-~ ~,n n2 E Q,n=-~ kn nR
Evaluations of these characteristics can be found by calculating the evaluations of
components mZn and BQn(T), and when the periods of correlatability of the process
T1 and T2 are coummensurate (that is, when qTl = pT2) they can also be calculated
directly. Unskewed evaluations of the components are the statistics
T
mQn = lim T I E(t)exp (-j/1nQt)dt,
T-*CD 0 ~ 1)
T
BQn(T) = lim T ! ~(t + T)Z(t)exp ('.JAnQt)dt.
0
These evaluations will be
relation function and the
uation of the characteris
points that are multiples
tions of the mathemaCical
tioned above, will be the
valid for certain conditions that are imposed on the cor-
fourth moment (see, for example, / 3/). The direct eval-
tics of a BKPSP is based on the properties of readings at
of the value pT2, Tl < T2. Unskewed and valid evalua-
expectation and covariation, under the conditions men-
statistics
1 N=0
m~( tp) = N nIo E,(tp + npT2)(2)
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. . . . . . . . (2)
1 N=0
B~(tO,T) = N 2: C(to + npT2 + T)~(to + npT2), Q= 0,9P.
n=0
In order to find the value of the correlation function, it is convenient to repre-
sent the data entered in a computer in the form of a matrix, the rows of which are
sequences of readings: = IIZRpII, fzp = y(t0 + Qp + npT2), A = quantification step.
BIBLIOGRAPHY
1. Dragan, Ya.P., and Yavorskiy, I.N., "Probability Description of Sea Waves," in
"Trudy Sed'moy Vsesoyuznoy shkoly-seminara po statistic}ieskoy gidroakustike"
/Works of the Seventh All-Union School Seminar on Statistical Hydroacoustics/,
- Novosibirsk, 1976.
2. Dragan, Ya.P., and Yavorskiy, I.N., "On the Representation of a Communication
Link With Reflection From a Sea Surface in the Form of a Linear Filter) " in
"Trudy Sed'moy Vsesoyuznoy shkoly-seminara po statisticheskoy gidroakustike",
Novosibirsk, 1976.
3. Gudzenko, D.I., "On Periodically Nonstationary Processes," RADIOTEKHNIKA I
ELEKTRONIKA, Vol 4, No G, 1959.
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INVESTIGATION OF THE INTERFERENCE STRUCTURE OF THE ACOUSTIC FIELD OF A MODEL
WAVEGUTAE
[Article by G. K. Ivanova, V. N. Il'ina, Ye. F. Orlov and G. A. Sharonov pp 59-61]
/Text/ In this work we conduct an experimental test of the method of generalized
holograms / 1/ during an investi;;ation of the mode structure of the acoustic field
in model waveguides of two types: a two-layer waveguide and a syimnetrical sound
channel with a deepened axis.
_ The sliding spectrum of an intensity hologram / 1/ with temporal averaging, allow-
ing only for the interference term at great distances, will be / 27:
t+TB - i ~t
- B(St,w,t) _ ~ FT(to,t) mE n P m (w,z,z0)P n (W,z,zo)cos Amn
(w)r dt. (1)
! where z, zO = horizons of the source and the receiver; r= vt; A mn = equality of
i the longitudinal wave numbers of the modes m, n. Extreme values of the function
j B( S t,w) will be seen at P = vtlrmn(w), The lines of the extreme values of A(Q,w) on
~ the plane 12,wwill correspond to the waveguide's characteristic curves, wllile the
i values of the function B(S2,w) on the line U=Q/v = A mn(w) will be determined by
~ the amplitudes of the excitation of the modes Pm(w,z,z0)Pn(W,z,z0)'
~ For a two-layer medium on the plane x,w, the area of modes encomPassed by the wave-
guide is limited by the straight lines w/.w = C1 and w/A = C2 / 3/. On the plane
u,w the area of existence of a difference in the modes' longitudinal wave numbers
will be bounded by the axis A>mn = 0 and the line Amn = W(C2 - C1)/(C1C2). The
behavior of the lines Lt'~mn =Ahmn(w) is such that as the frequency increases, the
values of ANtnn(w) diminish for a given pair m, n/3 The distribution of the
values of B(u,(Al) on the plane u,W is determined by the amplitudes of the excitation
oL thc modes Pm(w,z,zo)Pn((l),z,zo), which depend on the horizons of the emission and
reception points.
For a waveguide witfi a deepened cl~annel axis witii a profile
C(z) _(1/CD - qz)-1/2 for z> 0; C(z) _(1/C~ + q'z) at z 0,
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in the VKB /expansion unknown/ approximatiun / 37 we have:
Akm (w) = CO{[1 'uCm -u'1/2) 2/3 1/2 _ 1- 2uC~(n W1/2)2/3]1/2},
where
u = 2O [Z~r/(q + q~)]2/3.
~ 6P0 wM ~1p0 ~8~ri,~
0

a
ie
1.
tk~~
Figure 1.
these prufiles were obtained by the
to the two-layer waveguide, curve 2
(2)
The area of existence of differences in
the modes' wave numbers lies beneath the
straight line jemn(w) _ wpC/CQ, where AC =
= the maximum difference in the speeds of
sound in the distribution C(z) for the
link. From (2) it follows that the inter-
ference frequencies A.mn(w) tor fixed m, n
increase as the frequency does. Let us
examine the results of a modeled experi-
ment. Figure 1 shows the profiles of the
speed of sound in an experimental bath;
method described in /4 Curve 1 corresponds
to the waveguide with a deepened axis.
The working range of frequencies in the experiment was chosen to be 300-720 kHz
(A = 4.2-2.1 mm). Figure 2/not reproduced/ shows the hologram recordings for the
two waveguides / 5/. In a two-layer medium, the hologram recording was made for
movement of the receiver away from the emitter (r = 0.3 cm) to distances of up to
r= 500 cm 0ti1.2�1(13�A max)3 With horizons z= zo = 1 cm (2�4�amax)� rigure 3/not
repr.oduced/ gives the results of secondary processing of the hologram by a method
presented in /6 / for the distances: a. 0.3-165 cm, b. 165-300 cm, c. 330-495 cm
- witti averaging with respect to distance at 165 cm 0,390�Xmax)� In Figure 3b, the
boundary of the existence of B(u,w) is clearly visible: the line Ax = Aw, where
coeff?cient A, determined experimentally, equais 9..5�10-7 cm/s-1, wh-ich coincides
with the calculated value of 6 (9.3�10-~ cm/s- The experimental determination
of coefficient A makes it possible to determine the speed of sound in the under-
lying layer (CZ) if C1 is known. The structure of the lines u= Axmn(w), which
correspond to the extreme values of B(u,w)--as is obvious from Figure 3--corres-
pond to the tiieoretical structure as far as the nature of its dependence on ar is
concerned / 37, The number of the interfering modes is determined experimentally
according to the maximum value Ax mn =[1+e1M, On the lower frequency of 360 kHz,
Ax1M � 1�93 cm -1 (AiM = 3.3 cm), M= 18. Calculating M according to C(z) gives
the same value. The distance between adjacent modes along the u axis is on the
order of ti0.1 cm 1(at a frequency of ti400 k}lz). The areas of the greatest values
of B(u,w) on the plane u,w are localized in accordance with the distribution of the
amplitudes of excitation of the modes (Pm(w,z,z0)Pn(w,z,z0) and their location
does not depend on r.
In the channel with the deepened axis, the hologram recording was made at distances
of up to 330 cm. The source's horizon and the receiver's trace were the same: z=
z0 = 8 cm (til9'AmaY)� Figures 4a and 4b /not reproduced/ show the sliding spec-
trum of the hologram of I3(u,(x)) for the following distances: a. 0.3-165 cm, b.
165-330 cm with averaging at 165 cm. A large number of interference bands are seen
in the spectrum of R(u,b)) and Aac increases as the emission frequency does.
