SCIENTIFIC ABSTRACT KHALFIN, L.A. - KHALFINA. N.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000721710019-3
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 17, 2001
• Sequence Number: 19
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

3(0) Q(5) S011120
122
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14149
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AUTHOR: Khalfin, L. A.
TITLE: The Information Theory of the Interpretation of Geophyiocal
InveotiCations (Informatsionnaya tooriya interpretatsii
geofizicheskikh issledovaniy)
PERIODICAL: Doklady Akademii nauk SSSR, 1958, Vol 122, TIr t~,, PP 1007-1010
(US',R)
AMTRACT: The theory investigated by the Dresont pn-,,er differs from the
usual interpretation theory by the fact thzit it describos
the oeophysical investiCation methods as systems of "information
observa%ion". Besides the inform-aticn theory, also the classi.,
cal thtory of statistical entimation may serve as a basis
for investigations of the problems discussed. The probler.
of interpreting the data of the -eophysical method is known
to consist in determining the sources Q (information) of a
geophysical field 1Y,Q (i~) (signal) from this geophysicnl field.
For this purpose th~ followin- is obviously necessary: For
a given geopl)ysical field ?Q(r')o*iuch a characteristic of

S07/2o-122-6-14/49
The Information Theory of the Interpretation of Geopnysical Investigations
the sources of this field can be described as information Q
an is biuniquely (uniqu alto a a theoran) connected wl4th the t-eo-
rhyiscal field (signal (1): TQ('r) Q. in tiiis ca--e division
of the problems into direct and inverse problems 4,9 natural.
Interpretation may be either paletot-like (1,aletochnyy) or
analytic. In the case of neither of these two interpretation
methods is there a so-called geophysical interpretation, al-
LhouCh it is used in practice. This contradiction is due to
the fact that, if the usual method of the interpretation
theory is employed, the existeiice of obstacles (pomekha) is
neglected in the widest sense of the word. From the vcry out-
set, the author assumes that in the measured field (sit-nal) Y(r)
there exist 'a field (signal with a utilizable (polennyy)
Q-informatdofi and homogeneous obstacles n(r) with a disturb-
in-- information: +(-r*) 91 r) + n('r). 'I'lie term "obstacles"
is then discussed in de%il? Unfortunately, only some of the
characteristics of obstacle distribution are known. For a special
cast! stich a distribution p(n) is determined which warrants a
maximum quantity of n-information. '1,,. solvin'. the correspond-
ing variation Droblem an expression is obtainel for p(n).
CnTd--2714 Furthermore, an expression for the maximum quantity of informa-

SOV/20-122-6-14/49
The Infori;,.ation Yhoory of the Interpretation of Geophysical InveStigat ions
tion in T(r) is derived. Several principal variants are then
investigated: 1) That only normalization is known. 2) That
also the average number of obstacles is assumed to be known.
3) That also the dispersion with respect to the obstacles is
known. Also the complication of geophysical nethods is in-
cluded in the investigation of the information theory; next,
the interpretation of the physical properties of geological
objects is discussed. By means of the information theory
discussed in the present paper it is pos!3ible to compare
also various interpretation mothods hitherto employed with
one another. The principal result obtained by this paler is
the determination of an algorithm of' the information theory
of interpretation, which can bu realized b,,,- means of a com-
puter equipped with a memory. The results actually obtained
tire results of the general information theory of observation.
Tho nothor thnitka Profoanor Yu. V. Linnik uril Profoallor
A. S. Oemenov fortheir discusniono a9 well as for their use-
ful advice. There are 7 referenees. 4 of which are Soviet.
C -77-T
Ala-
V

SOV/49-59-4-1/20
AUTHORS:Khaykovich, I. M.,_&halfin, -L. A.
TITLE: On the Effective Dynamic Parameters of Heterogeneous Elastic
hiedia in whichPlane, Longitudinal Waves Propagate (0b
effektivnykh dinamicheakikh parametralch neoduorodnykli uprugikh
sred pri rasprostranenii ploskoy prodollnoy volny)
-PERIODICAL: Izvestiya Akademii nauk SSSR, Seriya geofiziches'aya, 1959,
Nr 4, PP 505-515 (USSR)
ABSTRACT: The effective parameters discussed by the authors are
illustrated in.Fig 1, where two components of the homogeneous
medium are denoted by 1 and 2 , and s - period of the
distribution of the uniform spherical particles which are sub-
jected, to the plane, monochromatic, longitudinal wave (p
propagated from the left-hand side. In these eircUM13tances
the wave becomes diffused, the rate of which del-)endson
the coordinate z. 9 It is assumed that the wavelength is
greater than the dimension of the spherical particles and that
every particle is in the state of a seismic di-polar vibration
in the direction of the axis z , Then the wave can be des-
cribed by the e prqsaion (1 1) where z) - polar
coordinates', (r'Ay" and H 5 - spherid al coordinates,
Card 1/4 b1 velocity of transverse waves, a 1 velocity of the
tg_" g
'TM~ N 1~
NN

