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Ray perturbation theory and the Born approximation. (English) Zbl 0692.73030

Summary: Ray perturbation theory and the Born approximation have both been used extensively in seismological studies to describe the effects of a slowness perturbation on body and surface wavefields. The relationship between the expressions for the perturbed wavefield calculated using the two methods is investigated here. Using the symplectic symmetry of the ray equations we demonstrate the agreement, in the far field, of the two methods to first order in the slowness perturbation and to leading order in the asymptotic ray series. Thus it is shown that geometrical ray effects, like the traveltime perturbation, ray bending and focusing, are contained within the Born scattering formalism, provided these effects are small. The propagator formalism used to present the results is sufficiently general to include body and surface waves with a smoothly varying inhomogeneous elastic reference medium.

MSC:

74J99 Waves in solid mechanics
86A15 Seismology (including tsunami modeling), earthquakes
74J15 Surface waves in solid mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
74J10 Bulk waves in solid mechanics
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