Sympletic structure of the Sturm-Liouville problem for the Rayleigh surface wavesстатья
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Аннотация:The boundary value problem describing Rayleigh surface waves in terms of the Fourier-Bessel transform can be reduced to a matrix Sturm-Liouville boundary value problem and its adjoint, because of a specific structure of the matrix potential of this Sturm-Liouville problem. As a result of this reduction one can find many vertically heterogeneous materials for which the boundary value problem can be solved analytically. Propagation of P-SV seismic waves in an arbitrary horizontally homogeneous elastic medium can be described using a piecewise approximation by the solution for such materials. The method is especially useful if the medium contains gradient layers. In this case the computation of synthetic seismograms is 20-30 times faster than with usual piecewise constant approximation. ┬й 1993.