The Reflection of Spherical Waves from Transition Zones with Arbitrary Depth-dependent Elastic Moduli and Density

A procedure has been presented for the numerical computation of synthetic seismo-grams of the reflected wave (including head waves and continuously refracted waves) arising from the incidence of a spherical wave on an inhomogeneous transition zone with arbitrary depth-dependent variation of the elastic moduli and density. The reflection phenomenon will be discussed in the frequency domain where the method of stationary phase gives a rapid estimate of the important features of the reflected wave field as a function of frequency, phase velocity and distance. Using this estimate synthetic seismograms are obtained by numerical integration with respect to wave number and by applying a fast Fourier transform technique. Synthetic seismogram sections for three typical examples of crust-mantle transition zones are discussed in detail. The procedure described in this paper provides a new means of placing more severe bounds on possible crustal and upper mantle models.