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

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.

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