Adaptive Mesh Refinement Algorithm Modeling Of Seismic Wave Propagation

Numerical method solving wave equation has been always an important research topic in the fields of geophysics and computiaonal mathematics. Numerical modeling of seismic wave propagation phenomena can provide a theoretical basis for earthquake prediction and seismic exploration. Existing numerical methods modeling of wave propagtion can gain good numerical solution using the fine mesh, but the computional time and computional storage will be increased. It has been the key to solving seismic wave equation that using high efficient numerical method modeling of seismic wave propagation phenomena.It is difficult for numerical modeling of seismic wave propagtion, because the subsurface media has complex distribution and wave volocity changing between discontinuous media. High resolution numerical solution can be obtained wave propagation in discontinuous media using high resolution finite volume method. In the thesis, high resolution finite volume method has been used to solve acoustic and elastic wave equations. The wave propagation operator is constructed, and it is implemented by wave correction limited. Numerical examples show that the numerical method can not only obtain high resolution snapshots of wave field, but also effectively control of numerical oscillations. The comparison of numerical solutions and exact solutions is given, and dispersion analysis is obtained. It is proved that the numerical method is effective for solving seismic wave equations.In order to improve the computational efficiency for modeling of seismic wave propagation, a combination of adaptive mesh refinement and high resolution finite volume algorithm is presented for solving seismic acoustic and elastic wave equations. The numerical solutions are obtained using high resolution finite volume method on the coarse mesh, then the local truncation error is gained by the error estimation procedure. If the truncation error is greater than a given threshold value, the local rectangular region is refined. The fine mesh will be nested in the coarse mesh. Adaptive mesh refinement algorithm can automatic generated of nested-type of adaptive mesh, and the time step with space step is refined. The grid pionts are stored by a tree data structure. Using adaptive mesh and non-adaptive solve of seismic acoustic and elastic equations, the computational time and compuation storage will be compared, the results indicated that adaptive mesh refinement algorithm is high efficient.Second generation wavelet transform is obtained by lifting scheme, its compational speed is faster than wavelet transform, and it maintains the characteristic of multi-level decomposition. In the thesis, second generation wavelet is used to construct nested-type adaptive mesh solving of two-dimensional acoustic wave equation, and the spatial derivatives of grid points are obtained by finite difference method. The snapshots of wave field are obtained by numerical modeling of acoustic wave propagation. Compuational accuracy analysis and the comparesion of computational efficiency are given. The applicability of adaptive mesh based on second generation wavelet solving wave equation is proved by numerical experiment results.