(Ph.D. Dissertation)

Yue Wang, University of Utah

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A new variable grid-size and time-step finite-difference (FD) method is developed and applied to three different geophysical problems: simulation of tube waves in boreholes, three-dimensional (3-D) ground-motion simulation in sedimentary basin models, and reverse-time migration of multicomponent data. Unlike the conventional FD method, which uses a fixed grid-size and time-step for the entire model region, spatially variable grid-sizes and time-steps are used to achieve the optimal computational efficiency. For tube wave simulations, a fine grid-spacing is used for simulation inside the borehole region, while a coarse grid is used in the exterior region. While the stability condition requires a very fine time step for the fine grid, a variable time-step method provides coarse time steps for simulation in the coarse grid. Variable grid-size and time-step changes are used to achieve both accuracy and efficiency in the simulations.

Numerical tests are performed for the Bayou Choctaw salt-flank model with different borehole models. The results show the important borehole effects on the seismic wavefield for a realistic source bandwidth. The combination of variable grid-size and time-step methods reduces computational costs by several orders of magnitude for the borehole models.

Viscoelastic 3-D simulations are performed for a three-layer Salt Lake basin model. The near-surface unconsolidated layer is modeled with a fine grid, and the deep part of the model is modeled by a coarse grid. Simulation results show that the 3-D basin features and the shallow layer significantly affect the amplitude and duration time of the ground motion. In the elastic case, the approximation by 2-D modeling is insufficient to simulate the 3-D ground motion response. A basin model without a shallow low-velocity layer underestimates the ground motion duration and cumulative kinetic energy by 50$\%$ or more. The simulation of a Bingham Mine blast suggests that a lower S-velocity should be used to get a good match between numerical results and observed field data.

For ocean-bottom or land survey data associated with a low shear-velocity unconsolidated layer near the geophone locations, the variable grid FD method can be used to extrapolate wavefields using a fine grid for the shallow part and a coarse grid for the deep part. It is found that a staggered-grid reverse-time migration scheme can image both primary and multiple energy to their correct reflection positions by using both pressure and particle-velocity data. This is a new result in that migration can now be used to simultaneously image both primary and receiver-side pegleg reflections. The new variable time-step method can be used for the staggered-grid FD scheme and provides optimal computational savings. The combination of variable grid-size and time-step methods speeds up the reverse-time migration by more than ten times for the multicomponent data set in this thesis, compared to a standard reverse-time migration method.