Comparative Study On Numerical Simulation Methods Of Elastic Wave Propagation Under Undulating Ground

With the increase of the exploration intensity in the complex area of the surface velocity,the velocity structure of the seismic exploration area is becoming more and more complex.In particular,area in China's western regions and the Piedmont,due to the influence of tectonic movement and weathering,the surface structure is particularly complex,low velocity anomalies exist generally,caused by the surface of the low signal-to-noise ratio and static correction problem of complex and difficult arrangement of observation system and other issues are affecting the work of complex regional earthquake.In order to study and solve this series of practical problems,it is necessary to have a clear understanding of the propagation law of seismic waves under the complex surface.In the study of seismic wave propagation,the geophysical community generally accept the numerical simulation of seismic wave propagation,that is,the usual forward modeling.The algorithm of forward modeling has many advantages,and the finite difference method and spectral element method are selected for the study.The finite difference method uses the difference scheme instead of the spatial partial derivation term.This method is widely used because of its low programming difficulty,high computation efficiency and the applicability to complex geological models.Spectral element method,as a high-order finite element method,has the computational efficiency of the finite element method and the spectral method,which has attracted more and more attention.This paper first summarizes the numerical simulation methods of seismic waves under complex surface conditions,and then starting from the finite difference method and spectral element method completed the following research work:(1)through the stress free boundary conditions after the implementation of the image method,using staggered grid difference finish rolling surface elastic wave equation finite difference method for numerical simulation(2)in the weak form based on elastics wave equation,using Galerkin spectral expansion method,Lagrange interpolation function and Gauss-Lobatto-Legendre integral method,the irregular surface elastic wave equation,spectral element method numerical simulation;(3)computational efficiency and computer memory usage accuracy,compared with the finite difference method and spectral element method;(4)using the spectral element method of surface and complex surface velocity model for numerical simulation of elastic wave propagation,and the wave field characteristics are analyzed in detail.Through the study found that:(1)the calculation accuracy of the spectral element method is higher than that of the finite difference method;(2)finite difference method,the computing time and computer memory is less than the spectral element method,but did not improve because of its numerical scattering caused by rectangular grid division;(3)in the rolling surface model of elastic wave propagation model great changes have taken place,the scattering wave and also affect the record,this is also the reason for the low fluctuation ratio signal-to-noise surface.