Complete synthetic seismograms for 3-D heterogeneous Earth models computed using modified DSM operators and their applicability to inversion for Earth structure

Ž . We compute complete including both body and surface waves synthetic seismograms for laterally and vertically Ž . heterogeneous Earth models using the Direct Solution Method DSM . We use the optimally accurate modified operators w derived by Geller and Takeuchi Geller, R.J., Takeuchi, N., 1995. A new method for computing highly accurate DSM x w synthetic seismograms. Geophys. J. Int. 123, 449–470 and extended to spherical coordinates by Takeuchi et al. Takeuchi, N., Geller, R.J., Cummins, P.R., 1996. Highly accurate P-SV complete synthetic seismograms using modified DSM x w operators. Geophys. Res. Lett. 23, 1175–1178 and Cummins et al. Cummins, P.R., Takeuchi, N., Geller, R.J., 1997. Computation of complete synthetic seismograms for laterally heterogenous models using the Direct Solution Method. x Geophys. J. Int. 130, 1–16 for 1and 3-D models, respectively. In this study we greatly reduce the CPU time by treating the Ž . laterally heterogeneous structure as a perturbation to a spherically symmetric model i.e., using the Born approximation . Ž . Ž . Note, however, that 1 our methods do not require the use of the Born approximation and 2 the reference model for the Born approximation is not required to be spherically symmetric. The synthetic seismograms in this paper are computed using the first-order Born approximation. However, accuracy can be greatly improved by using higher order terms of the Born series; theoretical results are presented in this paper, and some preliminary numerical examples are presented in this volume w by Igel et al. Igel, H., Takeuchi, N., Geller, R.J., Megnin, C., Bunge, H.P., Clevede, E., Dalkolmo, J., Romanowicz, B., ́ ́ ́ x 1998. The COSY project: verification of global seismic modeling algorithms, Phys. Earth Planet. Inter., this issue . q 2000 Elsevier Science B.V. All rights reserved.