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BIBLIOGRAPHY
l. Orlov, Ye.F., "The generalized Hologram Method in Acoustical Investigations of
the Ocean," this collection.
2. Brekhovskikh, L.M., "Volny v sloistykh sredakh" /Waves in Layered Mediums/,
Moscow, Izdatel'stvo "Nauka", 1967.
3. Tolstoy, I., and Kley, K.S., "Akustika okeana" /Ocean Acoustics/, Moscow, Izda-
tel'stvo "Mir", 1969.
4. Barkhatov, A.N., "Modelirovaniye rasprostraneniya zvuka v more" /Modeling the
Propagation of Sound in the Sea/, Leningrad, Gidrometeorologicheskoye izdatel'-
stvo, 1968.
,
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MULTIDIMENSIONAL MODCLING 1N STATISTICAL HYDROACOUSTICS
[Article by V. V. 01'shevskiy pn 61-64]
/Text/ 1. The special Leatures of the nathernatical modeling of acoustico-
oceanographic problems /1-4/ lead to the necessity of carrying out multidimensional
modeling of random variables, the functions of vector arguments, the vector func-
tions of scalar arguments and, finally, the vector functions of vector arguments.
However, even when the most productive computers are used, direct multidimensional
modeling entails practically unsurmountable difficulties. It is sufficient to say
that the sampling data volume Nn needed for the direct, combined modeling of n ran-
dom variables, when each of them is represented by m values, is determined by tlie
rela' ionship
Nn = mn. (1)
In time these difficulties gained the name of "the curse of dimensionality," and
=or a long time now researchers have been asking the following question: how can
the sampling data volume be reduced without discarding the e;sential regularities
(statistical connections) among the random variables being modeled? The contradic-
tion posed by these two tendencies (reducing the sampling data volume and losing
statistical regularities) is obvious; nevertheless, simplified multidimensional
models are now being introduced. In this article we propose one such simplified
= multidimensional. mociel that is based on the assignment of a full set of two-
dimensional distribtitions ot random variables.
2. The "Mixing" of Random Variables. Let y�, j= 1,M, be random variables for
which the unidimensional probability densities W(Yj), j= 1,M are given. Let us
form a new random variable
z = mix(yj,rj), j = 1,M, (2)
where "mix" is the "mixing" operator of the original random variables in pr.opor-
tions of r�. According to (2), "mixing" essentially means the formation of a new
ratidom variable z from the set yj, j= 1,M, it being the case that the sample ZR
x
consists of R= j E 1 rj values of the original variables yj, each of which is
- -
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represented in Zg by rj values. It can be shown that
w(z) = R JM1rjW(Yj). (3)
- 3. Evaluating the Two-Dimensional Distributions. Let us discuss the sample
xN = (xl,...,xn)N (4)
where n= a dimensional random variable consisting of N values. We will be inter-
ested in the two-dimensional joint probability densities
W(Xk,XQ); k> k; R,,k = l,n, (5)
or, which is equivalent, the unidimensional unconditional and two-dimensional con-
ditional probability densities
ca(xk>, w(xk/xk); k>t, k,u = l,n. (6)
These densities W(Xk,XQ), W(Xk) and W(XR/Xk), k> Q, Q,k = l,n, can be evaluated
with the help of polygrams / 5/ that minimize the error of the statistical evalua-
tions for any sampling volume N.
Thus, about the n-dimensional random variable (4) we know only the pair statistical
relationships of the type of (5) or (6) and according to these relationships, by
solving the following problem we attempt to achieve the most likely model of the
entire set of random variables. It is clear that such a description is incomplete;
however, it is related to a significant economy of all the statistical procedures.
4. Modeling a Multidimensional Random Variable With the Help of Two-Dimensional
Distributions. As soon as the distributions of type (5) and (6) are given for n-
dimensional variable (4), it is necessary to organize the modeling procedure on the
basis of the assignment of the two-dimensional probability distributions. As a ba-
sis for the modeling, let us examine conditional probability densities (6). In
this case, the modeling procedure takes form as the following sequence:
random variable xl is modeled in accordance with W(XI);
variable x2 is modeled in accordance with the conditional [d(X2/Xl) and uni-
dimensional W(X2) ciistributions;
variable x:; is modeled in accordance with the conditional iJ(X3/X1), W(X3/X2) and
unidimensional W(X3) distributions and so on.
Thus, in the gencral case the random variable x i.s modeled in accordance with the
distributions
WXR), W(XQ/Xk); k= 1,Q-1; Q='L,n. (7)
And now for the essential part of the modeling procedure: its algorithm. Under
the conditions that have been formulated, the choice of the multidimensional madel-
ing algorithm is not an unambiguous problem. However, it is possible to suggest
several heuristic procedures, one of which is being discussed here. This is the
"mixing" of random variables (see Section 2), in connection with which--according
to (2) and (3)--the resulting probability distribution equals the sum of the densi-
ties (with the appropriate weighting factors). Taking (7) into consideration, for
the probability density WM(XQ/X1,...,XQ_1) of the modeled random value xk, we have:
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[dM(Xy,/X1,...,Xp,-1) - Q 1 1 ~E1W(XQ/Xk). ~8)
k=1
It is not difficult to show that, according to (8) and (9), the unconditional prob-
ability distribution
WM(XQ) = t l
.f wM(xQ/x1,...,X2_ )W(X ,...,X _ ),ndxi (9)
W 1 1 Q 1 1=1
equals WM(XR) = W(XR). (lo)
Modeling algorithm (8) corresponds to the "mixing" that is being discussed and is
formulated on the basis of statistical evaluations of the probability densities of,
for example, the conditional two-dimensional polygrams.
Let us mention here tliat for the modeling of n random variable with the help of
two-climensional distributions on the condition that each of them is realized by m
values, the sampling data volume N2 will be
n(n - 1) z
N2= 2 M.
(11)
From a comparison of the values of N2 with the case of Lull n-dimensional modeling
(1), for n= 10 and m= 10 there is a vast savings (about 5 orders of magnitude) in
the amount of sample values of the random variables during multidimensional model.-
ing with the help of two-dimensional probability distributions.
BIBLIOGRAPHY
1. 01`shevskiy, V.V., "Simulation Experiments in Statistical Hydroacoustics: Se-
lecting Models and Testing Their Adequacy for Real Phenomena," in "Akusticheski-
ye metody issledovaniya okeana" /Acoustic Methods of Investigating the Ocean/,
Leningrad, Izdatel'stvo "Sudostroyeniye", tto 255, 1977.
2. Grubnik, N.A., and 01'shevskiy, V.V., "An Acoustic Model of the Ocean," in
_ "Trudy Pervogo seminara 'Akusticheskiye stat'istichekiye modeli okeana /WorkS
of the rirst Seminar on "Acoustic Statistical Models of the Ocean"/, Moscow, In-
stitute of Acoustics, USSR Academy of Sciences, 1977.
3. 01'shevskiy, V.V., "Models and Simulation Computer Experiments in Statistical
Hydroacoustics," in "Trudy Pervogo seminara 'Akusticheskiye statisticheskiye mo-
deli okeana Moscow, Institute of Acoustics, USSR Academy of Sciences, 1977.
- 4. Middleton, ll., and 01'shevskiy, V.V., "Contemporary Problems in the Construction
of Acoustical Statistical Models of the Ocean," in "Trudy Pervogo seminara
'Akusticheskiye statisticheskiye modeli okeana Moscow, Institute of Acoustics,
USSR Academy of Sciences, 1977.
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SPATIAL COVARIATION FUNCTION OF A SONIC FIELD
[Article by V. M. Kudryashov pp 64-67]
/Text/ The spatial correlation function of tlle stochastic par.t of a sonic field
for observation points moving along a line in the azimuthal plane has already been
calculated / 17. A new variant of the program is suitable for the case where the
line along which ttie observation points are moving is located along the z axis;
that is, along the cross-section of a waveguide. The program is written in FORTRAN
for a BESM-6 high-speed computer. The subject of discussion here is a sonic field
in a waveguide (s(r) z; H, p< r< r ={x,y}) filled with a liquid medium,
the speed of sound C in which depends on the depth z, since the density is constant.
