Differential-distance 21-Point stretched grid frequency-space acoustic equation domain finite difference forward modeling

Frequency-domain finite difference forward modeling is crucial for seismic inversion and imaging. However, the large memory requirements and extensive computations have long been major challenges in frequency-domain forward modeling. To address these difficulties, this paper proposes two improvements to the difference operator. First, the general optimization method of finite difference decomposition is employed to enhance the accuracy of the difference operator. Second, a stretched grid is introduced to reduce the computational burden of LU factorization of the impedance matrix by confining the sub-diagonals of the impedance matrix to both sides of the main diagonal. Based on these improvements, a Differential-Distance (DD) 21-point difference scheme tailored for rectangular grid sampling is developed. Dispersion analysis demonstrates that the DD 21-point difference scheme achieves higher accuracy compared to other methods, especially for large grid spacing ratio sampling. When the grid spacing ratio exceeds 1.5, the DD scheme requires only 2.13 grid points per wavelength to maintain the phase velocity error within 1%. Finally, through model testing and comparison with the Average-Derivative Method (ADM) and other comparable methods, the feasibility and efficiency of the DD 21-point difference scheme are thoroughly verified.