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.
· 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.