The waveguide's upper boundary is acoustically soft or is a solid plate with ir-
regular surfaces (the latter variant will not be discussed here). Let us assume
that the ir.regularities in the boundary are distributed according to the normal law
and are statistically uniform, isotropic and sloping, it being the case that
ound source is a point source emitting a harmonic wave of frequency f. The sound
source's coordinates are r= O,z = zo, Let us represent the sonic potenti.al in the
�orm 'k'(r,z1exp(-i2Trtt), where t= time. Let us look for a solution of the
Helmholtz equation Lor l!'(r,z) that satisfies the boundary conditions, the condition
an the sound source and the principle of extinguishabi.lity at infinity. Let us
represent the coherent field in the form of a superposition of normal waves:
1u
mF; _ (pm(z).
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' For the corresponding normalization of the eigenfunction om(z),
= i7rOm(z0)H0(1)(Cmr),
where {m = eigenvalue for the m-th normal wave of the coherent sonic field.
The complete field can be expanded with respect to the coherent field's eigen-
functions and we obtain:
Y(r,z) = E A (r)cD (z).
- m=1 m m
(2)
The sonic field's normalized covariation function K is determined by the relation-
ship
K(r,Ar,l1z) _ // 2.
.N
i
Thus, the proposed amplitudinal weighting
technique makes it possible to control the
~
gositions of zeroes in the DN's of antenna
�w
arrays with digital signal processing. In
connection with this, there is precise es-
`_32
i
tablishment of the establishment of DN ze-
'
roes in a given direction for any phase
~ �
discreteness values, although the level of
~
~
the DN's side lobes increases substantial-
~ i 1'64
ly as A~ does. Amplitudinal quantization
~
of the input signals has a more substan-
tial effect on the positions of DN zeroes.
io :o so +o to 60 ~
J-7c;
The precise establishment of a DN's zero
Figure 2.
in a given direction is possible for L>
> 32.
BIBLIOGRAPHY
1. Wang, H.S.C., J. ACOUST. SOC. AMER., Vol 57, No 5, 1975, pp 1076-1084.
2. Baturitskiy, M.A., Danilevskiy, L.N., Domanov, Yu.A., and Korobko, O.V., RADIO-
TEKHNIKA I ELEKTRONIKA, No 2, 1978.
~
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CONCENTRATION FACTOR OF A HORIZONTAL, LINEAR ANTENNA DURING MULTIBEAM PROPAGATION
OF' A NOISE SIGNAL IN THE SEA
[Article by V. I. Bardyshe v and V. A. Yeliseyemin pp 86-88]
/Text/ It is a well-known fact that the phenomenon of multibeamness leads to a de-
crease in the spatial cerrelation of a noise signal propagating in the sea 14hen
_ there is longitudinal (in the direction toward the source) dispersion of the hydro-
_ phones that pick it up. tJhen working with a horizontal antenna, this results in
t}ie expansion of its radiation pattern and the reduction of the concentration fac-
tor. Below we present the results of calculations of the effect of the propagation
conditions, which are described in /1,2/, on the value of the concentration factor
of a horizontal, linear antenna.
A noise signal at audio frequencies, with a relative band width of about 12 percent,
was propagated in the sea, under conditions of strongly developed multibeamness, at
a distance of up to 29 km. The signal emission and reception points were located
close to the underwater sound channel's axis. Signal fluctuation was insignificant,
the signal-to-noise ratio was high, and the basic effect on the correlation of the
reccived signal was exerted by its multibeam nature. The low coefficient of beata
reflection from the muddy bottom and the presence of a well-developed thermocline
res�lted i.n severe attenuation of the bottom and surface reflections and the forma-
tion of a sonic field that was basically composed of refracted "water" beams con-
centrate,l along the underwater sound channel's axis. Transverse (relative to the
direction to the emitter) dispersal of the hydrophones in the horizontal plane had
no effect on the cross-correlation of the recei.ved signals. For longitudinal dis-
persal l1L (along the direction to the emitter) of the hydrophones, the value of the
maximum of the spatiotemporal cross-correlation factor Rm was reduced because of
the distribution of the signal's energy relative to several correlation maximums
corresponding to cross-correlation of signals arriving along different beams with
differing propagation times. At distances of 20-29 km, F. (AL) was described quite
well by the empirical formula
Rm(L1L) _ ti 0.3 + 0.7 exp -0.06(AL/a - 8) OL/a > 8, , Ol./a < 8,
where a, = the wavelength corresponding to the noise signal's central frequency.
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The subject of discussion was a horizontal, linear, discrete, equidistant antenna
consisting of N point, nondirectional hydrophones placed at intervals d= a/2, -
where a= length of the audio wave. The antenna's radiation pattern was rotated in
the horizontal plane, through angle a, by a compensator that realized the time lag
in the channel of each i-th hydrophone according to the law Ti =(i - 1)(d/c)sin B,
where C= the speed of sound. With several simplifying assumptions, the signal's
correlation function at the antenna's output can be written in the form
N N *
BM = E E Rm(ALi.), (2)
i=1 ]=1 J ~
where the angular brackets designate temporal averaging; the asterisk a complexly
conjugated expression; u(t - T1) = signal at the output of the i-th hydrophone,
shifted by time Ti = T~ - Ti; T~ _(i - 1)(d/c)sin a= time lag of the front of the
- caave in the channel of the i-th hydrophone, which is rotated toward the antenna at
angle a; t= current time; T= lag time.
_ Assuming the emitted noise signal's spectrum to be constant in the frequency band
(w1,u+2) and equal to zero outside this band, by making the appropriate transforma-
tions it is possible to write the following expression for the antenna's radiation
pattern with respect to power:
N-1
D(a,R) = 2[N + 2 E(N - i)Rm(ALi~)cos VslP~P~I, (3),
N i=1
where V= 2ni(d/a)(sin a- sin R), P= Aw/wo , c~~ _(w2 - wl)/2, Aw = w2 - wl.
The antenna's concentration factor k was defined in terms of its radiation pattern
by the well-known formula
Tr/2
k = 2[f D(a,a)cos ada]-1. (4)
-IT/2
During reception of a noise signal, along with the main lobe the antenna's radia-
tion pattern has an "aureole" that reduces the antenna's concentration factor.
Discorrelation of the audio signal leads to an additional reduction in the concen-
tration factor.
s i The figure depicts the results of calcula-
RO :~:~:`:-~i:--�---� 1
tions of the dependence of k/n on the com-
~ pensation angle S during reception of a
0,8- noise signal (p = 0.12) that is dis-
~ correlated with respect to space according
�\'Jto expression (1), Lir antennas with dif-
06 �4 ferent numbers of elements (curves 1, 2, 3
and 4 correspond to N= 20, 60, 100 and
120, respectively). For comparison, curve
~04 0 i0� so� m~ go�~ 5 shows the dependence of k/n on S for N=
_ = 100 and a tonal signal, while curve 6
does the same for a noise signal with p=
0.12 that is completely correlated throughout the antenna's entire aperture. It
can be seen that the reduction in the signal's spatial correiation caused by the
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FnR nFFI('IAI. [iSF nN1.Y
multibeam nature of the propagation leads to a 20-30 percent reduction in the con-
centration factor for compensation angles of 500-900 for an antenna with an aper-
ture of 50a.
BIBLIOGRAPHY
1. Bardyshev, V.I., Vasil'yev, N.A., and Gershman, S.G., "Investigation of the Co-
herency of a Continuous Audio Signal in the Sea," AKUSTICHESKIY ZHURNAL, No 3,
1970.