SOV/49-59-4-1/20
On the Effective Dynamic Parameters of Heterogeneous Elastic Media
in which Plane, Longitudinal Waves Propagate
Ion itudinal waves, u - dislocation field expressed as
Eq R.2). The longitudinal and transverse potentials and
q) inside the sphere can be expressed as Eqs (1.3) and TI.4),
respectively. Thus the problem of diffusion of the longitud-
inal wave caused by the seismic di-poles can be solved when
the constants A , B. 5 At and BI for the limitirLg condit-
ions Eqs (1-5) and (1 6 are determined. This can be perfor-
med as shown in Eqs (1.7) and (1.15). In order to obtain the
integral of the longitudinal potential of the total dislocat-
ioni the value of u 0 for the point (xo Yo I z 0) is cal-
culated from Eq (2.1) and the relation uo ~(P /9z0is de-
fined as Eq (2.2). From this expression the integral equation
for the potential T is derived as Eq (2.3) which can be
written in the form Eq (2.6). The latter is solved by Eqs(2.8)
and (2.9). By substituting Eq (2.9) into (2.8), the velocity
of propagation of the longitudinal wave a in the 2-component
Card 2/4

SOV/49-59-4-1/20
On the Effective Dynamic Parameters of Heterogeneous Elastic Media
in which Plane, Longitudinal Waves Propagate
medium is obtained as Eqs (2.10) and (2.11). In order to de-
termine the effective parameters the reflected wave should be
derived from the second and third terms of the equation (2.6)
for negative values of zo . When Eq (2.9) is substituted
into these terms, the Eqs (2.14) and (2.15) are obtained, which
gives an accuracy of the order:
u2jk/a RI and v2jk/a R1 for a/al and D expressed by
Eqs (2.11) and (2.13). If f is sufficiently small and P
Q, , Q2 , M are limited, then the effective parameters can
be found from Eq (2.16). Thus the coefficient of the reflect-
ion for the plane,,longitudinal wave T at the boundary of two
media can be defined as Eqs (3-1) and (3.2) and the ratio
a/a as Eq (3-3). By equalising the equations (3.2) and (3.1)
witi application of the equation (3.3), a system of two equat-
ions is obtained, from which the effective dynamic parameters
(the effective velocity of the longitudinal wave and the
affective density of the 2-component medium) are obtained as
Eqs (3.4) and (3.5). These parameters may have complex mean-
Card 3/4 ings but the latter, in the case of homogeneous elastic media,
U
V

SOV/49-59-4-1/20
On the Effective Dynamic Parameters of Heterogeneous Elastic Media
in which Plane, Longitudinal Waves Propagate
are insignificant. Thanks are given to Professor G, I, Petra-
shen. There is 1 figure and there are 4 references, of which
3 are Soviet and 1 English~
ASSOCIATION: Vsesoyuznyy nauchno-issledovatel'skiy institut razved-
ochnoy geofiziki (All-Union Scientific Research Institute of
Survey Geophysics)
SUBMITTED: February 27, 1957.
Card 4/4

SOV/49-59-6-3/21
AUTHORS: Khaykovich, I. M., Khalfin, L.
TITLE: On the Effective ij;~aZ Parameters of an Elastic Medium
in the Propagation of a Plane, Transverse, Polarized Wave,
PERIODICAL: Izvestiya Akademii nauk SSSR, Seriya geofizicheskaya,
1959, Nr 6, PP 815-826 (USSR)
ABSTRACT: This work is a continuation of a similar one on the 'oro-
pagation of seismic waves published in this journal, 1959,
Nr 4, where the basic theoretical calculations were des-
cribed (Fig 1). The polarized wave is determined in the
present work by the potential, Eq (1.1), where _b I -
velocity of the transverse wave, j - ort in the direction
of the axis y . The following assumptions are made:
(1) The wavelength is much greater than the diameter of the
sphere and (2) the field, diffused by the sphere, is de:11-
cribed by the longitudinal (p and the transverse 0 pot-
entials, Eq (1.4). The potentials inside the sphere are
as shown by Eq (1.6). Thus the problem of diffusion is
confined to the determination of the constants A , B , A'
BI (Eqs 1.7 to 1.23). The formula expressing the field of
diffusion is defined in its final form as Eq (1.24). TAe
method of determining the effective dynamic parameters is
Card 1/3 based on the inte.gral equation of the transverse potential

