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

Wavefields in anisotropic media are well described by the anisotropic
elastic-wave equation. However, in practice, we often have little
information about shear waves and prefer to deal with
scalar wavefields, especially for conventional imaging
of subsurface structure.
Alkhalifah (2000) derived
an acoustic scalar wave equation for VTI media
by careful reparametrization followed by setting the shear velocity along the symmetry axis to zero,
which provided accurate kinematics for the
conventional elastic wavefield.
Later on, Alkhalifah (2003) followed the
same approach and introduced an acoustic wave equation of the sixth order
in axis-aligned orthorhombic media.
Fowler and King (2011) presented coupled
systems of partial differential equations for pseudo-acoustic
wave propagation in orthorhombic media by extending their previous
work in TI media (Fowler et al., 2010).
Zhang and Zhang (2011) extended
self-adjoint differential operators in TTI media (Duveneck and Bakker, 2011; Zhang et al., 2011)
to orthorhombic media.

Pseudo-acoustic P-wave modeling with coupled equations may have shear-wave numerical artifacts in the simulated wavefield (Zhang et al., 2009; Grechka et al., 2004; Duveneck et al., 2008). Those artifacts as well as sharp changes in symmetry axis tilting may introduce severe numerical dispersion and instability in modeling. Yoon et al. (2010) proposed to reduce the instability by making in regions with rapid tilt changes. Fletcher et al. (2009) suggested that including a finite shear-wave velocity enhances the stability when solving the coupled equations. These methods can alleviate the instability problem; however, they may alter the wave propagation kinematics or still leave shear-wave components in the P-wave simulation. Shear-wave artifacts can be removed from the P-wavefield in the phase-shift extrapolation method because the P- and S-wave solutions lie in a different part of the wavenumber spectrum (Bale, 2007). A number of spectral methods are proposed to provide solutions which can completely avoid the shear-wave artifacts (Fowler and Lapilli, 2012; Song and Fomel, 2011; Etgen and Brandsberg-Dahl, 2009; Chu and Stoffa, 2011; Fomel et al., 2012; Song et al., 2013; Zhan et al., 2012).

In this paper, we adopt a dispersion relation for orthorhombic anisotropic media (Alkhalifah, 2003) and introduce a mixed-domain acoustic wave extrapolator for time marching in orthorhombic media. We use the lowrank approximation (Fomel et al., 2010,2012) to handle this mixed-domain operator. We demonstrate by numerical examples that our method is kinematically accurate. Furthermore, there is no coupling of quasi-P and quasi-SV waves in the wavefield and no constraints on Thomsen's parameters required for stability.

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

2013-07-26