Use of Kirchhoff's formula for body wave calculations in the Earth

Abstract

Kirchhoff's time-dependent surface integral representation of a scalar wavefield is applied to the problem of computing synthetic seismograms for P-waves in the Earth. By means of an appropriate parameterization, the Kirchhoff integral is transformed into a convolution of a weight function with the derivative of the source function in the time domain. The weight function is calculated using simple ray theory. The method extends the applicability of simple ray theory to caustics and other diffraction phenomena and allows certain kinds of departures from spherical symmetry to be taken into account. The method is illustrated in detail by application to the PKP-wavefield in the Earth.