The 2.5D VTI pseudo-acoustic wave equation
DOI:
https://doi.org/10.5540/03.2021.008.01.0483Palavras-chave:
Wave equation, anisotropy, acoustic approximation.Resumo
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.
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