Simulating Seismic Wave Propagation by Using Finite-Difference Method and Applications
Hsieh Ming-Che
Abstract
The finite-difference is commonly applied in waveform simulation because the following benefits: (a) source insertion is straightforward and can be expressed in terms of velocity (via body force) or stress; (b) a stable and accurate representation for a planar free-surface boundary is easily implemented; (c) since the finite-difference operators are local, the entire model does not have to reside in core memory all at once; (d) it is easily extended to high-order spatial difference operators; (e) the method can be interfaced with other modeling techniques by expressing the input wave field along a boundary of the finite-difference grid; and (e) The algorithm is easily implemented on scalar, vector, or parallel computers. In this talk, I will present implementations of finite-difference method for
waveform simulation. We start from the equations of motion and their discrete forms by the difference operator. Source insertion should be considered as a body force term, so the moment tensor description is performed for modeling seismic source.Free-surface boundary conditions often require careful consideration in FD scheme due to numerical stability and accuracy. Two kinds of formulation will be discussed in this talk for computing response of free-surface. Also, two kinds of nonreflecting boundary conditions are performed and discussed for preventing artificial reflections from model boundaries. Finally, I take the full elastic waveform modeling of Taipei basin as an example. The results shows the amplification effects may be due to the geometry of the basin and the relative low S-wave velocity layer, Songshan
formation.
ReferencesGraves, R. W. (1996). Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences, Bull. Seismol. Soc. Am. 86, 1091-1106.
Lee, S. J., H. W. Chen, and B. S. Huang (2008). Simulations of strong ground motion and 3D amplification effect in the Taipei basin by using a composite grid finite-difference method, Bull. Seismol. Soc. Am. 98, 1229-1242.