On a numerical quasiconformal mapping method for the medium parameters identification using applied quasipotential tomography

Abstract

The problem of parameters identification of the bursts of the medium conductivity coefficient according to the tomography of the applied quasipotentials is considered. The method of image reconstruction is suggested, according to which the problem of analysis is reduced to the application of numerical methods of quasiconformal mappings, and the problem of synthesis is reduced to the solving the problem of parametric identification. The results of numerical experiments are presented and their analysis is carried out.

Generalization of numerical quasiconformal mapping methods for geological problems

“…As noted above, in ERT there is an «acute» problem of lack of input data, the use of Dirac functions in modeling the areas of application of potentials and the complexity of the implementation of quasiconformal mappings of a finite fragment of a half-plane. To increase in a qualitative sense the number of the first, to avoid the second and at the same time to flexibly take into account the third possible based on research [8][9][10]. In particular, they dealt with precisely these problems, but in environments with discretely specified boundary conditions along the entire boundary.…”

“…Namely, in [8], the issues of flow formation in the presence of several sections of application of quasipotentials were studied in detail. In [9,10], a new technique (method and corresponding algorithms) was developed for the complex analysis of solving tomography problems of applied quasipotentials. It provides, for each of the corresponding injection, the presence on the boundary of the domain of only equipotential lines, with given functions of local current densities, and streamlines, with known distributions of the quasipotential on them.…”

“…obtained in the process of transmission of electric charges and simultaneous measurements, where p = 1,2,… is the injection number [9,10];…”

“…are marked points on ¶G z ; a and b -longitudinal and transverse dimensions of the investigated domain (rectangle); B 0 B p , C 0 C p and A p D p are impenetrable boundary lines of currents. Current injection through the tomographic cross section, similarly to [9,10], is modeled by points…”

“…where M is the current point of the corresponding curve; n is the unit outward normal vector. Functions [9,10] can be constructed by interpolating their experimentally obtained values…”