Staggered-Grid Finite Difference Method For Numerical Simulation Of The Improved BISQ Model

Seismic wave exploration is the most widely used method for exploration and development of energy resources. Most of the major mineral and energy resources are buried in the Earth's lithosphere,which is of complicated geometry structures and complex physical properties.In practical engineering exploration, the complicated structure in the stratum which contains natural resources is usually simplified to a model in order to apply numerical simulation. It is hard to avoid errors during the simplification, which is because it will cause the inaccuracy in numerical simulation and thus will not match with the actual underground conditions. Therefore, establishing a more realistic numerical simulation of geological structure is the key of quickly resolving the issue in the field of seismic exploration nowadays.In seismic exploration, the two-phase medium wave theory can be used into practice to solve the problem of exploration. Seismic waves can be regarded as elastic waves spreading in the bed stratum, and elastic theory is the foundation of the elastic waves study. The paper is based on the numerical simulation with finite difference method by improving BISQ theory, and Improving BISQ theory is based on Biot assumption. Solid skeleton and interconnected pores form the fluid saturated porous media, and connected pores is filled with viscous fluid which is flow and can be compressed. The media formed by the solid skeleton and the fluid media is the basis of the theoretical research, which is closer to exploration and the actual situationStaggered-grid finite difference method is widely used in the numerical simulation of the two-phase media in the Seismic wave. Based on the improved BISQ model, we transform the elastic wave equation with two-dimensional (x, z) case into difference discrete situation with the method of staggered-grid finite difference, then use perfectly matched layer PML to absorb boundary reflection. By improving the PML difference scheme with the method of assigning the average of its two adjacent grid points to the variable in semi-grid point, we can eliminate the effect of artificial boundary reflection effectively. Then, by using FCT (Flux-Corrected Transport) simulation to suppress the numerical dispersion, we finally achieve numerical simulation for single and double-phase geological model. After getting wave field maps and synthetic seismograms, we further analysised and discussed the characteristics of the fast primary wave, low primary wave and S wave. At the same time, the impact of the selection of the different diffusion factors to the numerical dispersion effect in FCT method is also being analysised. The numerical simulation then explains the feasibility of the improved format discrete PML. Finally, the single and double numerical simulation of the geological model. Numerical simulation by observing the snapshots and synthetic seismograms, wave field analysis and discussion of the characteristics of the solid phase, fluid phase of the fast P wave, slow wave, wave characteristics discussed. Both methods suppress the observed numerical dispersion and the perfectly matched layer absorbing boundary reflection effect.