Geophysical Journal | 2013 volume 35 2

Application of methods of the theory of potential for solving direct problems of geophysics for three-dimensional media with complex structure

© Pyatakov Yu.V., Isayev V.I.

Algorithms of solving the problem to determine the components of gravity, geodynamic and temperature fields for three-dimensional heterogeneous media have been presented. For approximation of heterogeneities of the medium by gravity, rheological and thermalphysic parameters standard elements are used - vertical triangular prisms with arbitrary upper and lower bases. New analytical solution of direct problem of gravity for a standard element with density changing with the depth by linear law has been obtained. Mathematical statement has been carried out and general solution of the problem has been given for valuation of strains and instantaneous velocities of movement of heterogeneous viscous medium under the impact of the Earth's gravity field. The solution has been determined with application of hydrodynamic potentials (three-dimensional, ordinary and double layer). Mathematical statement has been considered and general solution of instable and stationary systems of thermal conductivity equation has been obtained for heterogeneous medium. It has been demonstrated that for numerical calculation of hydrodynamic and thermal potentials it is optimal to use the theory and standard technique for solving direct problems of gravity potential. Stability, accuracy and operation speed of the algorithms elaborated is demonstrated by calculations of test examples.

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