Abstract
An approximation, similar to the Born approximation, is developed for scattering of seismic waves by an irregular surface. It is assumed that the magnitude and slope of the irregularity are small. The irregularity is replaced by an equivalent stress distribution so that the problem is reduced to Lamb's problem for distributed surface sources; the latter problem can be solved by convolution methods. As examples, the problems of the scattering of plane P waves, plane S waves, and surface Rayleigh waves are treated. Solutions are obtained in terms of integrals of functions that arise in the theory of Lamb's problem for isolated surface line sources. The example of the scattering from a mountain with plane sides is worked out in detail. The result is valid for pulses whose durations are long compared with the vertical travel time across the irregularity and short compared with the horizontal travel time across the irregularity.
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