Comparative Study Of Finite Difference Method And Pseudo Spectral Method In Three-Dimensional Seismic Wave Simulation

In seismic prospecting,in order to invert or study the propagation properties of seismic waves in some complex media,it is always needed to simulate wave field.Since the finite difference method(FDM)has been applied to the simulation of seismic waves and successfully simulated the propagation of seismic waves in the underground,the finite difference method is becoming more and more popular in seismic wave simulation because of it's simplicity,intuition and high efficiency.The finite difference method directly starts from the wave equation and uses the difference method to solve the time derivative and the spatial derivative.The main disadvantage is that the numerical dispersion can be caused when the grid space is rough,and the precision is not very high.The calculation time and the memory occupation are greatly increased when using the fine grid space,especially in the case of three dimensions and above.Kosloff and Baysa put forward a method of solving wave equation by Fourier transform,which is called pseudo spectral method(PSM).The time derivative of pseudospectral method is the same as the finite difference method,and the spatial derivative is solved by the fast Fourier transform(FFT).Due to the accuracy of the fast Fourier transform,pseudospectral method can suppress dispersion effectively and improve the accuracy.The implicit periodicity of the fast Fourier transform will reduce the accuracy of the wave field simulation,and the high complexity of the fast Fourier transform will also hurt the efficiency of the pseudospectral method.On the other hand,the pseudospectral method can simulate precise result when using the coarse mesh spacing,which can reduce the number of grid points and thus improve the efficiency and save memory.In order to study the characteristics of the two methods,the accuracy,calculation efficiency and memory occupancy of the two methods are compared in detail,and the comparison of the accuracy is realized with the analytical solution of wave equation.It is found in the 3D seismic wave simulation that the finite difference method using fine mesh spacing and the pseudospectral method using the coarse mesh spacing both can suppress the dispersion(the simulated waveform has no trailing).The simulation results have different defects compared with the analytical solutions.In general,the accuracy of the pseudo spectral method is higher,and because the grid points of pseudospectral method are less,the time and memory of pseudospectral method is also less,so pseudospectral method is more suitable for 3D seismic wave simulation.