2. Bardyshev, V.I., and Gershman, S.G., "On the Horizontal Correlation of a Noise
Signal," in "Tezisy dokladov vos'moy Vsesoyuznoy Akustisheckoy konferentsii"
/Summaries of Reports Given at the Eighth All-Union Acoustics Conference/,
Moscow, 1973.
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PASSIVE AND ACTIVE INVERSE SYNTHESIS OF THE APERTURE IN DISPERSED SYSTEMS
[Article by V. V. Karavayev and V. V. Sazonov pp 88-901
/Text/ The research on active synthesis of an aperture that is available in the
literature is limited to the case where the locations of the receiver and the
transmitter coincide. For passive systems, the problem was solved in the first ap-
proximation according to the ratio of the system's base (the distance between the
positions) t'o the distance involved. Both of these problems were discussed in / 1/.
The second-order effects relative to the indicated ratio were taken into considera-
tion only in / 27, where only several special cases of the problem's geometry were
- examined.
In applied problems, on the other hand, a hydroacoustically observable moving ob-
. ject can turn out to be a:t distances comparable with the base of a dispersed system
_ (a.:tive or passive). Thio report is devoted to an analysis of this phenomenon,
- wtiich is a case that has :iot previously been discussed in the literature. We will
show that in the active case, two-position synthesis has a number of fundamental
special features in comparison with the traditional one-position variety.
The maximum resolution of systems is described by an ambiguity function. As was
shown in /1 it is given by the expression
I(~) = NII exp {i[O(t,0) - ~(t,_*)]}dtl2, ~1)
,
where N= normalizing multiplier, selected so that I(0) = 1; integration is carried
out with respect to observation time; 0(t,A) = phase of the received oscillation,
- which depends on the moment of observatian t(because of the movenent of the source
or base) and the 3isplacement of this source relative to some selected point 0. In
- active systems, O(t,4) must be understood as the phase of the reflected signal in
the receiver (we are not discussing eff ects related to modulation of the transmit-
ter, since they do not effect the synthesis process). In a passive system, however,
0(t,A) is the phase difference between the first and second receivers on which the
noise emissions of a random, delta-correlated source act.
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If we designate as R1 the radius vector of the indicated zero point that leads from
~
the transmitter (the first receiving position of a passive system), as R2 the radi-
- us vector of that same point that leads frorn the receiver (the second receiving
point in a passive system), as -L"(t) the vector from point 0 that describes the
source's motion, and as N the unit vector perpendicular to the plaae formed by vec-
tors k and h, in the Fresnel approximation for the source's movement relative to
point 0 we find
~(t,0) - ~(t,~) _ ~ L(t)M~,
where M= an operator that in dyad notation has the form
(2)
M= Ivl>-1-~-~ >-1-~
H= 2 j X N { I-[UP UN ] Rm mP U+ UP mRIIi [ I- N UP U] N Xdw, (7)
_00
>
where I= a unit matrix.
In the case of the reception of a signal from a single source (M = 1) on an antenna
consisting of nondirection receivers with unit sensitivity Zk(w,a) = 1 and a dis-
tance h between elements, from formula (7) we obtain
OD
H= 1 h cos a IX* (w)j l(k - p)exp [J4(k - p)sin a~1 I I[JwX~w)]dw~ (8)
2Tr ~ CLNO _co c
where L= total number of receivers in the antenna; k, p= 1,...,L. Analogously,
by computing the elements of G 1 we obtain
Aw h
= 2 ( ~ -cos a0 )29[8(L2 - 1)]~ (9)
00
where q= I Igw)I2w2dw/N~Awe = spectral signal-to-noise ratio; Owe = energy band
-m
of the signal. From (8) it follows that in order to construct a discriminating
goniometric system for a signal of unknown shape, we should set the antenna's radi-
ation pattern in the direction toward the source of the signal and organize cruss-
correlation processing between the signal at the k-th channel's outlet with the de-
rivative of the signal at the p-th channel's output. Compar.ing the obtained struc-
ture with that of a goniometer used for the processing of signals with known co-
variance, we see that in our case, at the outptit of the receiving channels there
are no filters that are matched with the signal's energy band.
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BIBLIOGRAPHY
1. Schweppe, F.C., IEEE TRANS. INF THEORY, IT-14, 1968, p 3.
2. Agr.snovslciy, K.Yu., Vyboldin, Yu.K., and Reshetov, L.A., "Vtoraya Dal'nevostoch-
naya akusticheskaya konferentsiya 'Chelovek i okean /Second Far Eastern
Acoustics Conference on "Man and the Ocean"/, Vladivostok, 1978.
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HOLOGRAPHIC METHODS FOR SPECTRAL ANALYSIS OF RANDOM SONIC FIELDS
[Article by B. I. Mel'treger and Ye. I. Kheyfets pp 97-991
_ /Text/ In order to carry out spectral analysis with the help of holographic meth-
ods, information about a sonic field is represented in the form of changes in opti-
cal thickness or transparency in a hologram. When it is reproduced in coherent
light in the rear focal plane of the lens, which is set behind the hologram, there
appears a light pattern, the analysis of which makes it possible to evaluate the
spectral characteristics of the sonic field. The methods of greatest inkerest ar.e
those in which the hologram represents an instantanenus samplinp2 of the field /1,27
or temporal changes in the field at the receiving aperture /2,3/. In the first
case, the hologram's carrier is a multichannel light modulator controlled by sig-
nals from'a receiving array. When there is weak modulation of the light field, in-
ertial registration of the distribution of the light's intensity in the Four.ier
plane (u,w) of the lens makes it possible to evaluate yl of the projection C(a) of
}
the field's angular spectrum C(Q) for a narrow band of temporal frequencies and to
evaluate y2 of the temporal spectrum for a narrow angular spectrum concentrated
near Y=(1,n) 0 0, where I = unit vector of the wave vector, n= normal to the re--
ceiving array, a= sin Y. In the second method signals are recorded in the form of
parallel tracks on the hologram carrier (photographic film, for example) that is
- moved along the direction of the tracks during reproduction. Inertial registration
of :he light's intensity I(p,~) makes it possible to evaluate y3 of the projection
F(w,cx) of the spectral-angular density of the field's dispersion F(wj), where p
and ~ are polar coordinates in the (u,w) plane. Besides this, analysis of the
light pattern makes it possible to evaluate Y4 of the projection C(a) of the
field's angular spectrum C(1) = F(wj)dw.
In order to ascertain the quality of these evaluations, assuming that the random
sonic field is a steady-state one and subject to the normal distribution law, ex-
pres:sions have been derived for the statistical moments of the first and second or-
ders. IL the field is created by noncorrelated sources located in the receiving
aperture's far zone, the average (for realizations of the field) light intensity in
the reproduced picture is composed of three parts, one of which is caused by the
,
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optical carrier alone, while the other two, which are symmetrical relative to point
u= 0, w= 0, represent the field's spectrum. Calculations and experimental inves-
tigations have shown that tiie evaluations that are obtained can be regarded as
asymptotical.ly unskewed, for all practical purposes. An analysis of the expres-
sions describing the relative dispersion of the fluctuations in the evaluations of
yq, q= 1,...,4, shows that for all the evaluations under discussion the following
relationship is fulfilled: ( -2)/TL-"--r 0, where T is the registration
time and L is the aperture size of the receiving array; that is, the evaluations
are valid. Thus, holographic methods are an effective means for the parallel spec-
tral analysis of random sonic fields.
BIBLIOGRAPHY
1. Shenderov, Ye.L., "Formation of Sonic Images in a Phase Holographic SYstem," in
"Radio- i akusticheskaya golografiya" /Radio- and Acoustic Holography/,
Leningrad, Izdatel'stvo "Nauka", 1976.
2. Svet, V.D., "Metody akusticheskoy golografii" /Methods of Acoustic Holographi/,
Leningrad, Izdatel'stvo "Rumb", 1976.
