Astronomy and Astrophysics – Astronomy
Scientific paper
May 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998geoji.133..413g&link_type=abstract
Geophysical Journal International, Volume 133, Issue 2, pp. 413-418.
Astronomy and Astrophysics
Astronomy
Diffraction, Ray Theory, Seismic Reflection, Seismic Refraction
Scientific paper
Bakker (1990) and, earlier, Klem-Musatov & Aizenberg (1984) have provided formulations for diffracted waves that complete the zero-order approximation to the seismic wavefield of asymptotic ray theory (ART). This combined solution is correct to O(1/√ ω). An advantage of ART is its ability to deal with complex geological situations, and hence one must establish that the diffracted waves of Klem-Musatov & Aizenberg (1984) and Bakker (1990) satisfy the relevant boundary conditions for a complex model. We show that the diffracted waves do indeed satisfy the elastic boundary conditions to O(1/√ ω) when they reflect from or transmit through a smooth interface. If a diffracted wave is incident near a point on the interface that is not smooth, then the above-mentioned formulation only applies to the reflected and transmitted diffracted waves on one side of the irregularity, and here the boundary conditions are met. (This is the side upon which the geometrical rays are incident.) Also, we calculate the synthetic seismograms for the so-called Amoco model of Hron & Chan (1995) for an impulsive source for zero-order ART, both with and without diffractions. This illustrates the effectiveness of the diffracted waves in smoothing discontinuities in the seismic wavefield common in the zero-order ART approximation.
Gallop B. J.
Hron F.
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