__1.
Development of the theory of geoelectrics.__

*The basic attention is
given to the solution and the analysis of electrodynamic
(EM) problems
in anisotropic and bianisotropic media by analytical
and numerical methods. Programs of calculation of electromagnetic fields in
such media are developed in horizontally and cylindrically layered models with
reference to requirements of
field geoelectrics and logging.*

__ __

__Anisotropic media.__ It has been developed
electrodynamics of EM fields in horizontally layered media with one-axis
electric and magnetic anisotropy. For electrodynamic
potentials generalized Lorenz conditions, are derived, a problem of definition
components of vector potentials and EM field are reduced to boundary problems
for tensor Green's functions. These functions are defined by two scalar
functions (of electric and magnetic types). Volume and surface integral Fredholm
equations for calculations of EM field in the layered anisotropic media,
including heterogeneity, are received. For convergence of integrals in the
surface integral equations the way of cancellation singularities tensor Green's
functions is offered. Development of a method of the surface integrated equations with reference to
anisotropic media allows to solve wide enough class of electrodynamic
problems at significant economy of computer time and the greater accuracy in
comparison with a method of the volume integral equations, though volume
integral equations are more universal.

__Bianisotropic____ media.__ Development of the theory of averaging for
heterogeneous rocks results* *in necessity of introduction macroscopic EM parameters
of bianisotropic media which describe the most
general linear properties of the geoelectric media.
The material equations for such media look like _{}_{}, where _{}, _{} - intensity electric and magnetic
fields, _{} - density of an electric current,
_{} - an induction of a magnetic
field. Parameters _{} (conductivity) and _{} (magnetic permeability) are
well-known in the geoelectrics. Other parameters _{} and _{} - are consequence of averaging of
system of conducting capillaries of complex geometry in a non-conducting
skeleton of rock. It is essentially important, that bianisotropic parameters carry the new important
information about petrophysical characteristics of
rock. In bianisotropic media the phenomena
not peculiar to continuous media are observed: occurrence oscillations in
transients, infringement of a principle of reciprocity. The direct problem for bianisotropic horizontally layered model is solved.
Algorithms and programs of the solving of direct 2D and 3D problems with bianisotropic parameters are developing. The basic
accent of the further researches is related to development of solution inverse problems for
such media.

__Numerical methods__ For practical
realization of theoretical results the various computer programs based on the
appropriate numerical algorithms are created. Now the basic interests of
Laboratory are related to the solution of direct and inverse problems of geoelectrics for complex models (!D,
2D, 3D) and development programs of processing of various experimental data (in
particular methods spectral and wavelet analysis). The basic attention at the
solving of 2D and 3D problems is given to development of methods of the surface
and volume integral equations. Aside from problems of classical geoelectrics the basic interests of Laboratory are
associated with
development of numerical methods (semianalytic,
finite difference and integral equations) 0f solution 2D and 3D problems seismoelectrics and the induced polarization.

__We invite to cooperation____: __

* - The scientific organizations
and the divisions,
interested in the given developments, for joint (or coordinated)
researches.*

__We offer:__

·
*The solution modelling and interpretating problems low- and high-frequency electroprospecting,
related to studying by EM fields at
prospecting of local objects (kimberlite tubes, ore bodies, petroleum deposits etc.), in anisotropic (or bianisotropic) sedimentary formations. *

__The basic publications:__

*1. Svetov B.S. Theory, technique and
interpretation of materials of low-frequency electroprospecting.
M., “Nedra” 1973, 254 p.*

*2. Svetov B.S., Gubatenko
V.P. Analytical solution of electrodynamic problems *

*М**., “Nauka”,
1988, 343 p.*

*3. Alexandrov
P.N. Effective electromagnetic parameters of conductive capillary system of
rock.** - Physics of the Solid Earth, 2000, N 2, p. 87-94.*

*4. Kevorkiants
S.S. To definition tensor Green's functions of an electrodynamic problem of the layered anisotropic media.
Physics of the Solid Earth, 2000, N 10, p. 84-92.*

* *