3. Penn, V.A., and Chovan, V.L., "Utilization of Holographic Methods in Hydro-
location," in "Akusticheskaya golografiya" /Acoustic HolographY/, Leningrad, Iz-
datel'stvo "Sudostroyeniye", 1975.
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ON THE EFFECT OF LARGE-SCALE NONUNIFORMITIES IN THE REFRACTIVE INDEX ON SHIFTS IN
- EVALUATIONS OF OPTIMUM GONIOMETRIC SYSTEMS
[Article by M. I. Levin, L. A. Reshetov and G. Kh. Takidi PP 99-1001
/Text/ In this article, on the basis of the method of small perturbations we eval-.
uate the effect of solitary, spherical heterogeneities on the discrimination char-
acteristic of a maximally probable goniometer, assuming that the emitted field is a
steady-state one and Gaussian in nature.
An optimum goniometer must form the following statistic / 1/:
N NTaK (t t )
E EII nkaal 2 xnWxk(t)dtldt2
" n k 0 (1)
a= N N T ~Knk(tl)t2) 2 ~
E EII [ 9a - ] dtldt2
n k0
where xn(t) = output signal of the n-th receiver; Knk(tl,t2) = cross-correlation of
the signals from the outputs of the n-th and k-th receivers.
Let a plane wave Po = Aoe- i(wt-kx) fall on a spherical heterogeneity with radius ro.
Let us assume that u=(Oc/co) � no = 1, where n0 and U are the refractive index in
the medium and the increase in the index at the limits of the extent of the hetero-
geneity; (kr0/r) � 1, where z= distance from a point inside the heterogeneity to
the observation point; 8�(1/kro), where d= angle between the x-axis and the di-
rection from the center of the heterogeneity to the observation point.
Then, using the method of small perturbations, we obtain the following expression
for the pressure in the far zone:
P = A0 e -i(wt-kx) [1 - 4,(k,6)e ik(R-x) (2)
where R= distance from the heterogeneity's center to the observation point,
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x = R cos 6 and
4k2ur0
~(k,d) = 3R ,
Let the incident wave have the form Po _~(cot - x), where ~(t) = a stationary
Gaussian procpss with a zero average, with an amplitude spectrum A(w) and a power
spectrum S(w):
S~, wl < w < w2
S(w) _ '
0, w < wl) w > W2 ,
For a narrow-band process, the computation of the cross-correlation function at
points with coordinates X1, R sin 8+ h/2, 0, where R� h, by integrating with re-
spect to frequency the product of the expressions of the type of (2), with due con-
_ sideration for the equality XBi and Xi = 0 for xAi < xgi. Let us
- designate pi = P{Xi = 1} and discuss the protatem of testing hypothesis H:p > 1/2
(methods A and B are equivalent) relative to the alternative K:pi > 1/2 for all i
(method A is better than method B).
The problem of testing these hypotheses remains invariant relative to the group of
n permutations of the values X1,...,Xn, and the MI relative to this group is the
n
function X= E Xi. There exists / 1/ an RNMI rule for testing these hypotheses
i=1 n
that rejects H if E X~ > C, where C is the threshold determined according to the
i=1 "
given significance level . At the same time, lemma 2/1, Chapter 8/ is applicable
to this problem. It shows that condition (9) is correct for our RNMI rule and that
it has a desirable maximin property (max inf Ep�(x)) in the class of all invariant
QK
rules.
Let us mention here that the problem of constructing a rule for determining the co-
ordinates of an object, which was solved in /8 was also reduced to testing hy-
potheses analogous to those written above, so that the rule for testing these hy-
potheses (formula (1) and (2) in / 8/) is also a maximin RNMI.
7. Conclusion. The suggestions that have been made about combining the principles
of invariance and nondisplaceability with other synthesis methods in order to solve
h,ydrolocation signal parameter classification and evaluation problems are feasible,
since their realization makes it possible to obtain solution schemes with addition-
- al desirable properties that make them even more desirable and effective when work-
ing under real conditions. Let us mention that combining the invariance and mini-
max principles sometimes results in optimization of the solving rules even if there
is nonparametric prior indeterminacy. For example, it is possible to construct
uniformly maximin most powerful rules for classifying and evaluating signal parame-
ters. However, the main uses of the minimax principle (or its inverse form--maxi-
min) will be found in problems with parametric prior indeterminacy.
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BIBLIOGRAPHY
1. Leman, E., "Proverka statisticheskikh gipotez" /Texting Statistical Hypotheses/,
Moscow, Izdatel'stvo "Nauka", 1964.
2. Linnik, Yu.V., "Statisticheskiye zadachi s meshayushchimi parametrami" /Statis-
tical Problems With Interfering Parameters/, Moscow, Izdatel'stvo "Nauka", 1966.
3. Zaks, Sh., "Teoriya statisticheskikh vyvodov" /Theory of Statistical Conclu-
sions/, Moscow, Izdatel'stvo "Mir", 19-115.
4. Prolcof'yev, V.N., "Using the Invariance Principle in the Sequential Detection
and Discrimination af Signals," RADIOTEKHNIKA I ELEKTRONIKA, No 5, 1975, pp
1027-1033.
- 5. Kendall, M., and St'yuart, A., "Statisticheskiye vyvody i svyazi" /Statistical
Conclusions and Connections/, Moscow, Izdatel'stvo "Nauka", 1973.
6. Prokof'yev, V.N., "Invariant Signal Detection Rules Based on the Maximum Proba-
bility Statistic," RADIOTEKHNIKA I ELEKTRONIKA, No 12, 1975, pp 2459-2466.
7. Sidorov, Yu.Ye., "The Principles of Nondisplaceability and Similarity in Prob-
lems of Classifying and Evaluating Parameters With Prior Indeterminacy," in
"Trudy Devyatoy Vsesoyuznoy shkoly-seminara po statisticheskoy gidroakustike"
/Works of the Ninth All-Union School-Seminar on Statistical Hydroacoustics/,
Novosibirsk, Institute of Mathematics, Siberian Department, USSR Academy of
Sciences, 1978.
8. Sidorov, Yu.Ye., "An Invariant Rule for Determining the Coordinates of Targets,"
RADIOTEKHNIKA I ELEKTRONIKA, No 8, 1476, pp 1759-1762.
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BASIC CONCEPTS OF THE STABILITY OF STATISTICAL PROCEDURES
[Article by F. P. Tarasenko and V. P. Shulenin pp 114-119]
/Text/ l. Introduction
The successful utilization of statistical procedures in hydrolocation problems is
made difficult by the lack of an adequate statistical model of the processes being
- observed. We will use the term "statistical model" to mean some set of assumptions
i relative tio the joint distribution of the sampling observations. The classical
methads that were developed within the framework of parametric statistics, proved
to be very sensitive to deviations from an adopted model /1,2/. For the solution
of practical problems, only in rare cases is a parametri.c model adequate and, be-
cause of their great sensitivity to deviations from a model, the classical methods
tuxn out to be not very effective. Searches for other methods that would be suffi-
ciently effective with less limited models or less sensitive to deviations from the
model, led to the development of nonparametric_procedures /3,4/ and stable statis-
tical procedures /1,2,5/. Bickel and Lehman / 67 present a useful classification
of statistical models. Different authors interpret the term "stable" (robust) dif-
ferently. Perhaps the most cousnon and, at the same time, diffuse definition is
given by (Kendall) and (St'yuart) / 77: "A statistical procedure that is in-
sensitive to deviations from the assumptions on which it is based is called sta-
ble." This definition can be given more concretely.if the type of statistical pro-
cedure is indicated, the possible deviations from the model are defined more pre-
cisely, and a definite meaning is given to the term "insensitive." Thus, when dis-
cussing stable procedures it is necessary to answer the following questions (see
_ Bickel / 8
1. Stability of what? It is necessary to define precisely the type of statistical
procedure.
2. Stability in relation to what? In order to answer this question it is necessary
to characterize the ideal statistical model and introduce some supermodel that in-
cludes the possible deviations from the ideal model.
