The development of an efficacious Finite-Difference(FD)operator holds paramount significance in enhancing the computational efficiency of frequency-domain FD forward modeling.The rotated-coordinate-system method is extensively employed across numerous numerical schemes due to its advantageous geometrical attributes.The previously generalized double 9-point scheme is highly accurate and suitable for arbitrary rectangular grid sampling.Affine coordinate system,as a kind of generalized coordinate system,has gained attention because it does not restrict their axes to be orthogonal.In this study,we analyze the generalized double 9-point scheme in depth based on the affine transformation and uncover that it does not strictly adhere to the rotated-coordinate-system method.This is because it has zero-order truncation accuracy at non-uniform grid intervals and low wavenumbers.Considering the suboptimal utilization of the FD template in the generalized double 9-point scheme,we leverage the affine transformation to develop an affine 25-point scheme that boasts higher accuracy.The affine 25-point scheme converges rigorously at low wavenumbers with equal or unequal grid intervals.At high wavenumbers,the affine 25-point scheme requires less than 2.2 grid points per minimum wavelength to restrict the phase velocity error to within 1％.Numerical examples demonstrate the accuracy and superiority of the affine 25-point scheme.
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