Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Abstract

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/ gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Trapezoid-Grid Finite-Difference Time-Domain Method for 3D Seismic Wavefield Modeling Using CPML Absorbing Boundary Condition

“…However, the resulting artificial reflection in the transition area and the possible instability make it inefficient for high-accuracy seismic wave simulation. Another variable-grid FD method adopts irregular FD coefficients to process the transition region (Huang and Dong, 2009;Liu et al, 2014), which can significantly avoid the artificial reflection and improve the stability. The disadvantage of this type of variable-grid method is the additional computing cost brought by calculating irregular FD coefficients.…”

A discontinuous collocated-grid implementation for high-order finite-difference modeling

“…As shown in Figure 1a, there is no discontinuous point located on the grid line; consequently, a high-order FD operator can be applied over the entire region (e.g., Falk et al, 1996;Opršal and Zahradnik, 1999;Pitarka, 1999;Wu et al, 2005). As shown in Figure 1b, the low-velocity area is discretized using a fine grid and the interpolation is required to refine the wavefield from the coarse grid to the fine grid (e.g., Jastram and Behle, 1992;Jastram and Tessmer, 1994;Wang and Schuster, 1996;Liu et al, 2014). The continuousgrid scheme has accuracy similar to the traditional uniform-grid FD method using the fine grid, but it saves less computational cost compared with the discontinuous-grid scheme.…”