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Published December 1975 | Published
Journal Article Open

A perturbation scheme for obtaining partial derivatives of Love-wave group-velocity dispersion

Kosloff, Dan

Abstract

A method is derived for obtaining partial derivatives of Love-wave group-velocity spectra for a layered medium using a second-order perturbation theory. These partials are a prerequisite for systematic inversion of group-velocity spectra but they are helpful as well in trial and error methods. Mathematically the equation of motion and boundary conditions for Love waves are a singular Sturm Liouville type eigenvalue problem. In the case of a fixed wave number, the eigenvalues are the negative of the square of the frequencies. Thus, by expressing the first- and second-order perturbations of the eigenvalues in terms of partial derivatives of the frequency with respect to the wave number and material parameters of the medium, one can relate these perturbations to group-velocity partials. The scheme should be relatively economical and easy to incorporate in Love-wave dispersion codes.

Additional Information

© 1975 Seismological Society of America. Manuscript received February 10, 1975. The author wishes to thank Dr. D. Harkrider for his encouragement during this research. This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract F44620-72-C-0078.

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Created:
August 19, 2023
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October 17, 2023