Discussion On Seismic Modeling And Numerical Dispersion Correcting In Double-Phase Medium Based On Reformulated BISQ Model

The double-phase medium theory considered fully the medium structure, the fluid and the gas special nature, the partial characteristic and the overall effect relations, can describe the actual stratum configuration and the stratum nature accurately. It can meet the actual needs of more and more complex oil gas preserve exploration naturally.Both of the Biot-flow and squirt-flow are important mechanisms for the fluid flow in the double-phase media. The BISQ equation including the two mechanical mechanisms can reflect the propagation law of seismic wave. But the BISQ model formula is complex and not good in practice. The reformulated BISQ model formula is simple and convenient for computation. The simulation result can reflect the wave-field propagation characteristics of double-phase media exactly and effectively.The dissertation, firstly the method of high-order staggered-grid finite-difference is described, base on first-order velocity-stress equations of reformulated BISQ theory in double-phase media, this paper constructs the simulation algorithm of the finite difference of 2-order time and 2N-order space staggered grids; and then discusses the two-dimensional first-order stress-velocity elastic wave equation in staggered difference schemes, boundary conditions, source functions, differential format compatibility, convergence and stability, and gives flow charts of the whole procedure; secondly, describes the dispersion of wave phenomena, wave equation derived from dispersion relations, the distinction between dispersion phenomena in the physical dispersion and dispersion, and explains the causes of numerical dispersion and eliminating method; thirdly, describes the basic theory and the FCT method calculation steps, and the algorithm of the finite difference of staggered grids is obtained; finally, The algorithm is validated by simulating the wave-fields in isotropic double-phase media and the influence of physical parameters, such as porosity, coefficient of viscosity and coupling density on seismic wave propagation law are respectively researched to obtain the propagation law in double-phase media. The results are:Firstly, the existence of "fast" compressional wave P1,"slow" compressional wave P2 and shear wave S V in wave-fiedls is accord with the response of the model, which shows that the simulation algorithm of staggered grids is viable; Secondly, With the use of algorithm of staggered grids which is corrected by FCT, dispersion can be effectively suppressed and the real wave-fields oscillation can be retained as well.