SYMPLECTIC STRUCTURE OF THE STURM-LIOUVILLE PROBLEM FOR THE RAYLEIGH SURFACE-WAVES

The boundary value problem describing Rayleigh surface waves in terms of the Fourier-Bessel transform can be reduced to a matrix Sturm-Liouv ille boundary value problem and its adjoint, because of a specific str ucture of the matrix potential of this Sturm-Liouville problem. As a r esult of this reduction one can find many vertically heterogeneous mat erials for which the boundary value problem can be solved analytically . Propagation of P-SV seismic waves in an arbitrary horizontally homog eneous elastic medium can be described using a piecewise approximation by the solution for such materials. The method is especially useful i f the medium contains gradient layers. In this case the computation of synthetic seismograms is 20-30 times faster than with usual piecewise constant approximation.