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3. Stability in what sense? In order to answer this question the quality criteria
that are used and the goal we hope to achieve should be defined specifically.
Generally speaking, the stability of statistical procedures can be defined in terms
of resistance to the most variegated violations of the statistical model's assump-
tions. Let us examine the most important deviations from a model. For a paramet-
ric model, the conditions of a specific experiment make it possible, to a great de-
gree, to guarantee assiimptions (1) and (2) and, therefore, deviations from the par-
ametric form of distribution are of the greatest practical interest. In such situ-
ations we will talk about resistance to a change in distribution, and henceforth our
basic attention will be devoted to this type of stability.
2. A Qualitative Approach to the Stability of Statistical Procedures
Let the sequence xl,.,,,xn of independent and identically distributed random varia-
bles with distribution function (FR) F(x) be given. Let T(xl,.,.,xn) = some sta-
tistic (this can be either an evaluation of a parameter or a criterion statistic).
_ The qualitative approach to the stability of T(xL,,,,,Xn) relative to a change in F
relies on the following intuitive requirement / 9/:
Quite small changes in F= L(x) must correspond to arbitrarily small changes in the
distribution law L(T(xl),,,,Xn)) of statistic T. This requirement can be formulated
more accurately as follows: for appropriately selected metrics d in the FR's space
S and an ideal model Fo S, let us define supermodel Sr in the form Sn =
_{F:d(Fo,F) n}, in connection with which it is required that for any e> 0 there
existed that d> 0 and no, such that for all n> n0,
d(Fo,F) < d d(LF0 (T),LF(T)) < E. (1)
As Hampel mentioned / 9/, requirement (1) is nonconstructive and therefore changes
to an asymptotically equivalent nonstochastic variant--the requirement of continui-
ty in the space of functionals of the FR. Let us mention here that many well-known
evaluations, including that of maximum probability, and many test statistics can be
consider.ed to be evaluations of the appropriate functionals /2,127. Let
T(xl,...)xn) = T(Fn(x)), where Fn(x) is an empirical FR, be an evaluation of the
functional T(F). It is then the case, as Hampel demonstrated /9 that (1) is
equivalent to the following requirement:
d(F1JF2) < d-). jT(F1) - T(F2) I` E, Sn E F1J 2� (2)
Condition (2) makes it possible, in the space of functionals T(F), to limit the pos-
sibilities of the selection of the functional appropriate for the given probleln for
the purpose of obtaining a stable (in the sense of (1)) evaluation T(F). Using the
concept of continuity and absolute continuity, in / 97 the author presents a whole
series of different definitions of qualirative stability.
3. A Quantitative Approach to Defining Stability
Let the statistic T(xl,.,,,xn) be given and the ideal model Fo E S and some super-
model Sn = U{F:d(Fp,F) < n} be defined. The quantitative approach to the sta-
FDe S
bility of statistical procedures reflects the goal that we wish to achieve with re-
spect to the criterion of the quality of statistic T. Of course, the goals can be
extremely variegated, which gives rise to a whole series of definitions /2,10/.
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Let us define the functional of the quality of statistic T for FR F in terms of
Q(T).
Definition 1. The real function T(F), which represents the FR's space in R1 and is
defined in the form '
I'T(F) = sup {QF(T),F e Sn} - inf {QF(T),F E Sn},
is called Q, or the stability of statistic T relative to the enlargement of S to Sn.
Definition 2. Statistic T1 is more stable than statistic T2 if for each F E Sn:
1'T1M rT2(F).
Definition 3. Statistic T is uniformly more s*_able in the class of statistics m if
1'T(F) ~ I'T, (F) for all F E Sn. and all T' E m.
Definition 4. Statistic T is absolutely stable if TT(F) = 0 for each F E Sn.
Let us now examine the given class of statistics T(Y';xl,...)xn), the specific
structure of which is determined by some function T E M and let us be interested in
achievi_ng the minimum of QF(T). The minimax approach then leads to the following
definition / 2
Definition 5. rT(F), defined in the form
- 1'T(F) = min max QF(T('~)xl,...,xn)),
`YEM FEsn
is called minimax Q, or the stability of statstic T in class m relative to the
supermodel Sn.
4. Characteristics of the Stability of Evaluations
Let it be necessary to evaluate some parameter 0, given in the form of a functional
T(F); FO,F E Sn. The choice of the appropriate functional is made on the basis of
the definitions of qualitative stability. We will look for the evaluation of the
parameter in the form T(Fn)_ For many known evaluations the following asymptotic
representation is correct / 2
_ T(Fn) = T(F) + I SZ(x;F,T)dFn(x) + OP(n 1/2(3)
where S2(x;F,T) is the effect function introduced by Hampel, which is defined in the
f orm
S2(x;F,T) = lim (T(Fx,e ) - T(F))/e,
e-0
where
FX)e(y) _ (1 - e)F(y) + ec(y - x), c(3.) _ {1:J , 0,0:3~ < 0}.
Effect function S2(x;F,T) is the most important local characteristic of the stabili-
ty of evaluaeion T and characterizes the effect of an individual observation on the
value of the evaluation. In connection with this, it is used intensively during
the study of the effect of "overshoots" and "malfunctions" on statistical proce-
dures. Besides this, from (3) it follows that T(T(Fn) - T(F))/6F(T) has an
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_ asymptotically standard normal distribution, with QF(T) = j St2~x;T,F)dF. For this
class of evaluations the natural quality criterion QFM is dispersion 6F(T), and
all the definitions in Paragraph 3 can be formulated by using QF(T). Some numeri-
cal characteristics of the stability of evaluations can be determined directly, in
terms of the effect function / 97:
1. Sensitivity of evaluations T to gross errors ("malfunctions") is defined in the
form yF(T) = sup ISt(x;F,T)I.
x
2. Sensitivity to grouping and rounding off is defined with the help of Lipshits's
constant aF(T) = sup {IP(x;F,T) - SZ(y;F,T)I/Ix - yl}.
x#y
The global characteristic of the stabi,.ity
it" (breakdown point), whicn characterizes
ideal model (in the sense of some distance
the evaluation still remains limited. Let
given with the help of Levi's metrics:
dL(FQ,F) = inf {E:F(x - E)
and
of an evaluation is the "stability lim-
the maximum possible deviation from the
, such as (Levi's)) at which the bias of
the deviation from the ideal model Fo be
- E< FD(x) < F(x + e) + e}
B(e) = sup {T(F):dL(FO)F) e}.
Stability limit ek is then defined in the form e* = sup {E:B(E) 6p. It
is then the case that nQ2(x) _(1 - e)a~ + eo21 For cto = 1, e= 0.1 and ctl = 3 we
have a2(x) = 1.8, while for Q1 = 5 we have aZ(x) = 3.4. Thus, the sampling mean's
dispersion increases rapidly as Q1 does and, moreover, it can even equal infinity
/5/.
In order to illustrate several of the concepts that have been introduced, let us
discuss the functional Ta(F), given inexplicitly in the f.orm
F-1(1-a) 1 - 2a
j F(2Ta(F) - x)dF(x) = 2 , 0~ a< 1/2.
F-l(a)
We will look for the evaluation of parameter 0 from (4) in the form Ta(F). It is
not difficult to satisfy ourselves that the evaluation (we will label it H/La) has
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the form
H/La = med {Mij,(i,j) E Sk+l,n-k}' k=[an],
where M1~ � �_(x(i) + x 1)/2� Sk+l n-k = the set of Pairs of indices (i~J) sucli tl;~t
~~r~ ,
k+ 1* i~ j` n- k; med means median. The characteristics of the H/La evalua-
tion are derived in /11/. .
The effect function of eval.uation H/La has the form
(1 - 2a)sgn x, Ixl > F-1(1 - a)
S2(x;F,H/La) = A(a,F)' 2F(x) - 1, Ixl < F-1(1 - a).
