Variable-grid frequency-domain finite-difference acoustic wave modeling method based on an optimized 21-point stretched stencil

The nonuniform-grid method is an effective approach for reducing storage requirements and computational effort in finite-difference (FD) modeling, with significant advancements made in the time domain. However, its application in the frequency domain has been limited due to the stringent symmetry requirements of the frequency-domain FD scheme. To address this, an optimized 21-point FD operator based on stretched grids was developed and a vertical-variable-grid FD scheme was proposed by combining the property of this operator. In our scheme, the vertical spacing ratio between coarse and fine grids can be set to any arbitrary integer. Compared with other nonuniform-grid modeling approaches, our scheme did not lose accuracy in the transition region between coarse and fine grids and was also suitable for models with small velocity variations. Furthermore, our scheme reduced the computational effort of matrix Lower–Upper (LU) factorization by generating narrow-bandwidth impedance matrices, thereby improving computational efficiency. Numerical simulations were conducted on a homogeneous model, the Hess model, and the Marmousi model. The results from the homogeneous models demonstrated the effectiveness of the optimized 21-point scheme and the vertical-variable-grid scheme. Additionally, simulations on the complex model revealed that our optimized schemes offer superior accuracy compared to other FD methods. Moreover, the optimized 21-point scheme reduced LU factorization efforts by minimizing matrix bandwidth, whereas the vertical-variable-grid scheme not only decreased matrix bandwidth but also significantly reduced the number of grid points, leading to further computational cost savings.