Seismic Wave Field Numerical Modeling Based On High-order Finite-differentical Method

Seismic wave filed numerical model calculation is an available method for seismic information acquisition,processing and interpretation of a complex area. It has two major species, one is geometry rays method and the other is wave equation method. Finite differential method is an important one of the wave equation solving methods. Its advantages are fast speed in calculation and less memory occupation. Its disadvantages is low precision. It only fits simple geophysics.Based on the previous research, starting from the establishment of wave equation, I derive the center finite-difference of displacement equation and the any order space and accurate time formulation of one-order stress-velocity equation. In order to deal with large computer storage and long time of calculation in the finite-difference modeling of seismic wave, we use finite domains to substitute for infinite domains, which is to say an artificial boundary need to be introduced. Reflection wave from artificial boundary is so strong that it can destroy seismic wave field, therefore the way of effectively absorbing reflection wave from artificial boundary is a very important research subject in seismic wave numerical simulation. There are many kinds of solvents for the artificial condition, we focused on the following two methods in the paper, the transmitting boundary condition and the perfectly matched layer. At the same, the paper analyze its stability and dispersion properties. Then implement two different equations modeling in istotropic medium and modeling one-order stress-velocity equation in transversely istotropic medium with Fortran language.Based on the theory above, from the computation of model and the effect validation we can know that staggered-grid finite-difference scheme based on the one-order stress-velocity equation has a high accuracy. It can be used to forward simulation for more complex medium model. The test result can reflect the characters of dynamics and kinematics of waves in seismic wave-field. The test results demonstrate that the high-order staggered-grid finite-difference scheme can be efficient and sufficiently accurate. It may also be an effective and robust tool in wide areas involving the numerical computation of partial differential equations.