On the computation of theoretical seismograms for multimode surface waves

Abstract

Summary It is needlessly expensive to use standard computational techniques, when applying inverse Fourier transformation to construct theoretical seismograms from frequency-domain data for multimode surface waves. Such techniques require the evaluation of dispersion and attenuation information for each mode, at each of a dense set of points which are equally spaced in frequency. These evaluations are by far the most expensive part of the computation of theoretical seismograms for surface waves. By further development of a method proposed by Aki, and departing from the standard, equal-frequency-interval computational techniques, it is possible to decrease the required number of dispersion and attenuation evaluations. With our new method a decrease of a factor of almost two for the fundamental mode, and approximately five for the higher modes is obtained, i.e. we obtain an increase in computational efficiency of 200 per cent for the fundamental mode and 500 per cent for the higher modes. The basis of the new method is the approximation of the amplitude and apparent initial phase spectra by quadratic and linear functions, respectively; this permits an analytic quadrature of the Fourier integral.