Modeling of pseudo-acoustic P-waves in orthorhombic media with a lowrank approximation

Published as Geophysics, 78, no. 4, C33-C40, (2013)

Modeling of pseudo-acoustic P-waves in orthorhombic media with a lowrank approximation

Xiaolei Song and Tariq Alkhalifah

[1]Bureau of Economic Geology
Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8924
USA
songxl@utexas.edu
[2]Physical Sciences and Engineering
King Abdullah University of Science and Technology
Mail box # 1280
Thuwal 23955-6900
Saudi Arabia
tariq.alkhalifah@kaust.edu.sa

Abstract:

Wavefield extrapolation in pseudo-acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We use the dispersion relation for scalar wave propagation in pseudo-acoustic orthorhombic media to model acoustic wavefields. The wavenumber-domain application of the Laplacian operator allows us to propagate the P-waves exclusively, without imposing any conditions on the parameter range of stability. It also allows us to avoid dispersion artifacts commonly associated with evaluating the Laplacian operator in space domain using practical finite difference stencils. To handle the corresponding space-wavenumber mixed-domain operator, we apply the lowrank approximation approach. Considering the number of parameters necessary to describe orthorhombic anisotropy, the lowrank approach yields space-wavenumber decomposition of the extrapolator operator that is dependent on space location regardless of the parameters, a feature necessary for orthorhombic anisotropy. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersion. Furthermore, there is no coupling of qSv and qP waves, because we use the analytical dispersion solution corresponding to the $P$-wave.

Modeling of pseudo-acoustic P-waves in orthorhombic media with a lowrank approximation