To the solution of geoelectric problem on a direct current based on the global decomposition

Abstract

The solution of a three-dimensional problem of geoelectric on a direct current is discussed. The solution of this task is constructed on the basis of global decomposition (GDAM). The algorithm consists in iterative reconstruction of the decision from two basic elements — field of a point source in the layered (background) environment and solution in a local insertion. As a background (normal) model, the horizontally layered environment is used, in one of layers of which the point source of direct current is located. The background environment contains limited inclusion with enough arbitrary distribution of specific electrical resistance. The problem consists in studying of influence of an insertion on the normal field. The work of the algorithm of the solution of a task is illustrated on the example of a homogeneous half-space (the three-layer horizontally layered environment with identical conductivity of layers). The point source is located in the first layer. The second layer contains a homogeneous local body (a rectangular parallelepiped or a finite cylinder). Solutions of tasks of Dirikhle for Laplace’s equation in these bodies are known. For the improving of the accuracy of calculations in a parallelepiped, the little change of an algorithm of calculation of potential was needed. Acceleration of calculations was provided by the calculations of Fourier coefficients with the use of direct discrete sine transformation.On the basis of the algorithms given in the work, the programs of calculation of potential in local insertions are developed and the numerical experiments which allowed presenting graphically calculation results and making assessments of accuracy of calculations, are executed.

Keywords

• прямые задачи
• модели геоэлектрики
• многомасштабное моделирование
• глобальная декомпозиция
• метод шварца
• метод итераций