2.5D finite-difference solution of the acoustic wave equation

The finite-difference method applied to the full 3D wave equation is a rather time-consuming process. However, in the 2.5D case, we can take advantage of the medium symmetry. By taking the Fourier transform with respect to the out-of-plane direction (the symmetry axis), the 3D problem can be reduced to a repeated 2D problem. The third dimension is taken into account by a sum over the corresponding wave-vector component. A criterion for where to end this theoretically infinite sum derives from the stability conditions of the finite-difference schemes employed. In this way, the computation time of the finite-difference calculations can be considerably reduced. The quality of the modelling results obtained with this 2.5D finite-difference scheme is comparable to that obtained using a standard 3D finite-difference scheme.