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.