The 2.5D VTI pseudo-acoustic wave equation

Rafael Aleixo, Francisco de Assis Silva Neto, Daniela Amazonas


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 médium  symmetry. By taking the Fourier transform with respect to the out-of-plane direction (the  symmetry axis) and then, 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 compo-  nent. 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. In this work we apply this idea to the anisotropic  pseudo-acoustic wave equation.  


Wave equation; anisotropy; acoustic approximation.

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