Finite Difference Time Domain Wave Equation Seismic Forward Modeling Method Research

The rapid development of computer technology is making Full WaveformInversion from theory research to the seismic exploration practical seismic explorationbecoming possible. The finite-difference time-domain forward modeling technology ofwave equation is one of the key technologies in the Full Waveform Inversion. The focusof this paper is on the forward problem part of the Full Waveform Inversion method.The main researches and innovations of this paper are as follows:(1) From the point of view of solid mechanics, We analysis three commonly earthmedium model, and then give their corresponding mathematical physics wave equations,the acoustic wave equation of which is the main research object.(2) This paper mainly researches the regular grid and the staggered gridfinite-difference discrete formats of acoustic wave equation. Firstly, we derivedifferential approximation in the space and time derivatives of acoustic wave equation,respectively by the regular grid and the staggered grid finite difference method. Andthen we develop the high order finite difference formats of acoustic wave equation. Weconduct model calculations, and comparatively analysis the forward effect in thesituation of different grid spacing, time step and space differential accuracy.(3) We research the key problems of the finite-difference time-domain forwardmodeling technology, such as the source function, the initial conditions, stabilityconditions, boundary conditions and frequency dispersion problem. Through modelingcalculation, we give the appropriate wavelet frequency range and the spatial attenuationfactor of source function. We analyze the effect between absorbing boundary conditionand the perfectly matched layer technology by modeling calculation. We research theFlux Corrected Transport technology respectively in the regular grid and the staggeredgrid finite-difference discrete formats. In order to verify the effectivity of the FluxCorrected Transport technology and the four order difference accuracy, we conductmodel calculations to suppress the numerical frequency dispersion.(4) We develop seismic wave equation time-domain finite-difference forward modeling module in Windows system, VC++platform. And we make several commongeological model into forward modeling to demonstrate the validity by the forwardmodeling method of this paper.