The finite-difference frequency domain (FDFD) method is widely applied for simulating seismic wavefields, and a key to achieving successful FDFD simulation is to construct FDFD coefficients that can effectively suppress numerical dispersion. Among the existing FDFD coefficients for seismic wavefield simulation, adaptive FDFD coefficients that vary with the number of wavelengths per grid can suppress numerical dispersion to the maximum extent. The current methods for calculating adaptive FDFD coefficients involve numerical integration, conjugate gradient (CG) optimization, sequential initial value selection, and smooth regularization, which are difficult to implement and inefficient in calculations. To simplify the calculation of adaptive FDFD coefficients and improve the corresponding computational efficiency, this paper proposes a new method for calculating adaptive FDFD coefficients. First, plane-wave solutions with different discrete propagation angles are substituted in the FDFD scheme, and the corresponding least-squares problem is constructed. As this problem is ill-conditioned and obtaining smooth adaptive FDFD coefficients by the conventional solving method based on normal equations is difficult, this paper proposes solving the least-squares problem by solving the corresponding overdetermined linear system of equations through QR matrix decomposition. Compared with the existing methods for calculating adaptive FDFD coefficients based on numerical integration, CG optimization, and sequential initial value selection, the proposed method allows for a simplified computational process and considerably higher computational efficiency. Numerical wavefield simulation results show that the adaptive-coefficient FDFD method based on QR matrix decomposition can achieve the same accuracy as those based on numerical integration, CG optimization, and sequential initial value selection while requiring less computation time.

频域有限差分(FDFD)方法广泛应用于地震波场模拟，而FDFD模拟成功的关键是构造能够有效抑制数值色散的FDFD系数。在现有的地震波场模拟FDFD系数中，随每网格波长数变化的自适应FDFD系数可以最大程度地抑制数值色散。目前计算自适应FDFD系数的方法包括数值积分、共轭梯度(CG)优化、顺序初始值选择和平滑正则化，这些方法实现困难且计算效率低。为了简化自适应FDFD系数的计算并提高相应的计算效率，提出一种新的自适应FDFD系数计算方法。首先，将不同离散传播角的平面波解代入FDFD方案中，构造相应的最小二乘问题。由于该问题是病态的，并且通过基于正规方程的常规求解方法很难获得平滑的自适应FDFD系数，因此本文提出通过QR矩阵分解求解相应的超定线性方程组来求解最小二乘问题。与现有基于数值积分、CG优化和顺序初始值选择的自适应FDFD系数计算方法相比，该方法可以简化计算过程并显着提高计算效率。 数值波场仿真结果表明，基于QR矩阵分解的自适应系数FDFD方法可以达到与基于数值积分、CG优化和顺序初始值选择的方法相同的精度，同时需要更少的计算时间。