A generalized optimal 9-point scheme for frequency-domain scalar wave equation

The rotated optimal 9-point scheme for frequency-domain scalar wave equation is widely used in frequency-domain full waveform inversion. This scheme requires equal directional sampling intervals, which limits its applicability. Recently, an average-derivative method was proposed to overcome this restriction. However, the average-derivative method is an algebraic approach, and therefore it does not inherit the geometrical property (coordinate transformations) of the rotated optimal 9-point scheme. In this paper, a geometrical approach is developed, and a generalized optimal 9-point scheme is constructed. This new scheme is based on a directional-derivative method, and includes the rotated optimal 9-point scheme as a special case. Like the average-derivative method, the number of grid points per wavelength is reduced from approximately 13 to approximately 4 by this new 9-point optimal scheme for both equal and unequal directional sampling intervals in comparison with the classical 5-point scheme. Unlike the average-derivative method, this generalized optimal 9-point scheme shares the geometrical property of the rotated optimal 9-point scheme.

► A new 9-point scheme is presented to overcome sampling limitations of the old scheme. ► The geometrical property of the old scheme is preserved. ► Numerical examples demonstrate greater accuracy and flexibility of this scheme.