Seismic Wavefield Modeling By Pseudo Spectral Method

The pseudo-spectral method (PSM) is an important numerical modeling technique, whichhas successfully been applied for the seismic wave propagation simulation. The PSM schemeuses a fast Fourier transform (FFT) for calculating spatial derivatives in wave equation, whichcan obtain accurate results even employing a larger grid intervals in the simulation modelingwhen compared with a low-order finite-difference scheme.This thesis includes three parts:(1) the introduction of wave field modeling by using PSMalgorithm;(2) wave field modeling in isotropic medium and (3) wave field modeling inanisotropic medium, such as VTI, HTI and TTI media.In the first part, we firstly discuss some important elements of the PSM, such as the meshgeneration, the boundary condition, the numerical stable condition for calculation and so on.Considering the importance of the stable condition, we derive the formula for the stablecondition by using the Von Neumann method in detail.With respect to the wavefield modeling in the isotropic medium, we design several typicalmodels: lamellar, fault, basin model and so on. From the wavefield modeling in basin model,we successfully observe the strongly ground motion phenomenon regardless of the sourcelocation.Regarding the anisotropic media, we briefly introduce and discuss about anisotropicmedia’s property first, and then give the classification of anisotropic media and the Thomsonparameters. Then we choose the vertical transverse isotropy (VTI), the horizontaltransverse isotropy (HTI) and the tilt transverse isotropy (TTI) as objects of study,which are the typical examples of transverse isotropy. The numerical results show thatthe PSM scheme is an efficient and accurate numerical modeling technique for seismicwave propagation.