ELASTIC WAVE PROPAGATION IN TRANSVERSELY ISOTROPIC MEDIA USING FINITE DIFFERENCES¹

Abstract

TSINGAS, C., VAFIDIS, A. and KANASEWICH, E.R. 1990. Elastic wave propagation in transversely isotropic media using finite differences. Geophysical Prospecting 38,933-949.When treating the forward full waveform case, a fast and accurate algorithm for modelling seismic wave propagation in anisotropic inhomogeneous media is of considerable value in current exploration seismology. Synthetic seismograms were computed for P-SV wave propagation in transversely isotropic media. Among the various techniques available for seismic modelling, the finite-difference method possesses both the power and flexibility to model wave propagation accurately in anisotropic inhomogeneous media bounded by irregular interfaces. We have developed a fast high-order vectorized finite-difference algorithm adapted for the vector supercomputer. The algorithm is based on the fourth-order accurate MacCormacktype splitting scheme. Solving the equivalent first-order hyperbolic system of equations, instead of the second-order wave equation, avoids computation of the spatial derivatives of the medium's anisotropic elastic parameters. Examples indicate that anisotropy plays an important role in modelling the kinematic and the dynamic properties of the wave propagation and should be taken into account when necessary.

Ionization fronts in coupled MHD-gas simulations

“…In either case, the truncation errors can become of a magnitude comparable to the solution and therefore introduce spurious signal in the form of short wavelength, compared to the mesh, oscillations. 39 The scheme could be improved to remove these nonphysical oscillations by adding a flux corrected transport (FCT) term devised by Boris and Book 41 such as in Tsingas et al 42 or the more modern approach of total variation diminishing (TVD) schemes, devised by Harten, 43 such as in Liang et al 44 While these types of approach can successfully capture shocks, they add significant complexity to the condition (NRBC) are possible. Theoretical solutions for this have existed for many years (for example, Givoli; 45 Tsynkov, 46 and Hagstrom 47 ), but problems in implementation can still be present.…”

The pseudo-acoustic equations of the scalar wavefield in anisotropic media

“…Relations (16) and (17)(18)(19)(20) define process of wave propagation in the determined direction in anisotropic media.…”

“…To verify the correctness of wave propagation in media with different properties of anisotropy some numerical experiments using one-way equation (17) and Taylor's relations (18)(19)(20) were made. The main aim of those experiments was the estimation of the usefulness of the applied signals.…”

“…Równania bazują na dyspersyjnych relacjach wyznaczających wartości własne -częstotliwości w funkcji liczb falowych i parametrów anizotropii na podstawie pełnego systemu równań akustycznych. Zaprezentowano kilka przypadków propagacji falowej określonej jednostronnym równaniem w formie migawkowych zdjęć dla różnych typów sygnału.Słowa kluczowe: anizotropia, poprzeczna izotropia (TI), modelowanie, jednostronne równanie falowe, relacja dyspersyjna.Forward modelling of seismic waves in anisotropic media should be executed by solving a full system of elastic wave equations using numerical techniques such as finite-difference, spectral and pseudo-spectral method [3,7,9,10,11,17,19,20,23]. Due to the very time-consuming calculation system of modelling three component acoustic field and insufficient data concerning elastic parameters, in practical seismic research the tendency to simplify the theory and to limit oneself to the considerations of a few models of anisotropy can be noted.…”

“…Forward modelling of seismic waves in anisotropic media should be executed by solving a full system of elastic wave equations using numerical techniques such as finite-difference, spectral and pseudo-spectral method [3,7,9,10,11,17,19,20,23]. Due to the very time-consuming calculation system of modelling three component acoustic field and insufficient data concerning elastic parameters, in practical seismic research the tendency to simplify the theory and to limit oneself to the considerations of a few models of anisotropy can be noted.…”