Simulation Modeling Of Seismic Wave Field In TI Mediu

The seismic wave equation is a hyperbolic partial differential equation and the finite difference method uses the difference quotient to replace the partial derivative to solve the wave equation.The advantage is that the mathematical calculation is simple,easy to be realized and has good adaptability.It is an important numerical simulation technique to study the law of seismic wave propagation in seismology.In this paper,the staggered grid finite difference method is applied to simulate the seismic wave field in isotropic and anisotropic media.Anisotropic phenomenon is widespread in sedimentary rocks.In theory,TI medium is usually described by VTI and HTI medium models.The TI medium has columnar symmetry,its symmetrical axis is called VTI medium in space vertical direction,and it is called HTI medium in space level.When the polarization angle of VTI medium or the azimuth angle of HTI medium are not 0 degrees.VTI medium becomes polarized medium,and HTI medium becomes azimuthal anisotropy.In this paper,the wave equations of anisotropic medium(TTI medium,VTI medium)are derived and discrete,and the propagation of seismic waves in different media is simulated by the staggered grid finite difference method.Through the comparison and analysis of the simulation results,it is found that the use of the staggered grid finite difference method can reduce the numerical dispersion at a certain level,but cannot eliminate it completely.The frequency dispersion can be alleviated with the improvement of the difference precision,but after a certain order,the improved effect can be weaken obviously.When the seismic wave propagates in isotropy medium,the velocity of each particle is the same in different directions,and the wave field is the standard circle.Shear wave splitting occurs when seismic waves propagate in anisotropic media.,the shear wave field is divided into fast transverse wave(qS1 wave)and slow transverse wave(qS2 wave)when it passes through the anisotropic media,and the shape of the dielectric wave field is controlled by the elastic parameters.In this paper,the wave field under different elastic parameters of the VTI medium is compared,and the different beta wave fields of the TTI medium are also compared.Using the attenuation boundary condition combined with the PML boundary condition,we can effectively reduce the boundary reflection and refraction phenomenon,and help us understand the propagation path of wave in the underground medium.Based on the simulation results of homogeneous medium and mixed double model,The simulation results show that staggered grid finite difference method can well solve the problem of seismic wave propagation in complex media.