The sensitivity to gross errors is YF(H/La) _(1 - 2a)A(dF).
The sensitivity to grouping and rounding off if
aF(H/La) = 2A(a,F)�f(xm
1-a
where xm = the mode of the density f(x), A(a,F) = 1/2 ! f(F-1(t))dt.
a
Sensitivity limit e" of evaluation H/La is
fl- 1/2(2(1 - 4a2))1/21 a< 1/6,
e'` = 4-1(1 + 2a), a> 1/6.
_ For the purpose of comparison, the characteristics of
several evaluations for a
normal distribution are
presented in
the table
below.
Evaluation
v~
Y
a
E
~
~
x
1.000
co
1.00
0.00
med
1.571
1.25
co
0.50
H/L
1.047
1.77
1.41
0.29
H/L0 1
1.092
1.52
1.52
0.31
H/LD 2
1.170
1.40
1.86
0.35
Thus, the evaluations' characteristics are substantially different and the choice
of the appropriate evaluation must be determined by the goal we wish to achieve.
BIBLIOGRAPHY
1. Tukey, T.W., "A Survey of Sampling From Contaminated Distributions," in "Contri-
butions to Probability and Statistics," Stanford University Press, 1960, pp 448-
486.
2. Iiuber, P.J., "Robust Statistics: a Review," ANN. MATH. STAT., Vol 43, 1972, pp
1041-1067.
3. Fraser, D.A.S., "Nonparametric Methods in Statistics," W., N.V., 1957.
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4. Gayek, Ya., and Shidak, Z., "Teoriya rangovykh kriteriyev," /Theory of Rank
Criteria/, Izdatel'stvo "Nauka", 1971.
5. Yershov, A.L., "Stable Methods for Evaluating Parameters," AVTOMATIKA I TELE-
MEKHANIKA, No 8, 1978, pp 66-100.
6. Bickel, P.J., and Lehman, E.L., "Descriptive St.atistics for Nonparametric Mod-
els: I. Introduction," ANN. STAT., Vol 3, 1975; pp 1038-1044.
7. Kendall, M.Dzh., and St'yuart, A., "Statisticheskiye vyvody i svyazi" /Statis-
tical Conclusions and Connections/, Izdatel'stvo "Nauka", 1973.
8. Bickel, P.J., SCAND. J. STATIST. THEORY AND APPL., Vol 3, No 4, 1976, pp 145-
168.
9. Hampel, F.R., Ph.D dissertation, University of California (Berkeley), 1968.
10. Zielinski, R., BULL. DE L'ACADEMIE POLONAISE DES SCIENCES. SERIE DES SCIENCES
MATH., ASTR. ET PHYS., Vol 25, No 12, 1977, pp 1281-1286.
11. Shulenin, V.P., "On the Stabilit-I of the Hodges-Leman Class of Evaluations,"
in "VII Vsesoyuznaya konferentsiya po teorii kodirovaniya i peredachi informa-
tsii" /Seventh All-Union Conference on the Theory of Information Encoding and
Transmission/, Moscow-Vil'nyus, Part 6, 1978, pp 147-151.
12. Dmitriyev, Yu.G., Koshkin, G.M., Simakhin, V.A., Tarasenko, F.P., and Shulenin,
V.P., "Neparametricheskoe otsenivaniye funktsionalov po statsionarnym vyborkam"
/Nonparametric Evaluation of Functionals According to Fixed Samples/, Iz3atel'-
stvo Tomskogo universiteta, 1974.
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ADAPTIVE PROCESSING OF TWO-COMPONENT NOISE SIGNALS
[Article by V. P. Peshkov pp 119-121]
/Text/ Let us discuss the problem of detecting an additive mixture S(t) = S1(t) +
+ S2(t) of narrow-band S1(t) = A(t)cos [wpt +'Y(t)] and broad-band S2(t) Gaussian
signals against a background of Gaussian interference N(t) under conditions of pri-
or indeterminacy (the central frequency and band Ow of signal S1(t) are unknown, as
are the correlation functions KS2(t,t1) and KN(t,tl).
According to Yesults published in /1,27, the optimum receiver for a two-component
signal is a two-channel one.
The Broad-Band Channel. The adaptive detector of the signal's broad-band component
is realized on the basis of narrow-band spectral analysis (on the basis of a BPF
/expansion unknown/, for example) with subsequent weighted storage that allows for
the spectral properties of the signals and the interference / 2/. In connection
with this, detection is accomplished in two stages.
During the first stage, nonoptimum temporal processing with a preselector in the
form of an ideal band-pass filter takes place for the purpose of determining the
reFerence channels. In order to do this, the results of the processing in each
spatial channel are retained for several review cycles. The matrix of numbers
M= N x m that is obtained is used to determine the threshold by successive deter-
mination of the signal channels and the elimination of them from the procedure of
computing the threshold in the next iteration. The procedure is repeated until
newly segregated signal channels are not observed after a normal iteration.
In the second stage there is an evaluation ur the spectral densities gN(w) and
gSN(�'), the transmission factor / 27 is formed, and there is adaptive processing in
each spatial channel, using the iterative procedure for computing the thresholds.
The results of modeling showed that a given algorithm makes it possible, after sev-
eral iterations, to eliminate almost completely the effect of the signal channels
on the magnitude of the threshold, achieve a given false alarm probability, and de-
tect a signal with a higYi degree of reliability.
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Ttie Narrow-Band Channel. The above-mentioned iterative procedure for determining
the threshold can also be used in the channel ior the detection of narrow-band sig-
nals, in connection with which: spectral analysis of the input sample is performed
according to the BPF's algorithm; from the mass of numbers that is obtained, slid-
ing is used to form groups of numbers (with 2Q + 1 numbers per group), in each of
which there is a minimum number; from the mass of numbers that is obtained, an
evaluation of the interference spectrum is formed by smoothing it with respect to
2p + 1 numbers; obeleniye /translation unknown/ of the input signal's spectrum is
carried out by dividing it by the obtained evaluation of the input spectrum; the
recurrent threshold computation procedure that was explained above is applied, with
- segregation and elimination of the signal channels, and the excesses above the
threshold are found.
The results of modeling of this algorithm showed that the error in evaluating the
spectral density of the signal's narrow-band component does not exceed 1 dB, even
in the most unfavorable situation, when there are also narrow-band components in
the neighboring frequency channels.
In order to accomplish adaptation with respect to the band, it is necessary to com-
bine all the adjacent elementary components that exceeded the threshold. An inves-
_ tigation of the algorithm that accomplishes the band adaptation showed that it is
_ necessary to introduce two thresholds into the system: one threshold is used to
evaluate the signal's band (gate), while the other, which provides a given false
alarm probability, finds the excesses inside the gate that are then combined by cu-
mulative or weighted storage. The determination of the gate can be by optimum or
cumulative storage of the results of spectral analysis for several cycles. The
medeling results showed that band adaptation increases resistance to interference
and eliminates ambiguity in determining the number of discrete signal components
during detection.
BIBLIOGRAPHY
1. Peshkov, V.P., "Band Optimization," in "Tezisy dokladov na Respublikanskoy
nauchno-tekhnicheskoy konferenksii 'Problemy peredachi informatsii provodnymi
kanalami svyazi"' /Summaries of Reports Given at the Republic Scientific and
Technical Conference on "Problems of Information Transmission Over Wire Communi-
_ cation Links"/, Kiev, 1975.
2. Krasnyy, L.G., and Peshkov, V.P., "Adaptive Detection of Noise Signals," in
"Trudy VIII Vsesoyuznoy shkoly-seminara po statisticheskoy gidroakustike" /Works
of the Eighth All-Union School-Seminar on Statistical Hydroacoustics/, Novo-
sibirsk, Institute of Mathematics, Siberian Department, USSR Academy of Sciences,
1977.
