The effect of a second-order velocity discontinuity on elastic waves near their turning point

Abstract

Summary. The rather abrupt changes in velocity gradient which have some- times been proposed, notably in the upper mantle and near the base of the mantle, have an effect equivalent to that of one or more second-order discon- tinuities, where partial reflection occurs due to a change in curvature of the wavefront across these discontinuities. The effect is ignored in the classical WKBJ approximation to the wave functions, but it can be explicitly demon- strated by applying the extended WKBJ method (Langer's approximation) to a piecewise smooth layered model. For the purpose of ths study it is convenient to represent the response of such a model by a generalized reflection coefficient. For a model of one or a system of several second-order discontinui- ties (approximating a change in velocity gradient over a finite depth interval), the reflection coefficient can be perhaps surprisingly large for long-period waves near their turning point. It is shown that this effect can significantly alter the amplitude decay of sfj waves diffracted around the core, in models where a change in velocity gradient near the core-mantle boundary consti- tutes a low-velocity zone at the base of the mantle; such models have recently been proposed. With the same velocity gradients, the effect on P diffraction is less important. The results for SH diffraction in these models support the conclusion that a small amplitude decay must be explained by a velocity decrease with depth, i.e. a low-velocity zone at the base of the mantle.