The Research Of Finite Difference-Pseudospectral Hybrid Approach For Reverse Time Migration

Finite difference method is widely used in seismic wave field calculation as a result of its simple algorithm, high calculation efficiency and wide application. Pseudospectral method(PSM) has higher accuracy in solving spatial derivative, its calculation accuracy is extremely high, PSM can be also use a larger grid and guarantee accuracy. In this paper, I combine the characteristics of the finite difference method and pseudospectral method, using the staggered-grid finite difference algorithm in a spatial coordinate direction and using pseudo-spectral algorithm in the other direction of spatial coordinates, forming a hybrid calculation method of reverse-time migration.Staggered grid high-order finite-difference compute wave field with half grid, thus its calculation accuracy and stability are better than calculation in center grid. I deduce difference scheme that time 2M order accuracy and space 2 N order accuracy basing on staggered-grid. I introduce the principle of calculating partial derivative with pseudo-spectral method, giving pseudo-spectral method operator that suitable for staggered grid, and examining the operator precision of the pseudo-spectral method and finite difference method respectively, finding the accuracy of pseudo-spectral method operator is the staggered-grid finite difference method operator derivation limit value. Taking acoustic wave equation as an example, I give the reverse extrapolation equation in finite difference- pseudo-spectral hybrid method, and analyze its stability and numerical dispersion based on the concrete model case. I describe the basic theory and achieve reverse-time migration with the hybrid method, also introduce two important factors that the reverse-time migration implementation involved: boundary conditions, imaging conditions. The numerical example of using attenuation absorbing boundary indicates that boundary reflection interference can effectively eliminated and the effect to wave field calculation area can be reduced.The paper presents the results of the hybrid method post-stack migration for the different model data and the real data, and compares the imaging precision of the hybrid method and finite difference method. The results indicate the hybrid method is superior to the pure staggered grid high-order finite difference method in imaging precision. The examples of synthetic and real data show that combine the finite difference-pseudospectral hybrid method have good adaptability and imaging precision in complex model migration with large dip angle, strong vertical and lateral velocity changes. Therefore, the finite difference-pseudospectral hybrid method can meet the needs of complex structure imaging. The hybrid method is a reliable and effective seismic migration method that has stronger practicability.