Generally applicable solutions of Zoeppritz' amplitude equations

Abstract

A crustal model, in addition to satisfying travel-time data, should agree with the observed distribution of amplitude in time and range. The study of observed amplitudes in seismic crustal work depends directly on the partition of the amplitude of an incident wave front at an interface. The Zoeppritz equations describe this partition for a plane wave and while they are simple simultaneous linear equations, their solution by hand methods is tedious and receptive to errors. Solutions of these equations have been obtained by numerical methods for both the incident P and SV cases and are presented in the form of curves showing the ratio of the amplitude of the resultant ray to that of the incident ray plotted against the angle of incidence. By solving the equations for velocity ratios ranging from 0.25 to 4.0, families of curves covering most realistic situations were obtained. That generally applicable solutions of these equations can be presented in curve families ranging over velocity contrast alone, is demonstrable from the studies of the velocity vs. density relation made by Nafe and Drake and independently by Woollard. The curves presented permit rapid, quantitative solution of the amplitude partition at an interface, thereby, greatly facilitating the study of wave train modifications.