Three-dimensional analysis of scattered P waves on the basis of the PP single isotropic scattering model.

Abstract

Wave trains immediately following the initial motion of P waves are analyzed assuming that they are scattered P waves by heterogeneities in the earth medium. Three-dimensional partition of the energy density of scattered P waves is theoretically studied, where PP single isotropic scattering and homogeneous and random distribution of scatterers are assumed. The theoretical analysis shows that the three-dimensional mean trajectory for scattered P waves in velocity space is represented by a spheroid, which is prolate to the propagation direction of the direct P wave, and the spheroid tends to become spherical as time goes on. This model is applied to an analysis of short-period (1-30Hz) records of small local earthquakes observed by a three-component velocity seismometer installed at the bottom of a deep borehole. The three-dimensional partition of energy density is calculated by using the covariance tensor for particle velocity observed. The observed horizontal component of energy density of scattered P waves agrees well with the theoretical one, although the observed vertical component is larger than and the observed radial component is smaller than the theoretical one. Our theoretical model is proved to be good in accounting for horizontal component. In order to explain changes in vertical plane, it is suggested that refraction and reflection at horizontal lateral boundaries and the earth's surface, and/or PS conversion scattering should be considered.