Study On Forward Modeling For Irregular Free-Surface In Viscoelastic Media Based On Body-Fitted Grid

Real earth media are anelastic,which affects both the kinematics and dynamics of propagating waves: waves are attenuated and dispersed.If anelastic effects are neglected,it is difficult to obtain detailed subsurface information and high resolution image directly.The anelastic effects in real rocks can be well described by a viscoelastic model.And forward modeling is the base of migration and inversion.So the numerical simulation in viscoelastic media are researched and studied in this thesis.On the other hand,rough topography is very common,especially in western China,because of the extrusion of Indian Plate.Irregular free surface would have rather huge influences on seismic wave propagating,which induces strong scattering and diffraction and makes the wave field more complicated with waveform distortion.The research on the propagation of seismic wave with irregular surface has an important significance to the design of observation system,data processing and interpretation,and the development of inversion algorithm.Body-fitted grid is usually termed as “boundary conforming grid”,and it can eliminate the artifacts caused by staircase approximation of irregular free surface using classical finite-difference method.This paper models seismic wave in viscoelastic media with irregular free surface.Starting from basic theory of viscoelastic media,we deduce the viscoelstic wave equation of GSLS,and develop and consummate the high-order staggered grid finite-difference method which solves the wave equation.Based on body-fitted grid,we adopts a Lebedev Grid as the new kind of staggered grid scheme for curvilinear coordinate's finite-difference modeling in viscoelastic media,and this scheme can avoid the numerical error from the interpolate wavefield compared to Standard Staggered Grid.In process of simulation,first of all,we deduced viscoelastic medium wave equation based on the generalized standard linear solid under the curved coordinate system,then discrete the wave equation with Lebedev Grid finite-difference scheme which is usually used in anisotropy media.The traction image method is used to implement the free surface conditions.Numerical tests on synthetic data analyze the dual impacts both viscosity and topographyPerfectly Matched Layer(PML)absorbing boundary is certified an efficient method to suppress spurious edge reflections.However,when modeling Rayleigh waves with the existence of irregular free-surface,the classical PML algorithm may become unstable.In order to implement stable seismic wave simulation with an irregular free-surface,in this paper,we extend the boundary condition to the improved PML and compare stability of the four perfectly matched layer techniques and figure out the instability mechanism of PML.The numerical results suggest that MC-PML technique,which combines M-PML with C-PML,obtains both higher stability and better absorption effect.