By Barry Saltzman, Renata Dmowska

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

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Extra resources for Advances in Geophysics, Vol. 43

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Given an initial wavefront to = 0(x, x0), the rays and the following wavefronts can be computed using (66) with so-called ray tracing. As in geometrical optics, an alternative to the above mentioned approach, based on Huygens principle, is represented by a variational formulation corresponding to the Fermat principle: the ray corresponds to the trajectory between two given points for which the travel time is minimum. Expression (65) can become unstable or singular under certain conditions, for instance, in the vicinity of a caustic, where ray theory predicts an infinite amplitude.

2-D model with a topographic step. The variability of thickness (H 0-Hi) of the uppermost layer of medium II defines a variable topographic step that is assumed positive when the thickness is larger in medium II, and negative in the opposite case. In Fig. 15 we show the coupling energy (for three different steps: 1, 5, and 10 km) of the fundamental mode of model C (medium I in Fig. 14) with the fundamental mode (FF;1, FF;5, and FF;10) and with the first higher mode (F1;1, F1;5, and F1;10) of medium II.

71) [3(x, z) - [3o(z) + e~[3(x, z) The transmitted wavefield can then be written as follows U -'- UO + e ~ U ( ~ p , ~OL, ~[~) -~- 0(/32). (72) Perturbation of the wavefield in (72) can be written as a function of the so-called "scattering matrix" that describes the coupling between modes (Snieder, 1986). If we assume normal incidence and that the lateral variations exist only along the x direction, there are no conversions between Love and Rayleigh modes both in the transmitted and in the reflected wavefields.

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