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

SEISMOLOGICAL LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY, PASADENA, CALIFORNIA, 91125

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.