RAYLEIGH WAVES IN {\bf D}-CONSTANT MEDIA AT CHARACTERISTIC FREQUENCIES. I. POISSONIAN MEDIA

V. M. Markushevich and A. S. Tsemahman

Abstract

Sturm-Liouville's matrix problem, which is equivalent to the system of equations for Rayleigh surface waves, is described. A potential of the system is generated by a symmetric matrix. Under the assumption that the matrix is constant, we analytically construct elastic parameters and density as functions of depth. The construction is especially simple in the case of a Poissonian body, i.e., if $\lambda=\mu$. The parameters of the medium are determined from the {\bf D} matrix, and the modal structure of Rayleigh waves at characteristic frequencies is analyzed. Examples of media are given where Rayleigh waves do not propagate at the characteristic frequencies.

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Computational Seismology, Vol. 2.