Abstract
The numerical modeling of wave field in porous media generally requires more computation time than that of acoustic or elastic media. Usually used finite difference methods adopt finite difference operators with fixed-order accuracy to calculate space derivatives for a heterogeneous medium. A finite difference scheme with variable-order accuracy for acoustic wave equation has been proposed to reduce the computation time. In this paper, we develop this scheme for wave equations in porous media based on dispersion relation with high-order staggered-grid finite difference (SFD) method. High-order finite difference operators are adopted for low-velocity regions, and low-order finite difference operators are adopted for high-velocity regions. Dispersion analysis and modeling results demonstrate that the proposed SFD method can decrease computational costs without reducing accuracy.
Highlights
Seismic wave modeling for porous media is usually used to study the properties of rocks and to characterize the seismic response of geologic formation
A finite difference scheme with variable-order accuracy for acoustic wave equation has been proposed to reduce the computation time. We develop this scheme for wave equations in porous media based on dispersion relation with high-order staggered-grid finite difference (SFD) method
A variety of different numerical methods have been used for poroelasticity modeling [4, 5], such as spectral method [6], finite difference method [7], time domain method [8], discontinuous Galerkin method [9], and finite volume method [10]
Summary
Seismic wave modeling for porous media is usually used to study the properties of rocks and to characterize the seismic response of geologic formation. Owing to the low memory requirement and computational cost, finite difference methods [11, 12] are widely applied for porous wave equations. To improve the efficiency and accuracy, several variants of finite difference methods have been investigated to simulate porous media [13, 14]. These include implicit finite difference method [15], variable-grids [16], irregular-grids, staggeredgrids [17], discontinuous-grids [18], quadrangle-grids [19], rotated-staggered-grids [20] finite difference methods, and spatially varying time steps finite difference methods [21]. In order to avoid the spurious reflection from the artificial boundaries in finite difference modeling, perfectly matched layer (PML) absorbing boundary conditions [22, 23] have been widely used
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