Study On Forward Modeling For Irregular Free-surface In VTI Media

In the process of seismic exploration,the undulating surface is common.Due to the complex surface structure brings many difficulties to seismic exploration,eliminating the influence of surface topography on seismic data has always been a worldwide difficult problem in seismic exploration.Violent terrain fluctuations have a great impact on the mode of propagation of seismic waves.It causes the strong scattering and diffraction of body and surface waves,resulting in the mode transformation between various wave patterns.The wave field becomes richer and more complex,and the waveforms will also be distorted,which will bring great difficulties to the subsequent processing such as static correction.The real underground medium is anisotropic.If the seismic data processing method based on isotropic medium is applied to deal with seismic data of anisotropic medium,it will result in seismic resolution reduction and seismic imaging error.Therefore,the research of seismic anisotropy is the development trend of seismologists' cognition of earth media and seismological research.As a "boundary fitted grid",the body fitted grid can effectively improve the false diffraction produced by the existence of stepped grids when the traditional finite difference processes the rough terrain.Based on the body fitted grid,the forward modeling of VTI medium under the surface condition is studied.In this paper,based on the basic theory of elastic medium,the wave equation of VTI medium in Descartes coordinates is derived.The characteristics of seismic wave propagation in VTI medium are analyzed by forward modeling and model trial calculation.Then based on the body fitted grid,the wave equation of the VTI medium in the curvilinear coordinate system is derived.Then the boundary condition and the wave equation are discrete,and the finite difference scheme is deduced.At last,the double influence of VTI medium and undulating terrain is analyzed by forward modeling and model trial,and the forward modeling of complex surface VTI medium is realized.