Energy Ratio of the Seismic Waves Reflected and Refracted at a Rock Water Boundary. Amplitudes of PcP, PcS, ScS, and ScP in Deep-Focus Earthquakes

Citation

Ergin, Kazim (1950) Energy Ratio of the Seismic Waves Reflected and Refracted at a Rock Water Boundary. Amplitudes of PcP, PcS, ScS, and ScP in Deep-Focus Earthquakes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/eynv-8f51. https://resolver.caltech.edu/CaltechTHESIS:11242020-173649715

Abstract

Part I.

Using the Knott-Zoeppritz equations, the general behavior, zero points and extreme points of the energy ratio that goes into reflected and refracted waves upon the incidence of a wave at either side of the rock-water boundary at the bottom of the ocean are computed as a function of the angle of incidence, for a possible range of values of the parameters involved, namely, Poisson's ratio, the ratio of the longitudinal wave velocities in two media, and the density ratio.

From the computed results it is found that:
1. Poisson's ratio of the solid medium is a dominating factor in the general behavior, zero points and extreme points of the reflected and refracted waves that travel in the solid.
2. Any change in the ratio of the two longitudinal velocities produces pronounced results in the refracted wave energy.
3. The effect of changing the density ratio is very slight.
4. Peculiar behavior occurs just before and right after the critical angle of incidences.
5. At a critical angle of incidence, all of the incident energy goes into the reflected wave of the same kind as the incident wave.
6. Most of the incident energy is reflected either as P or as S wave depending upon the angle of incidence.

Part II.

A systematic study has been made of the ratios of the displacements of the core reflections to the direct body waves as well as of the individual displacements, using intermediate and deep focus earthquake seismograms recorded at Pasadena. Theoretical values of the horizontal and the vertical ground displacements have been computed for the direct P and S as well as for PcP, PcS, ScS and ScP waves as a function of the epicentral distance for three focal depths, namely, 100, 400 and 700 km. The results indicate that the observed ratios of the horizontal displacements of the waves that are reflected at the core-mantle boundary as P waves (i.e., PcP/P and ScP/S) and that of the observed vertical displacements of the waves that are reflected as S waves (i,e., PcS/P and ScS/S) are five or more times larger than the theoretical ones. The ratios of the vertical components of the first group and the ratios of the horizontal components of the second group are in fairly good agreement with the theoretical values. It is further found that the behavior of the direct P and SV waves are in accord with the theory, but the vibrations are not in the direction of propagation for the reflected P waves and the vibrations are not perpendicular to the direction of propagation for the reflected S waves. The effect of aelotropic crustal structure on the ground displacements is discussed.

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