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Published February 15, 1963 | Published
Journal Article Open

Generalized Two-Dimensional Model Seismology with Application to Anisotropic Earth Models


The theory of two-dimensional seismic modeling is generalized to include the effect of anisotropy. The elastic coefficient matrix for a plate with orthorhombic symmetry is derived and is used to convert three-dimensional anisotropic problems into corresponding two-dimensional model problems. This is equivalent to replacing directional body velocities by the directional plate velocities. In addition to the application to seismic modeling, this can be considered a contribution to the basic theory of long waves in anisotropic plates. As such it has application to such problems as long waves in floating ice sheets. A model consisting of an anisotropic layer over an anisotropic half-space is constructed using a formica layer and a grooved aluminum plate. It is shown that rolled metal sheets can be made appreciably anisotropic by machining grooves in the surface. The experimental Rayleigh wave phase velocities are compared with the theoretical dispersion curves computed using isotropic and anisotropic theories. Two-layer circular models of the earth, one with an isotropic and the other with an anisotropic upper mantle, are fabricated, and a comparative study of body and surface waves is made. It is found that the relative effect of anisotropy is greater on surface waves than on body waves.

Additional Information

Copyright 1963 by the American Geophysical Union. Manuscript Received: 27 SEP 1962. The theoretical work described in this paper was supported by grant AF-AFOSR-25-63 of the Air Force Office of Scientific Research as part of the Advanced Research Projects Agency project Vela. The experimental portion was supported under grant DA-ARO(D)-31-124-G216 of the Army Research Office (Durham). We gratefully acknowledge the help of Carl Holmstrom in fabricating the models, and the help of Laszlo Lenches in preparing the manuscript. Shelton Alexander wrote the Fourier analysis program used in this study.

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