Frequency-domain finite-difference (FDFD) modeling plays an important role in exploration seismology. However, a major disadvantage of FDFD modeling is the computational cost, especially for large-scale models. By compactly distributing nonzero strips, the elongated stencil helps to generate a narrow-bandwidth impedance matrix, improving computational efficiency without sacrificing numerical accuracy. To further improve the accuracy and efficiency of modeling, we have developed an optimal FDFD method with an elongated stencil for 2D acoustic-wave modeling. The Laplacian term is approximated using the directional-derivative method and the average-derivative method. The dispersion analysis indicates that this elongated-stencil-based method (ESM) achieves higher accuracy than other finite-difference methods with the elongated stencil, and it is more suitable for large grid-spacing ratios. To keep the phase-velocity error within 1%, 15-point and 21-point schemes in the ESM only require approximately 2.28 and 2.19 grid points per wavelength, respectively, when the grid-spacing ratio, namely, the ratio of directional sampling intervals, is not less than 1.5. Moreover, we also adopt a variable-stencil-length scheme, in which the stencil length varies with the velocity, to further reduce the computational cost in frequency-domain modeling. Several numerical examples are presented to demonstrate the effectiveness of our ESM.
