Stability and speedup issues in TTI RTM implementation

Abstract

In the implementation of TTI RTM, we meet stability problems and demands for speedup. Staggered Fourier first derivative and linear interpolation improves stability and accuracy. Areas with high gradients of the symmetry axis give rise to unstable numerical computations and make the wavefield blow up. Selective matching of anisotropy parameters helps to eliminate these areas. The acoustic TTI wave equation needs intensive computing. The finite difference method is more flexible than pseudo-spectral method. However, the pseudo-spectral method gives a more accurate solution than the finite difference method. Efficiency can be improved by combining pseudo-spectral and finite difference methods.

Elastic wavefield decomposition for reverse time migration in 3D TI media

“…However, the assumption does not prevent the shear waves from propagating in other directions. It generates diamond-shaped pseudo-shear wavefronts that make the ARTM unstable which jeopardizes the image's quality (Grechka et al, 2004;Zhang et al, 2009;Yoon et al, 2010). With the development of multi-component data acquisition technology, elastic reverse-time migration (ERTM) has been gradually applied to oil and gas exploration and production.…”

Modeling of pseudoacoustic P-waves in orthorhombic media with a low-rank approximation

“…Those artifacts as well as sharp changes in symmetry axis tilting may introduce severe numerical dispersion and instability in modeling. Yoon et al (2010) propose to reduce the instability by making ϵ ¼ δ in regions with rapid tilt changes. Fletcher et al (2009) suggest that including a finite shear-wave velocity enhances the stability when solving the coupled equations.…”