Response of Transition Zones to Nearby Sources

Abstract

In this study we develop a method to compute the seismic response to a P-wave source in or near an inhomogeneous transition zone. Our method is applicable to the cases in which the characteristic dimension of the transition zone is comparable to the wavelength and the source is located near (within a few wavelengths) or in the transition zone. Our method can take a fuller account of the frequency dependent effects of the transition zone than ray-theoretical methods do, in order that we may determine the nature of the transition zones more precisely. In our method we avoid the complexity of scattering in the near field of a point source by considering the reciprocal problem, which is simply related to the forward problem. We solve the reciprocal problem by using a plane wave approximation in the far field. An exact wave solution for plane waves incident on a one-dimensional acoustic or elastic linear transition layer is used. An algorithm is developed to evaluate the wave solutions for a general class of linear transition zones. The ratio of the magnitude of the first order correction term to the leading term in the steepest descent expansion indicates the region where the steepest descent solution is accurate.