3-D finite-difference simulation of elastic wave propagation in borehole, refraction, earthquake and whole earth applications

Modeling of elastic wave propagation in three dimensional (3-D) geological structures provides insight that is difficult to obtain through one or two dimensional modeling. The finite-difference method on a staggered grid can be useful in investigating the structural effects of media and the spatially distributed source problems in 3-D models. Recent advances in both computing hardware and algorithms make it feasible to apply this method to more general seismological problems. 3-D finite-difference method on the staggered grid has been used to simulate wave propagation in four different applications grouped into three projects whose scales range from a few meters to the whole Earth. Their applications include full waveform borehole sonic logs, refraction data, strong motions near a shear dislocation fault and wave propagation through the whole Earth. All these models contain sharp boundaries across which the Poisson's ratio where staggered grid method provides stable solutions. By using the staggered grid, an optimal high-order scheme can be chosen to use a coarse grid, thus saving computer memory and time. In the borehole modeling study of fullwave sonic logs, even a small three dimensional feature makes the wavefield significantly complicated. Detected wavefield changes significantly depending an the orientation and the coupling of the logging tool clamped to the wall of the hole. Refraction data modeling was used to constrain the shallow part of a larger model used for strong motion studies associated with a shear dislocation source that is spatially distributed on the fault plane. The strong motion modeling reproduced the main observed features in earthquake data. The initial arrival times and amplitudes are determined by the position and orientation of the initial rupture; the shapes of the trailing edges of the pulses are modified by the actual source distribution. Regional velocity distributions determine travel times, but do not significantly alter the amplitude observations. Discontinuities in material properties produce a coda of multiples and converted waves. Lateral variations in velocities change the energy distribution among the trace components as well as contributing to the coda. The whole earth modeling simulated large explosion and double-couple shear sources in 3-D models. Synthetic seismogram results resemble GDSN seismic data. A slight smooth bump in the core-mantle boundary was found to affect a large number of phases. The study reveals that 3-D numerical modelling of whole earth response is a potentially valuable diagnostic and interpretive tool, and a basis for globalization of traveltime tables.