Open AccessComputation of complete waveforms in general anisotropic media—results from an explosion source in an anisotropic medium
Author(s) -
Mandal B.,
Toksöz M. N.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb01750.x
Subject(s) - wavenumber , seismogram , anisotropy , eigenvalues and eigenvectors , computation , physics , computational physics , mathematical analysis , geometry , optics , mathematics , algorithm , geology , quantum mechanics , seismology
SUMMARY An algorithm of generating complete waveforms in general anisotropic media (21 constants) is presented. Complete waveforms have been computed including a point‐source in the anisotropic medium and the reflection and transmission properties of individual interfaces. A recursive scheme of scatterer operators and the numerical wavenumber integration technique are used. The 6times6 system matrix A of each layer is derived. Each element of A is expressed in such a manner that the wavenumber could be used as an inner loop (vectorizing loop). A numerical algorithm is used to compute simultaneously the eigenvalues and eigenvectors of A. The upgoing and downgoing eigenvalues are separated according to a radiation condition and the properties of the z‐component Poynting vector. Filon integration is applied to evaluate the integrals over horizontal wavenumbers. Since wave propagation in an anisotropic medium is a 3‐D problem, it requires an enormous number of computations. To reduce the computation time, the wavenumber is used as the deepest loop. An efficient computer code has been developed for vectorization in the super computer. Both source and receivers can be placed at arbitrary depths. Three‐component synthetic seismograms are computed from an explosion in the anisotropic medium. Examples are calculated for half‐space multilayered anisotropic media. Theoretical seismograms show that radiation patterns are strongly affected by the anisotropy. For example, an explosion in an anisotropic medium with horizontal axes of symmetry generates P‐, SV‐ , and Rayleigh waves, all whose amplitudes are varying with azimuth, and significant transverse (SH) waves at certain azimuths. These effects could be explained by the non‐spherical behaviour of the source due to the directional dependence of elastic moduli. The waveforms are further complicated by the reflection and conversion phenomena of waves propagating in anisotropic media.