Seismic Data Curved Grid Simulation With Stack Depth Migration

When applying the conventional Fourier pseudospectral method on Cartesian grids, curved interfaces are represented in a 'staircase fashion' causing spurious diffractions. It is demonstrated that these non-physical diffractions can be eliminated by using curved grids that generally follow all curved interfaces.The curved grids are generated by using the transfinite interpolation and the so-called multiblock techniques that originally developed for computation fluid dynamics. The curved grid is taken to constitute a generalized curvilinear system. Thus, the wave equations have to be written in curvilinear coordinates before applying the numerical scheme. Because the grid is Cartesian in the curvilinear domain, standard pseudospectral technique can be applied. At last the synthetic record of physical configuration can be evaluated. Compared to similar methods on Cartesian grids, the same accuracy is obtained with a lot fewer grid points, which means that considerable savings in computer memory can be obtained. This fact has an important implication for extension to 3D configurations. Comparing the synthetic seismogram by using Cartesian grids with the synthetic seismogram by using the curved grid, it can prove the approach is effective.A hybrid migration method, named "Fourier finite-difference migration", is a post-stack depth migration scheme. The downward extrapolation operator is split into three operators: one operator is a phase-shift operator for a chosen constant background velocity, another operator is the well-known first-order correction term, and the third operator is a finite-difference operator for the varying of the velocity function. Phase-shift downward extrapolation and finite-difference downward extrapolation preserves the advantage of phase-shift method and finite-difference method. So FFD migration method is an effective scheme. In the thesis, the fundamental formula of FFD method derives from the square root that is approximated by a continued fraction expansion in the one-way wave equation. Optimizations of the parameters of the finite-difference operator improve the validity of the method.