Abstract
The large computational memory requirement is an important issue in 3D large-scale wave modeling, especially for GPU calculation. Based on the observation that wave propagation velocity tends to gradually increase with depth, we propose a 3D trapezoid-grid finite-difference time-domain (FDTD) method to achieve the reduction of memory usage without a significant increase of computational time or a decrease of modeling accuracy. It adopts the size-increasing trapezoid-grid mesh to fit the increasing trend of seismic wave velocity in depth, which can significantly reduce the oversampling in the high-velocity region. The trapezoid coordinate transformation is used to alleviate the difficulty of processing ununiform grids. We derive the 3D acoustic equation in the new trapezoid coordinate system and adopt the corresponding trapezoid-grid convolutional perfectly matched layer (CPML) absorbing boundary condition to eliminate the artificial boundary reflection. Stability analysis is given to generate stable modeling results. Numerical tests on the 3D homogenous model verify the effectiveness of our method and the trapezoid-grid CPML absorbing boundary condition, while numerical tests on the SEG/EAGE overthrust model indicate that for comparable computational time and accuracy, our method can achieve about 50% reduction on memory usage compared with those on the uniform-grid FDTD method.
Highlights
Reverse time migration (RTM) (Baysal et al, 1983; Xuan et al, 2014; Qu et al, 2015; Xu et al, 2021a; Du et al, 2021) and full-waveform inversion (FWI) (Tarantola, 1984; Virieux and Operto, 2009; Cai and Zhang, 2015; Xia et al, 2017; Jia et al, 2019) play a fundamental role in geophysical exploration
We use a 3D homogenous model with a constant velocity of 2000 m/s to verify the effectiveness of our trapezoid-grid finite-difference time-domain (FDTD) method and corresponding convolutional perfectly matched layer (CPML) absorbing boundary condition
We propose a 3D trapezoid-grid FDTD seismic wave modeling method based on the increasing trend of seismic wave velocity with depth
Summary
Reverse time migration (RTM) (Baysal et al, 1983; Xuan et al, 2014; Qu et al, 2015; Xu et al, 2021a; Du et al, 2021) and full-waveform inversion (FWI) (Tarantola, 1984; Virieux and Operto, 2009; Cai and Zhang, 2015; Xia et al, 2017; Jia et al, 2019) play a fundamental role in geophysical exploration. The conventional FD method literally adopts a weighted summation of neighboring grid points’ values to estimate the derivative for a designated grid point (Zhou et al, 2021), where the grid size (h) is fixed and the FD coefficients are calculated by Taylor expansion. In this way, the approximation error ε can be expressed as (Liu and Sen, 2011a; Wu et al, 2019b) follows:
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