An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator

In this study, a new finite-difference technique is designed to reduce the number of grid points needed in frequency-space domain modeling. The new algorithm uses optimal nine-point operators for the approximation of the Laplacian and the mass acceleration terms. The coefficients can be found by using the steepest descent method so that the best normalized phase curves can be obtained. This method reduces the number of grid points per wavelength to 4 or less, with consequent reductions of computer memory and CPU time that are factors of tens less than those involved in the conventional second order approximation formula when a band type solver is used on a scalar machine.