Numerical Modeling In Biot's Porous Media By Staggered-grid Difference Scheme

Staggered-grid difference method is widely used in seismic wave-field simulation. In this article we apply this method on the simulation of Biot's fluid-saturated porous media. Instead of the prevailing second-order differential equations, we consider a first-order velocity-stress hyperbolic system that is equivalent to Biot's equations. The vector of unknowns in this system consists of the solid and fluid particle velocity components and stress components. Then the staggered-grid difference scheme is available. A P-wave line source in a uniform poroelastic medium is derived in the simulation. With this method the wave-fields of homogeneous and heterogeneous poroelastic media are studied with single-layer and two-layer models. For"slow"compress ional wave is highly attenuated in porous media saturated by a viscous fluid, the attenuation mechanism is also considered. The results of this study suggest that on the interface of two-layer media, when seismic wave are reflected or transmitted two kinds of P-wave and shear wave can be observed, and"slow"compress ional wave is hardly seen in the media that has large damping coefficient. We also try to study the wave-field characteristics and the synthetic record when seismic propagating in gas hydrate sediment.Finite-difference schemes for numerically solving the wave equation suffer from undesirable ripples, that is numerical dispersion. The numerical dispersion interferes with the seismic modeling seriously and decrease the precision of simulation. Here, the reasons of this phenomenon is discussed. To eliminate the numerical dispersion higher-order finite-difference equation and the flux-corrected transport (FCT) method are introduced.In this paper, a method is developed to extend the perfectly matched layer (PML) to simulating seismic wave propagation in poroelastic media to avoid the reflection on the artificial boundaries. This nonphysical material is used at the computational edge of a finite-difference algorithm as an absorbing boundary condition to truncate unbounded media. The incorporation of PML in Biot's equations is different from other PML applications and a loss coefficient in the PML region is required. Numerical results show that the PML attenuates the outgoing waves effectively.