Introduction

VTI media is one of the simplest and most practically important types of anisotropic media. Steeply dipping structures, such as faults and salt flanks, are important for the interpretation of seismic data. The waves relating to steeply dipping reflectors usually propagate in a direction far from vertical. If we do not account for the anisotropy in the migration, steeply dipping reflectors will be imaged with large positional errors or will vanish from the image. To image steeply dipping reflectors in anisotropic media, we need an anisotropic wavefield-extrapolation operator that can handle waves propagating in a direction far from the vertical direction.

Many methods have been proposed to extrapolate wavefields and image reflectors in VTI or tilted TI media Ferguson and Margrave (1998); Ristow and Ruhl (1997); Rousseau (1997); Uzcategui (1995); Zhang et al. (2001a,b). Baumstein and Anderson (2003) extrapolate wavefields in VTI media with a reference anisotropic phase-shift operator plus an explicit correction filter. Shan and Biondi (2004b) extrapolate wavefields in tilted TI media with an isotropic operator followed by an explicit anisotropic correction filter.

The waves related to steeply dipping reflectors usually propagate far from the vertical direction. Kirchhoff methods can propagate these waves correctly, but they are less reliable for imaging complex structure because of the high-frequency approximation. Reverse-time migration Baysal et al. (1983); Biondi and Shan (2002); Whitmore (1983), which is based on the two-way wave equation, can propagate these waves accurately; however anisotropic reverse-time migration is still prohibitively expensive. Algorithms such as beam migration Albertin et al. (2001); Brandsberg-Dahl and Etgen (2003); Gray et al. (2002); Hill (2001) and coordinate-transformation-based migration Etgen (2002); Higginbotham et al. (1985); Sava and Fomel (2004); Shan and Biondi (2004a), extrapolate wavefields in a direction close to the propagation direction, and can handle these waves at a wide angle.

In this paper, we apply plane-wave migration in tilted coordinates for VTI media. VTI media in Cartesian coordinates become to tilted TI media in tilted coordinates. We extrapolate the wavefields with an isotropic operator followed by an explicit anisotropic correction. We first discuss VTI media in tilted coordinates, then review plane-wave migration in tilted coordinates, and finally show the migration results for a synthetic dataset.