The application of high-order differencing to the scalar wave equation

Abstract

Abstract The second-order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high-order approximations for these derivatives. A one-dimensional model is used to illustrate the relative accuracy of O(Delta t 2 , Delta x 2 ), O(Delta t 2 , Delta x 4 ), O(Delta t 4 , Delta x 4 ), and O(Delta t 4 , Delta x 10 ) central-difference schemes. For comparison, O(Delta t 2 ) and O(Delta t 4 ) pseudo-spectral schemes are used as an additional measure of performance. The results indicate that O(Delta t 4 , Delta x 10 ) differencing can achieve similar accuracy as the O(Delta t 4 ) spectral scheme. For practical illustration, a two-dimensional form of the O(Delta t 4 , Delta x 10 ) algorithm is used to compute the exploding reflector response of a salt-dome model and compared with a fine-grid O(Delta t 2 , Delta x 4 ) result. Transmissive sponge-like boundary conditions are also examined and shown to be effective.