Numerical Analysis and Applications

, Volume 7, Issue 2, pp 136–146 | Cite as

Numerical-analytical simulation of wave fields for complex subsurface geometries and structures



In this paper, we propose an analytical method of modeling seismic wave fields over a wide range of geophysical media: elastic, inelastic, anisotropic, anisotropic-inelastic, porous, random-inhomogeneous, etc., at very large distances. Since no finite-difference approximations are used, no grid dispersion occurs in computing wave fields for arbitrary media models and observation points. An analytical solution representation in the spectral domain makes it possible to analyze the wave field by parts, specifically, to obtain primary waves. A program of computing the wave fields has been developed, and a simulation of water waves and seismic “ringing” of the Moon has been carried out. The phenomenon of a monotonic shift of the resonance to the lower frequency area with increasing distance of recording is explained. This phenomenon was detected in some experiments with a seismic vibrator.


mathematical modeling analytical solution full wave fields primary waves elastic inelastic anisotropic-inelastic porous random-inhomogeneous media 


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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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