Институт вычислительной математики
и математической геофизики

The International Conference on Computational Mathematics


Numerical solution of differential and integral equations

Numerical model of seismic wave propagation in viscoelastic media

Sabinin V., Ronquillo-Jarillo G., Chichinina T.

Instituto Mexicano del Petroleo (Mexico,

The development of the known viscoelastic model, by more accurate definition of the numerical scheme, by adding the modification of the PML method for boundary conditions, and by realizing the model for parallel computing at the cluster Beowulf, is presented.

The 2D propagation of seismic waves in viscoelastic media is governed by the system of three equations: for the velocity vector (equation of motion), for the stress tensor (Hooke's law for the viscoelastic media), and for the memory variable. The system is approximated by the explicit finite-difference scheme at a uniform grid. For decreasing undesirable wave reflections from outer boundaries of the computation area, the area is surrounded by the Perfectly Matched absorbing Layer. The numerical model is realized in the software for parallel computing. It is applied to obtaining the synthetic seismograms of waves reflected from the target layers for large-scale problems.

The dependence of the quality factor Q on the stress and strain relaxation times of media is investigated numerically, by estimating the factor Q from the synthetic seismograms for different values of the relaxation times. For the estimation of factor Q, the Spectral Ratio Method and the Centroid Frequency Shift Method is used.

The comparison of synthetic seismogram with one obtained by the ray tracing method, the synthetic seismograms for different factors Q, and the synthetic seismogram with the real one is carried out. These comparisons and the presented example of computation at the fine mesh give an imagination of a good outlook of the numerical approach.

Note. Abstracts are published in author's edition

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