Numerical Simulation Of Two-dimensional Transverse Isotropic Dielectric Wave Equation By Pseudo-spectral Method

The actual internal medium of the earth is often not under our ideal conditions,generally widely exist in the an-isotropic fluctuations,and there are a variety of seismic wave an-isotropic forms,the main performance of seismic wave propagation speed and direction of the relationship between the function,seismic wave shear wave splitting.At present,for the research of seismic an-isotropic,has become a hot of seismological research frontiers of an-isotropic research for the development of comprehensive cognitive structure of the earth's interior medium,looking for favorable complex trap(reservoirs)and geological investigation,shock absorption and reduction is of great importance in such aspects as theoretical basis for guidance and practical application value.The most direct mathematical method to understand the earth's interior is to conduct numerical simulation of seismic waves by simulating the propagation characteristics of seismic waves in underground media.There are many methods for forward numerical simulation,the most common of which are finite difference(FDM),finite element(FEM)and pseudo-spectral(PSM).As the most simple and direct numerical simulation method,finite difference method is widely used and relatively mature.However,it still has some more or less defects,such as improving the calculation accuracy while reducing the operation efficiency,and encountering stability problems at the formation interface where poisson's ratio changes greatly.Considering the accuracy and efficiency of numerical simulation,it is very important to select a middle method for numerical simulation of elastic wave.And the core of the pseudo-spectral method is by simplify the complexity of derivation on spatial domain discretization,thus improve the efficiency,it is a kind of formula through fast Fourier(FFT)to transform spatial domain to the time-wave number domain to calculation method,to avoid the direct derivation of trouble on the spatial domain,just as a simple difference operation can in time domain.Compared with finite difference method,pseudo-spectral method has the advantages of high simulation accuracy,small memory and high computational efficiency.However,it has its own limitations and is not suitable for complex media with undulating interfaces.This thesis mainly discusses the based on an-isotropic medium pseudo-spectral method of seismic wave field numerical simulation,the main contents include the following aspects:(1)the pseudo spectral method of numerical simulation of the basic theoretical knowledge and problems,considering the derivation of basic problems including the pseudo-spectral method principle,spatial grid subdivision,seismic wavelet source selection and the boundary conditions and stability,etc.;(2)the pseudo-spectral method for elastic wave field numerical simulation of isotropic medium was compared with the finite difference method,and different types of isotropic medium models were selected for corresponding wave field numerical simulation research;(3)pseudo-spectral elastic wave numerical simulation of an-isotropic media: this paper mainly discusses three transverse isotropic media,VTI,HTI and TTI,and USES Thomsen parameter characterization to realize the corresponding numerical simulation program of TI medium elastic wave pseudo-spectral method.The wave field characteristics of TI media under different media models are simulated.The simulation results show that the pseudo-spectral method is an accurate seismic numerical simulation method,which is beneficial to the study of wave field characteristics of an-isotropic media.