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

Abstract

The discontinuous-grid method can greatly reduce the storage requirements and computational costs of finite-difference (FD) modeling for large-velocity-contrast models. However, traditional discontinuous-grid methods have to use interpolation when refining the wavefield in transition zones and would cause apparent artifacts. We have developed a new discontinuous collocated-grid scheme for highorder FD modeling. We refined the wavefield on a rotated coordinate system, where the interpolation is not required again. The horizontal and vertical spatial derivatives can be accurately converted into diagonal derivatives within the rotated coordinate system; thus, our scheme would be free of artifacts caused by improper interpolation. The ratio from coarse-to fine-grid spacing is restricted to 2 n for our scheme, where n is a positive integer. Numerical experiments demonstrate that the proposed discontinuous collocated-grid scheme reduces the artificial reflections by about two orders of magnitude compared to the interpolation scheme and yields a wavefield that is almost identical to that of the uniform-grid simulation. The rotated FD operator with arbitrary even-order accuracy is applied in the transition zones; thus, it significantly improves the spatial accuracy while saving computational cost.

Adaptive variable-grid least-squares reverse-time migration

“…It varies more smoothly between two layers than the blue line. For conventional variable-grid methods (Jastram and Tessmer, 1994;Wang and Schuster, 1996;Ha and Shin, 2012;Fan et al, 2015), it is inevitable to add a transition area between two layers with different velocity, change the finite-difference scheme of the seismic wave equation, or modify the finite-difference coefficients. When the modeling parameters are not reasonable, strong spurious reflections will occur in the transition area.…”

Diffraction Extraction and Least-Squares Reverse Time Migration Imaging for the Fault-Karst Structure With Adaptive Sampling Strategy

“…Variable-grid methods, which are implemented by decreasing the grid points of a model, can reduce memory costs and improve computational efficiency (Moczo, 1989;Jastram and Behle, 1992;Fan et al, 2015;Huang et al, 2015). Several variable-grid methods have shown their potential in imaging.…”

3D variable-grid full-waveform inversion on GPU

“…Zhang et al (2018) used a discrete fracture model (DFM) to reflect the shape and distribution of the fractures in the flow model and to simulate reservoir production with different fracture parameters. Fan et al (2015) applied a rotated grid system to the transition region for high-order finite-difference modeling that is capable of doubling the grid spacing without artificial reflections. Fan et al (2018) further developed a discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling.…”

“…Fan et al (2018) further developed a discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling. However, the fine-to-coarse spacing ratio of both modeling methods (Fan et al 2015(Fan et al , 2018 is restricted to a power of two. To double the grid size, a transition zone in the coarse-grid area is indispensable.…”