Journal of Conference Abstracts

Prospects for Waveform Inversion for 3-D Earth Structure Using DSM Synthetic Seismograms

Nozomu Takeuchi (takeuchi@geoph.s.u-tokyo.ac.jp)¹, Robert Geller (bob@global.geoph.s.u-tokyo.ac.jp)¹ & Phil Cummins (cummins@jamstec.go.jp)²

¹Earth & Planetary Physics, Tokyo Univ., Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan

²Ocean Crust Dynamics Research, JAMSTEC, Natsushima-cho 2-15, Yokosuka, Kanagawa, 237-0061, Japan

Direct inversion of complete seismic waveforms (including both body and surface waves) appears to be the most promising approach to inversion for 3-D earth structure, but it poses formidable computational challenges. In particular, accurate and efficient methods for computing synthetics and their partial derivatives are essential.

We compute complete synthetic seismograms for laterally and vertically heterogeneous Earth models using the Direct Solution Method (DSM). We use the optimally accurate modified operators derived by Geller and Takeuchi (1995) and extended to spherical coordinates by Takeuchi et al. (1996) and Cummins et al. (1997) for 1-D and 3-D models respectively. The CPU time can be greatly reduced by treating the laterally heterogeneous structure as a small perturbation to a spherically symmetric model, but our methods do not require the use of this approximation.

We also derive efficient algorithm for waveform inversion. Computation of partial derivatives, the most intensive step in the inversion, can generally formulated in terms of the multiplication of sparse matrices (Geller and Hara 1993). Efficiency can be further optimized by determining the order of multiplication to minimize the number of floating-point operations. The best order is different for spherically symmetric starting models and 3-D heterogeneous starting model.

Using the above methods for computing synthetics and their partials we can efficiently invert for 3-D Earth structure. The CPU times for a 3-D whole mantle heterogeneous structure up to degree-6 were 13 hrs and 100 hrs respectively for computing SH (toroidal) synthetics in the bands 32 - 8000 s and 16 - 8000 s using an UltraSPARC (170MHz). These CPU times are of the same order as the CPU times required for a waveform inversion with respect to a spherically symmetric initial model for one earthquake. We hope to have preliminary examples of applications to actual data by the time of the meeting.

Cummins et al., GJI, 130, 1-16, (1997)

Geller & Hara, GJI, 115, 699-710, (1993)

Geller & Takeuchi, GJI, 123, 449-470, (1995)

Takeuchi et al., GRL, 23, 1175-1178, (1996)