SOV/49--59-6-3/21
On the Effective Dynamic Parameters of an Elastic Medium in the
Propagation of a Plane, Transverse, Polarized Wave
of the total field displacement, the solut'Lon of which can
be written as a potential-, of the plane, transverse. polar-
ized wave. The total displacement ux at the point
(X ) consists of the displacement of the wave.
o 9 Y09 ZO
Eq (2.1) and the displacement caused by the diffusion Lue.
to all spheres. This total displacement, in the direction
of the axis z depends on the coordinate z 0 and is re.-
lated to the potential (~ as shown in Ea (2.2). The dis-
placement along the axis x is defined ~y Eq (2,3). DIUS
the expression (2.4) is obtained, which can be written as
Eq.(2-5). The latter can be shown in tile simplified form
Eqs (2-7) and (2.8), when the assumption, Eq (2.6) is uade,
Now it is possible to determine (~ as it is shown in
on (2.18) can be dafiz.ed
Eqs (2 9) to (2.17). The conditi,
Card 2/3

SOV/49-59-6-3/21
Dn the Effective Dynamic Parameters of an Elastic Medium in the
Propagation of a Plane, Transverse, �1olarized Wave
in two ways: from the effective wave velocity or from the
effective density of the medium the determination of
which is shown in Eqs (3-1) to b.?). Thanks are given
to G. I. Petrashen' for taking part in the solution of
the problems described in the article. There is 1 figure
and there are 2 Soviet references.
ASSOCIATION: Vsesoyuznyy nauchno-issledovatellskiy institut
razvedochnoy geofiziki (All-Union Scientific Research
Institute of Geophysical Prospecting)
SUBMITTED: April 22, 195?.
Card 3/3

24(5) SOV/56- 36 -4-~;/70
AUTHOR: Khalfin, L. A,
TITLE: On New Dispersion Relations in the Quantum Field Theory
(0 novykh dispersionnykh sootnosheniyakh v kvantn-jzy teorli
polya)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki: 1959,..
Vol 36, Nr 4 PP 1088-1092 (USSR)
ABSTRACT: In the present paper two dispersion relations between the
module and the phase shift of the forward scattering
E(E) are derived. f(E) is here represented by means of the
iEt i-(E)
F, ~ ....
Fourier integral f(E) - F(t)e dt 5,r(EJ',3 fo~ '~ ,t) -~ I
~F(t) t ';~ t 0t jK- 0. f(E) M'.1st- 5a+isfy
holds that . k 1. 4to
0
the symmetry condition f(E) - f" (-,E), and on the barsis ~f the
"cptical" theorem it holds that Im f(E) tE); E c
Tit % ) -
where d(E) denotes the total scattering cross section ana
2 _ 2 2
k E - ~& ~ A&- rest mass of the particles. By procoeding
Card 1/2 herefrom relat~ions between log,,P(E) and w(E) are dsrived in the
j I

SOV/1:6-36-4-19/70
0
On New Dispersion Relations in the quantum Field Theory
following on the basis of the analyticity of f(E) in the upper
semiplane Im E >0 and of the criterion of physical realizability
by means of a method which is analogous to that employed in the
quantum decay theory. The expressions obtained, formulaB (8)
and (9), are very complicated* They are, however, contrary to
the usual relations between real and imaginary parts of forward
scattering amplitudes, independent of the detailed behavior
(degree of increase or decrease) of the forward scattering
amplitude at infinitely high energies E->oo. In connection
with the relations derived here, the problem concerning the
possible zerces of f(E) in the upper semiplane Im E > 0 is dis-
cussed. Within the range of analyticity, it holds for partixilea
with the rest mass e,,..= 0 that Im f(E) ~ 0, EF-[O,-! and fc,
particles with finite rest mass O_j-4_O, if the relation Jg(Ek)-g(Em)jL-AjE k - Eml I"
(where A >0) holds for any E k and Em from IEVoo). p