Staggered Grid Numerical Simulation Of Seismic Wave Field In Viscoelastic Vertical Anisotropic Media

Numerical simulation method of seismic wave field is not only an important foundation of geophysical exploration,but also an important part of geophysical exploration.It has the advantages of simple description model and flexible parameter selection,and plays an important role in studying the dynamics and kinematics of seismic wave propagation.When the parameters and structures of underground media are known,the propagation law of seismic wave in underground media can be studied and analyzed by numerical calculation method,and then the wave field snapshots and synthetic seismograms at different times can be obtained,which is of great significance to comprehensively and thoroughly understand the law and mechanism of seismic wave propagation.There are three kinds of numerical simulation methods for wave field forward modeling,among which the wave equation method is the most important one.The simulation results obtained by this method can reflect the dynamic and kinematic information of seismic wave propagation,and provide a basis for the study of wave field of complex geological structures.This method also plays an important role in the process of seismic data acquisition,processing and interpretation,so it has been widely used.The finite difference method is one of the classical methods,which has the advantages of fast calculation speed,small memory occupancy and high accuracy.Its principle is to simplify the underground geological body into a model and divide the model area into finite grids;then use discrete space and time to replace the continuous physical quantity,use the approximate relation of difference and differential,and change the wave equation of differential form into the difference equation suitable for calculation;then give an initial condition and use the wave field of the front time in space.Distribution and variation of values are used to derive thedistribution of wave field values at the present time,so as to simulate the propagation of seismic waves.In the process of numerical simulation,we usually assume that the underground medium is a completely elastic isotropic medium.,however,the actual earth medium is not an ideal elastomer,it has a certain viscosity;Energy will be absorbed when seismic wave propagates in medium.At the same time,the high frequency component of seismic wave will decay and the amplitude will decrease,so that we can not get detailed underground information directly.In addition,In the study of seismic wave propagation,the homogeneous isotropic medium is usually used to approximate the real medium.This simplification will cause considerable errors.Therefore,we use viscoelastic anisotropic medium model to simulate,so as to be more objective and accurate.In this paper,based on wave theory,staggered grid high-order finite difference numerical simulation method is used to obtain high-order staggered grid finite difference schemes suitable for wave equation.The PML absorbing boundary conditions are used to simulate the elastic and viscoelastic isotropic media,VTI media,HTI media and TTI media.At the same time,by comparing the similarities and differences of simulation results under different quality factors,the relationship between Q value and medium viscoelasticity is analyzed.In addition,the forward modeling of layered medium model and fault medium model is also carried out,and the simulation results contain abundant fluctuation information.The simulation results show that the simulation method is correct and effective,with high accuracy and reliability.