Comparison of two schemes for Laplace-domain 2D scalar wave equation

• Two 9-point Laplace-domain schemes are compared for general sampling.
• The optimal scheme makes substantial improvements on the finite-element scheme.
• Numerical examples show the great efficiency of the optimal scheme.

Laplace-domain modeling plays an important role in Laplace-domain full waveform inversion. In order to provide efficient numerical schemes for Laplace-domain modeling, two 9-point schemes for Laplace-domain 2D scalar equation are compared in this paper. Compared to the finite-element 9-point scheme, the average-derivative optimal 9-point scheme reduces the number of grid points per pseudo-wavelength from 16 to 4 for equal directional sampling intervals. For unequal directional sampling intervals, the average-derivative optimal 9-point scheme reduces the number of grid points per pseudo-wavelength from 13 to 4. Numerical experiments demonstrate that the average-derivative optimal 9-point scheme is more accurate than the finite-element 9-point scheme for the same sampling intervals. By using smaller sampling intervals, the finite-element 9-point scheme can approach the accuracy of the average-derivative optimal 9-point scheme, but the corresponding computational cost and storage requirement are much higher.