Method Study Of High-order Finite Difference Numerical Modeling

At present, Oil and gas exploration is turning to the areas with irregulartopography and complex geologic structures. The complex geological structure, require better and more accurate method to simulate the real underground wave field propagation. To increase seismic wave numerical simulation accuracy, the high-order finite difference method which is to process numerical modeling and wave field analysis is used.Firstly, This paper derive simply high order differential approximation in the space and time derivatives of seismic wave field .The regular Grid high-order finite difference and staggered grid high-order difference numerical simulation is used to the acoustic wave equation ,the modeling results indicate that high-order staggered grid finite but also has good simulation results and highefficiency. In addition, an annoying problem in the seismic wave modeling is the seismic topography. The finite-difference seismic modeling method based on triangular grids method can be used to describe more accurately irregular surface and curved boundaries. On this basis, we achieve the numerical modeling of 2-D elastic wave equation, viscoacoustic wave equation and viscoelastic wave equation (Kelvin model) using the high-order staggered grid finite difference, derive the first-order velocity-stress elastic wave-field decomposition equation, and successfully obtain totally separated wave-field of pure P-wave and S-wave from the hybrid wave-field, from received the wave-fields snap and shot records in numerical modeling, to analyze reflection, transmission, diffraction, Scattering and attenuation of energy kinematic and dynamic characteristics in complex medium.Stability, numerical dispersion and boundary condition are the several key problems in the seismic modeling. By comparing the merits and demerits of boundary conditions, the combining boundary condition is used to eliminate the boundary reflection well, the flux-corrected transport method is used to avoid both space-grid dispersion and time-grid dispersion and high-order difference can to some extent reduce the numerical dispersion and improve accuracy.We analyze simply stability of staggered grid high-order finite difference method in the acoustic and elastic wave equation .The test results of various model proved that this method applied is characteristic of good stability and high simulation precision.