Trapezoid-grid finite difference frequency domain method for seismic wave simulation

The large computational cost and memory requirement for the finite difference frequency domain (FDFD) method limit its applications in seismic wave simulation, especially for large models. For conventional FDFD methods, the discretisation based on minimum model velocity leads to oversampling in high-velocity regions. To reduce the oversampling of the conventional FDFD method, we propose a trapezoid-grid FDFD scheme to improve the efficiency of wave modeling. To alleviate the difficulty of processing irregular grids, we transform trapezoid grids in the Cartesian coordinate system to square grids in the trapezoid coordinate system. The regular grid sizes in the trapezoid coordinate system correspond to physical grid sizes increasing with depth, which is consistent with the increasing trend of seismic velocity. We derive the trapezoid coordinate system Helmholtz equation and the corresponding absorbing boundary condition, then get the FDFD stencil by combining the central difference method and the average-derivative method (ADM). Dispersion analysis indicates that our method can satisfy the requirement of maximum phase velocity error less than $1\%$ with appropriate parameters. Numerical tests on the Marmousi model show that, compared with the regular-grid ADM 9-point FDFD scheme, our method can achieve about $80\%$ computation efficiency improvement and $80\%$ memory reduction for comparable accuracy.

Semi-exact local absorbing boundary condition for seismic wave simulation

An absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.