A Numerical Method for Calculating Complete Theoretical Seismograms in Vertically Varying Media
A numerical method is presented for calculating complete theoretical seismograms. The earth models are assumed to have velocity, density and attenuation profiles which are arbitrary piecewise-continuous functions of depth only. Solutions for the stress-displacement vectors in the medium are expanded in terms of orthogonal cylindrical functions. The resulting two-point boundary value problems are integrated by a variety of schemes, automatically chosen to suit the type of wave solution. These schemes include collocation for low-frequency and for highly evanescent waves, various special methods for highly oscillatory waves and for turning waves, and combinations of those. A Fourier-Bessel transform is then applied to get back into the space-time domain.
KeywordsCollocation Method Collocation Point Body Wave Evanescent Wave Synthetic Seismogram
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