An efficient numerical method for computing synthetic seismograms for a layered half-space with sources and receivers at close or same depths

It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (KENNETT, 1983; LUCO and APSEL, 1983; YAO and HARKRIDER, 1983; CHEN, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (APSEL and LUCO, 1983; HISADA, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (DAHLQUIST and BJORCK, 1974; CHANG, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.