| Numerical seismic modeling can aid in the understanding of wave patterns observed on seismograms and can provide crucial guidance on seismic experiment design, data processing, and data interpretation. However, modeling wave propagation in multi-scale heterogeneous media can be extremely computationally intensive, especially if small spatial sampling, required by small features, is used throughout a large domain.; In this thesis, I present a new variable grid finite-difference (FD) method for solving wave equations. This method accommodates multi-scale features by allowing fine grid spacing for zones with small-scale features, and coarse grid spacing for zones with large-scale structures. Since the FD stability condition requires a very small timestep for the finest grid spacing, a spatially variable timestep FD technique is implemented to further reduce computational time by providing small timesteps for zones with fine grid spacing and large timesteps for zones with coarse grid spacing. Comparing numerical results of the variable grid, and the variable grid and timestep FD methods with those obtained by the conventional constant grid and timestep FD method demonstrates their high accuracy and efficiency. Furthermore, parallel versions of the variable grid FD codes are developed for efficient solution of large problems.; Four applications are used to demonstrate the efficacy and the benefits of the developed techniques. First, I directly model an open fluid-filled fracture using the variable grid FD method and compare the numerical results with those obtained using an equivalent medium theory. Then, the variable grid and timestep FD method is used for efficient single-well seismic modeling with a realistic-sized borehole in the modeling scheme. Third, I use a parallel variable grid FD code to model cross-well field data with inclusion of tube-waves and tube-wave-related arrivals caused by the presence of the perforated cased boreholes. Finally, I apply the variable grid FD method for DARS (Differential Acoustic Resonance Spectroscopy) lab data simulation to better understand the theory and to guide experimental design and data analysis. |
