Particle amplitude profiles for Rayleigh waves on a heterogeneous Earth

Abstract

The relationship between vertical and horizontal particle amplitude and depth for Rayleigh waves was obtained for several models of a heterogeneous, solid half-space using a new computing program for the IBM 650. The data show how the well-known characteristics of Rayleigh wave motion on a homogeneous half-space are modified in the common case in which compressional and shear velocities increase downward in the earth and also in the case in which a low-velocity region such as the mantle or asthenospheric low-velocity channel exists. Theoretical particle amplitude profiles and dispersion curves, computed on the basis of bore hole measurements of compressional and shear velocities made by Dobrin, Simon, and Lawrence, are compared with data on explosion-generated Rayleigh waves of 4 to 8 cps recorded by them in the bore hole. Observed particle trajectories and computed amplitude profiles are in good agreement except in the upper 10 feet, where the very large horizontal amplitudes predicted by theory, particularly for short periods, are not shown in the field observations. Particle amplitude profiles based on Gutenberg's model of the mantle are given for a broad spectrum of mantle Rayleigh wave and long-period crustal Rayleigh wave frequencies. These data show that the heterogeneous character of the mantle cannot be neglected in the problem of crustal Rayleigh wave dispersion. They also show that no ‘captured waves’ or ‘channelled waves’ of unusual character exist in the Rayleigh mode. Instead, particle motion profiles for the heterogeneous earth differ only slightly from the profile for Rayleigh waves on a homogeneous half-space throughout the spectrum of this mode.