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EFFECT OF CONCENTRATED REFLECTORS ON THE EFFECTIVENESS OF HYDROACOUSTIC
INFORMATION PROCESSING
[Article by A. P. Trifonov and Yu. S. Radchenko pp 121-1231
/Text/ For a hydroacoustic information transmission channel, it is typical that
- - }
reception of the useful signal's field SD(t,x; o) takes place against a background
not only of fluctuation noises, but also of interfering signals reflected from the
bottom, the surface and intervening objects. Let us given the name "quasi-
determined interference" to the group of n interfer.ing signals {Sk(t,x;tk)
(k = l,n) with unknown parameters tk -{%kl-�,Zku} Et that are present in the ob-
served data with probabilities pk.
-
Into receiving aperture D over time [O,T], let there enter a mixture y(t,x) of the
useful signal's field SO(t,x;1a) (which depends on the vector of the parameters
QO -{QO1, QO }E t), the quasidetermined interference and Gaussian noise; the
signal at the output of the receiver's linear part then has the form
m(t) = I t y(t,x)B(t,x)dtdx = z2{a0S(k,R~,0) + E ZkSk(k,kk)} + zN(R), ~1)
0 D k=1 k

where B(t,x) defines the structure of the receiving system / 17; z = useful signal-
to-noise ratio; zk = ratio of the useful signal's amplitude to the amplitude of the
k-th interfering signal; {gi(tJi)} (i = O,n) = normalized signal functions (gener-
alized indeterminacy functions) of the useful and interfering signals / 2/. The
term ao equals either 0 or 1, with probability pk:ak = 1 and with probability
qk = 1 - Pk:ak = 0. .
Assuming that the receiving system is optimum only in the presence of a useful sig-
- nal and noise at the input, let us find its characteristics when it is affected by
quasidetermined interference. If the parameters of the useful and interfering sig-
nals are not known, one method for overcoming the prior indeterminacy is the
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maximum likelihood method
~
rithm has the form M(9..m) ~
of parameter Qo we will u
P1('A ) in area t. In order
(MMP). In accordance with the MMP, the detection algo-
= max M(R) ~ h, where h= the threshold. As an estimate
3e Qm, which is the location of t.he absolute maximum of
to calculate the characteristics of the maximum likeli-
hood receiver (PMP), it is necessary to know the distribution function of the abso-
~
lute maximums of the field M(Q) in area t. There is no precise solution to this
problem, so let us use an appr.oximate (asymptotically accurate) approximation of
this distribution function. The approximation can be written as
n
F(h) = P[max M(k) < h] = FN(h) TI Fk(h), (2)
k=0
where, according to / 27,
~~-1 2
exP +leXP 2 h >,~l
FN(h) _ (27r) 2 (3)
0, h < U - 1
and for high signal-to-noise ratios z, Fk(h) has the form
Here, pQ= 0, qo = 1 if ao = 0 and zo _
(2), (3) and (4), we used a method with
{tk} (k = O,n) in the vicinity of point
plementary to them. In the case where
wave fietds with a random phase,
Fk(h) = qk + pk(P(h - z/zk). (4)
1, po = 1, q0 = 0 if ao = 1. When deriving
division of the area into signal subareas
~
s{kk} and the noise subarea N that is sup-
SO(t,x;Qo) and {Sk(t,x;Rk)} are narrow-band
n
F(h) - FN(h) I[ {1 - pkQ(z/zk,h)}. (5)
k=0
In (5), Q(u,v) = a (Markum) function.
The probability a of a false a13rm and S of signal transmission into the PMP can be
written, using (2), (3) and (5), as
n
a= P[max M(~) > hla~ = 0] = 1- FN(h) II{1 - pkQ(z/zk,h)},
k=1
n
S= P[max M(1) < hlxo = 1] = FN(h) ]I {1 - pkQ(z/zk,h)}.
k=0
(6)
In (6), po = 1, zo = l. The results of the calculation of the characteristics of
detection of an object at an unknown range according to formulas (6) for n= 1, in
accordance with the criterion of an ideal observer, are presented in Figure 1. The
solid curves are calculated for an optimum threshold h, which was selected with due
consideration for the possible presence of interference. The broken curves are
calculated for the threshold h= z/2, which is asymptotically optimum when detect-
a signal against a backpround of noise.
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R
`
v,�~

~.rvo
~
R.o
P~�a
2
1~~ �2
P ~
!O+ .
roa
so' ~o
,
~i�I

.z
I I
0~~~ I�
!G~
(e 9 4 d 8 t0 I
Figure 1. Total probability of detec-
tion error.
i 3 s r 9 i
Figure 2. ProVisional scattering of
range estimate.
Let us characterize the reliability of the evaluation by probabilities p(k) _
= P[Qm E Lk] (k = O,n). Using (2), (3) and (5), p(k) can be written as
p~k) = j{FN(h) II Fi(h)}dFk(h) _
- -co i=0 (7)
co h2 + (z/z ) 2 n
FN(h)h exp 2 k ]I~(ZZ) n{1 - piQ(z/zi.h)}dh.
k i=0
If the accuracy of the evaluation is characterized by the scattering matrix (of the
second starting moments of the errors) V(t0) _, we obtain
V(ko) = E p ~k)~ak + Dk] +(1 - E p~k))VN(k0). (8)
k=0 k=0
Here, ak kk QD) +(Qk - k0Dk =(zk/z)2Sk1SOSk1, where Sk =
= II[a2Sk(Q~~k~~aQiaR~]RJ I, The systematic and fluctuatianal errors in the evalua-
tion are determined in the subareas {Lk}, while VN(Q O~ -(ItzOj + Lidij/l2ll = ma-
trix of anomalous errors related to taking a noise spike f or a signal. The results
of the calculation of the distance to an object, using formula (7) and (8) for n=
= 1, u= 2 are presented in Figure 2. Here, p= 12V/L2, A = Q1 - Ro. The signal
functions {Si(JC,JCi)} (i = 0,1) were assumed to be bell shaped and of unit duration.
Theoretical relationships (6), (7) and (8) are asymptotically precise for h� 1,
1, z� 1. In order to establish the limits of their applicability, the detec-
tion and evaluation algorithms (according to the MMP) were modeled on a computer.
The results are plotted in Figures 1 and 2.
BIBLIOGRAPHY
l. Gatkin, N.G., "Algorithms for the Optimum Spatiotemporal Processing of Random
Fields; in "Trudy IV Vsesoyuznoy shkoly-seminara po statisticheskoy gidro-
akustike" /Works of the Fourth All-Union School Seminar on Statistical Hydro-
acoustics/, Kiev, 1972.
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Kulikov, Ye.N., Radchenko, Yu.S., and Trifonov, A.P., "Characteristics of a
Maximum Likelihood Receiver in the Presence of Quasidetermined Interference,"
IZVESTIYA WZOV. RADIOELEKTRONIKA, Vol 9, 1978, pp 3-9.
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ON THE QUALITY OF SOME EVALUATIONS OF MAXIMUM LIKELIHOOD
[Article by V. V. Borodin pp 123-125]
/Text/ The maximum likelihood principle is frequently used in problems involving
the evaluation of random or unknown quantities.
It is frequently necessary to evaluate parameters on which the mean of the normal
distribution depends in a complex, nonlinear fashion. In this article we investi-
gate the quality of the maximum likelihood evaluation (OMP) in such a case.
Let there be a random vector quantity y={yl,y2,y3}, distributed according to the
normal law, with a unit covariance matrix and an average value y(x) that depends
functionally on the two-dimensional vector x, with
F(y~}) = eXP {-(i/2)IIy - y(x)IIZ . ~1)
x
~2-ff)3/2
Also, let:
1. the condition of separability be fulfilled for vector y(xthat is, y~xl) #
# y(x2) for all xl # x2 E D, where D= the area of change in vector x;
~
2. function y(x) be continuously and twice differentiable;
3. Gramme's matrix rij (X) _