Modeling and reverse time migration based on the tilted transverse isotropic (TTI) acoustic wave equation suffers from instability in media of general inhomogeniety, especially in areas where the tilt abruptly changes. We develop a stable TTI acoustic wave equation implementation based on the original elastic anisotropic wave equation. We, specifically, derive a vertical transversely isotropic wave system of equations that is equivalent to their elastic counterpart and introduce the self-adjoint differential operators in rotated coordinates to stabilize the TTI acoustic wave equations. Compared to the conventional formulations, the new system of equations does not add numerical complexity; a stable solution can be found by either a pseudospectral method or a high-order explicit finite difference scheme. We demonstrate by examples that our method provides stable and high-quality TTI reverse time migration images.

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In this paper, following the recent work of Xu et al. (2012b,a), we implement the Reflection-based Full Waveform Inversion (RFWI) in the frequency domain, by taking advantage of a massively parallel direct matrix solver. The earth model is splitted into a long wavelength part (background model) and a short wavelength part (reflectivity model). At each iteration, we update the background model by resorting to a demigration process on the reflectivity model obtained from migration. We make use of a 2D synthetic lens model to validate our workflow, and demonstrate that low frequency data is essential.

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