Elastic Wave Modeling Including Surface Topography

As China's increasing demand for oil and gas resources. Seismic exploration work gradually to the northwest and southwest ,where have complex terrain. Complex surface topography bring lots of difficulties to seismic exploration, data processing and data interpretation. Understanding wave propagation in complex surface topography become very necessary. We use staggered-grid method to solve velocity-stress formulation. Staggered-grid method have high accuracy, high efficiency and able to use parallel algorithm. We introduced mapping grid method to deal with topography problem. Applicable to both 2-D and 3-D case is the advantage of mapping grid method. We use perfect match layer (PML) absorbing boundary condition to solve unbounded problems. The core of PML method is matching and splitting. We derived PML absorbing boundary condition formula which fit mapping grid method.We write program based on Matlab program language after through in-depth study of wave field simulation.First, constructed high order staggered-grid difference formulas,and discussed the stability and numerical dispersion of staggered grid method. Second, discussed formulas and stability of mapping grid method, and derived PML absorbing boundary conditions which adapted to the mapping grid method. Third, the wave equation is converted to program code. Forth, several kinds of models were designed to use to prove the exactitude of the program. To the model which has level surface, we can get good numerical simulation result. But to the model has topography, we need the model has smooth and topography function have continuous first-order derivatives. Because of the advantage of mapping grid method, it is worth for further study.In a word, if the model has smooth surface, simple structure and little velocity difference between layers, that the program can get good elastic wave simulation results. PML absorbing boundary conditions works well. Further work is to improve the applicability of grid mapping and optimization of program code.