Parallel WNAD Algorithm And Its Wave Fields Simulation

A fast, high efficient forward modeling method with low numerical dispersioncan improve the inversion accuracy and accelerate the inversion procedure. It'ssignificantly important to conduct forward modeling research of seismic wave field.In this thesis, I extend and give a3D parallel Weighted Nearly Analytical Discrete(WNAD) algorithm for the elastic wave simulation in the3D model. The stability,dispersion relation, speedup and parallel efficiency of the WNAD algorithm areinvestigated by using the nonlinear optimization theory, Monto-Carlo method, andFourier analysis. Theoretical analysis reveals that the WNAD can effectivelysuppress the numerical dispersion and has a good performance in capturing theinformation on a amplitude and phase when large spatial steps are adopted. Itsuggests that we can reduce the storage and improve the computationalefficiency by using the WNAD method with coarser grid. Meanwhile, as thespatial discrete operators of the WNAD method only involve three points inone direction, the speedup and the parallel efficiency of the WNAD are higherthan conventional finite-difference methods. In fact, Numerical results of thisthesis show that the computational speed of the parallel WNAD is about6.38times ofthe SG method on a finer grid by using the same number of processors. Additionaly,the required memory of the WNAD is about14.8%of that of the SG method and therequired communication of WNAD is about14.8%of that of the SG method. Byusing the parallel the WNAD algorithm, I have thorough analysis of the elastics wavepropagating in TI media. The important anisotropic features (such as the wavesvelocities varying with the propagation directions, the cusps generated by body wavescoupling and the shear wave splitting) are observed. I also study the elastic wavesreflected, refracted and converted at the three basic discontinuities fault. All of thewave fields are very clear without any numerical dispsion. It means the parallelWNAD can be used to study the wave propagating in complex earth media.This thesis also studies the free surface problem by combining the WNAD algorithm with the stress images method. It's convenient to handle the free surfaceproblem for the WNAD algorithm calculated the displacement gradient.Furthermore, in order to meet with the actual requirements in exploration, Ihave developed a non-uniform algorithm based on the WNAD method. Toobtain the accurate information on wavefield, fine grids are needed near thefree surface, in the low-velocity zones and other regions with special interests,while in the rest computational domain coarse grids are used to speed up thesimulation. Hermite interpolation is used in the transferring regions to reduceartificial noises. All these treatments further improve the efficiency of theforward modelling.