REPRESENTATION OF MATRIX POTENTIALS IN THE
RAYLEIGH WAVE EQUATION BY A SYMMETRIC MATRIX
V. M. Markushevich
Abstract
To invert the stationary Rayleightype vibrations we describe them in
a matrix SturmLiouville form. Information on the elastic parameters
and density as functions of depth is contained in the matrix potential
of this problem. Understanding the potential structure is very
important for an inversion. The paper presents a study of the
SturmLiouville matrix equation which governs Rayleigh waves. The
potential of the equation is proved to be, in general, a nonsymmetric
matrixfunction of a symmetric matrix depending on Lame's parameters.
Consequently, the properties of Rayleigh waves are determined by the
symmetric matrix and the boundary condition at the surface. We describe
the structure of the matrix in terms of Lame's parameters, density, and
frequency.
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