The 2.5D VTI pseudo-acoustic wave equation

Autores

  • Rafael Aleixo
  • Francisco de Assis Silva Neto
  • Daniela Amazonas

DOI:

https://doi.org/10.5540/03.2021.008.01.0483

Palavras-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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Biografia do Autor

Rafael Aleixo

Federal University of Santa Catarina, Department of Mathematics, Blumenau, Brazil

Francisco de Assis Silva Neto

Pontifical Catholic University of Rio de Janeiro, TECGRAF, Rio de Janeiro, Brazil

Daniela Amazonas

Federal University of Santa Catarina, Department of Mathematics, Blumenau, Brazil

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2021-12-20

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