Amplitude, energy, and phase angles of plane SV waves and their application to earth crustal studies

Abstract

Abstract Energy ratios from Knott's energy equation and amplitude ratios and phase angles from the Zoeppritz equations were calculated for a plane SV wave incident on a plane elastic discontinuity. All computations were programmed in Fortran for an IBM 1620 digital computer. Incident angles were varied from 0° to 90° in increments of two degrees except near the critical angles, where the ratios were calculated in increments of 0.25 degree generally. Both real and imaginary coefficients were considered in the calculations. The varying parameters were the velocity ratio and density ratio across each interface, and the angle of incidence. Poisson's ratio was kept constant at 0.25. Compressional velocity ratios (transmitted/incident) of 0.7, 0.8, and 0.9, and density ratios (transmitted/incident) of 0.7, 0.8, 0.9, and 1.0 were used. The data are presented in an integrated album which consists of a total of 144 curves (48 curves for each of the 3 characteristics studied). The theoretical amplitudes of PS converted waves, which are seismic body waves resulting from the conversion of an incident parent P wave at a boundary within the earth's crust to a refracted vertically polarized SV wave, were computed (using a fortran program on an IBM 1620 digital computer) for several multi-layered hypothetical and actual crustal models. Preliminary results indicate that the amplitudes of successive PS converted waves arriving from successively deeper layers will continually increase provided that the velocity ratios (upper medium/lower medium) continually decrease with depth. The effects of the wave period have not yet been considered. Particle-motion diagrams obtained from seismograms of two underground nuclear explosions show some shear motion in the first ten seconds which is provisionally interpreted to be from PS converted waves.