The Research And Application Of High Accuracy Finite Difference Wave Field Forward Modeling

The finite difference method for wave equation forward modeling, theunderstanding of seismic wave propagation, seismic attribute studies and geologicalinterpretation of seismic data, reservoir evaluation, has important theoretical andpractical significance.The seismological including two core theory first reveals the wave theory ofseismic waves dynamic characteristics of the two is to reveal the kinematiccharacteristics of the seismic wave ray theory. Therefore, based on two theories in theforward modeling to produce the two branches of the forward method based on wavetheory and forward method based on ray theory. The wave theory of the forwardmethod is the model grid, using the difference method or finite element methods,according to the wave equation approximation, calculate the wave field in the longiteration time step to obtain the forward wave field simulation results. It ischaracterized to be able to accurately reveal the changes of amplitude, frequency,phase, wave propagation in the medium, a true reflection of the wave kineticcharacteristics of the wave field research. Solving the wave equation using finitedifference techniques, will cause unnecessary vibration, numerical dispersion.Numerical frequency, The dispersion of a serious impact on the simulation results, toreduce the simulation accuracy. This article discusses the cause of numericaldispersion, and gives a higher order differential equations and the flux correctedtransport (FCT) a combination of approaches to eliminate the dispersion.To the wave equation and Taylor formula, the derivation of the elastic waveequation in spatial and temporal accuracy of any order staggered grid finite differenceformat, the format of the differential high precision, can be applied to complexmedia model, forward modeling, also the stability of the dispersion phenomena andboundary conditions. Then simulated based on the elastic wave equation in isotropicmedia and anisotropic media, the elastic wave field, obtained by forward modelingresults clearly reflect the kinematic and dynamic characteristics of the seismic wavefield wave propagation. According to the actual exploration of the situation, based on the acoustic wave equation is modeling and reverse time migration.In this paper, the theoretical model and the actual complex structural modelnumerical experiments to verify the order staggered grid finite difference fluxcorrected transport (FCT) algorithm combining the effects of forward modeling andreverse time migration. The experimental results show that the order staggered gridfinite-difference and flux corrected transport (FCT) method of combining efficient,accurate, and useful features, has broad application prospects and practicalsignificance.