Reverse Time Migration Of Seismic Data Based On Boundary-conforming Grids

Finite difference method(FDM)is fast and accurate,so it is one of the most widely used solution method for numerical simulation of wave equation.However,when surface topography and irregular interfaces exist,finite difference method faces obstacles since the discretization by regular grids usually bring the staircase approximation and degrade the accuracy of simulation.Boundary-conforming grids by the elliptic method provide an effective tool for finite difference wavefield simulation in complicated domains containing not only surface topography but also irregular interfaces.By such grids,the calculations of spatial derivatives are transformed by a chain rule into those in the regular computational space,where traditional finite difference schemes are still applicable.Boundary-conforming grids are superior to other irregular grid methods,such as interpolation method,mapping method and unstructured grids,on the aspects of generality,in accuracy and stability.This thesis comprehensively applies the boundary-confroming grids and acoustic wave equation simulation,reverse time migration(RTM),perfectly matched layers(PML)in complicated regions.First the boundary-conforming grids are generated by solving elliptic partial differential equations.Due to the different order in substituation of chain rule,two forms of the two-dimensional acoustic wave equation in second order displacement formulation are reformulated into the boundary-conforming grid system.The first form of wave equation is more symmetric and more compact compared with the second one.Two forms of perfectly matched layers corresponding with the wave equation in curvilinear coordinate system are derived to suppress artificial reflections caused by truncating the boundaries.The explicit summation-by-parts finite difference operator is a natural way to use for discretization for wavefield simulation in complicated domains containing surface topography.The application of SBP finite difference method guarantees stability of the numerical approximation for heterogeneous materials on curvilinear grids.It is especially suitable to deal with the solution of derivative term with viarable coefficients.Aiming at the two forms of wave equations and PMLs,different finite difference methods are applied.Central finite difference method is used for the first form of equation where the coefficient of derivative terms can be precalculated.The explicit second order accuracy SBP finite difference method is applied for the second form of wave equation and PML where viarable coefficients exist.The stability of the SBP finite difference scheme is analyzed by Fourier spectral method.Compared with finite difference method,the second order SBP method is more stable.The finite difference scheme of fourth order accuracy is known advantageous in reducing memory and improving efficiency.The discretizations for derivative terms of acoustic wave equation and perfect matched layer in boundary-conforming grids by the second order accuracy SBP finite difference method are extended to the fourth order accuracy.The stability of the fourth order SBP finite difference scheme is analyzed by Fourier spectral method,and it is verified that the fourth order accuracy SBP finite difference method is more stable than central finite difference method.Meanwhile,the computing time and memory requirement by second and fourth order accuracy SBP finite difference methods are compared in the model of same size.It is illustrated that the fourth order method has the properties of high accuracy and low dispersion,and the ability in improving efficiency and decreasing memory requirement.The technique of boundary-conforming grids is applied to the reverse time migration of surface seismic and vertical seismic profiling(VSP)data respectively in this thesis.The corresponding imaging data volumes in curvilinear coordinate system are obtained.It offers an effective technical means for dealing with the problem of data processing in regions with irregular geometry and surface topography in seismic data acquisition.