A fourth-order finite-difference method for the acoustic wave equation on irregular grids

Revista: Geophysics, 2003, 68, 1–5.

This paper presents a FD approximation for the acoustic wave equation which is able to handle nonuniform rectangular grids. The new scheme has achieved the same accuracy of a thin regular-grid calculation while reducing the computational cost. The inevitable variation of the numerical phase velocity as a function of the grid step requires some care when designing irregular meshes because contrasts in the phase velocity can produce numerical reflections. To deal with this problem and to keep the accuracy of the scheme, the grid step should not be greater than λmin/5 in all regions of the irregular grid. This condition guarantees that contrasts in the grid step, no matter how large and abrupt they are, will not generate numerical reflections with significant amplitude to be noted in practical applications. In this work, only the approximation for the 2D acousticwave equation is presented, but an extension to the 3D or 1D case is straightforward. FD schemes for the elastic case may also be designed using the approach developed in this work. It is also possible to obtain spatial derivatives approximations using more than five grid points which gives accuracy of higher order. In this case, however, the expressions for the correspondent mesh-dependent coefficients may become very cumbersome.

Autor: Sérgio Adriano Moura Oliveira