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Barry Saltzman, Renata Dmowska's Advances in Geophysics, Vol. 43 PDF

By Barry Saltzman, Renata Dmowska

ISBN-10: 0120188430

ISBN-13: 9780120188437

This sequence presents a venue for longer studies of present advances in geophysics. Written at a degree available to graduate scholars, the articles serve to increase wisdom of assorted fields and should be invaluable in classes and seminars.

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In such a way (65) becomes a form of the solution suitable for computation of a synthetic seismogram, since its FT can very easily be computed. SEISMIC WAVE PROPAGATION IN HETEROGENEOUS MEDIA 27 Introducing (65) in the equations of motion, we obtain an independent set of solutions that, for SH-waves, can be written as (Cerveny, 1987) (V0) 2 = 1 [3 -- (66) A0. (V0) - 0, also called the eikonal equation. We define the surface 0(x) = const as a wavefront. The slowness vector, p = V0, is normal to the wavefront and has modulus 1/[3: its trajectory describes a ray.

Wentzel, H. Kramers, L. Brillouin, and H. Jeffreys), where the source is represented as a sum of Snell waves, each one propagating independently from the other ones. The seismogram is then calculated summing all the propagated waves (Chapman, 1978). Recently, advances in ray theory have been obtained applying the ray perturbation theory. In this way the techniques known as paraxial rays and Gaussian beams have been developed (Farra and Madariaga, 1987; Madariaga, 1989). The ray perturbation theory is used for evaluation of ray amplitude and for solving iteratively ray tracing problems.

018 1 (Hz) frequency FIG. 11. Transmission of energy from incident fundamental mode of model C to first five modes of model P. SUM T and SUM are the curves describing the outgoing energy, without and with the inclusion of reflected energy. 6- .......... \ ~ Cl PF SUM T ClP1 SUM ClP2 %. Cl P3 -- - -- ClP4 \ 0, / ---- ____ --. 8 1 FIG. 12. Transmission of energy from incident first higher mode of model C to first five modes of model P. SUM T and SUM are the curves obtained summing the outgoing energy, without and with the inclusion of reflected energy.

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Advances in Geophysics, Vol. 43 by Barry Saltzman, Renata Dmowska

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