Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998geoji.135..449x&link_type=abstract
Geophysical Journal International, Volume 135, Issue 2, pp. 449-462.
Astronomy and Astrophysics
Astronomy
Layered Media, Seismic Anisotropy, Seismic Modelling, Seismic Velocities, Theory, Wave Propagation
Scientific paper
The `auxiliary' symmetry properties of the system matrix (symmetry with respect to the trailing diagonal) for a general anisotropic dissipative medium and the special form for a monoclinic medium are revealed by rearranging the motion-stress vector. The propagator matrix of a single-layer general anisotropic dissipative medium is also shown to have auxiliary symmetry. For the multilayered case, a relatively simple matrix method is utilized to obtain the inverse of the propagator matrix. Further, Woodhouse's inverse of the propagator matrix for a transversely isotropic medium is extended in a clearer form to handle the monoclinic symmetric medium.
The properties of a periodic layer system are studied through its system matrix Aly , which is computed from the propagator matrix P. The matrix Aly is then compared with Aeq , the system matrix for the long-wavelength equivalent medium of the periodic isotropic layers. Then we can find how the periodic layered medium departs from its long-wavelength equivalent medium when the wavelength decreases. In our numerical example, the results show that, when λ/D decreases to 6-8, the components of the two matrices will depart from each other. The component ratio of these two matrices increases to its maximum (more than 15 in our numerical test) when λ/D is reduced to 2.3, and then oscillates with λ/D when it is further reduced. The eigenvalues of the system matrix Aly show that the velocities of P and S waves decrease when λ/D is reduced from 6-8 and reach their minimum values when λ/D is reduced to 2.3 and then oscillate afterwards. We compute the time shifts between the peaks of the transmitted waves and the incident waves. The resulting velocity curves show a similar variation to those computed from the eigenvalues of the system matrix Aly , but on a smaller scale. This can be explained by the spectrum width of the incident waves.
Ni Si-Dao
Xu Guo-Ming
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