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Prestack reverse-time migration, a wave-equation technique using two-way propagation, correctly handles multiarrivals and enables imaging of overturned reflections. However, image artifacts occur when backscattered waves cross-correlate. These artifacts are particularly strong where high-velocity contrasts occur. A method for removing unwanted internal reflections during propagation of both the source and receiver wavefields is presented. This method applies a directional damping term to the wave equation in areas of the velocity model where unwanted reflections occur. Tests on synthetic data show good suppression of image artifacts.

Symmetry groups commonly used to describe seismic anisotropy include transverse isotropy, orthorhombic, monoclinic, and triclinic. For all but the last, the choice of particular orientations of the coordinate system can substantially simplify parameterization of the anisotropy. Choosing a coordinate system requires defining a rotation in three-dimensional space relative to fixed world coordinates. We discuss here two major families of rotation parameterizations: Euler angles and axis/angle quaternion representations. Either method can work well for forward modeling. However, for traveltime tomography or full-waveform inversion, the inverse problem formulated in Euler angles can become ill-posed because very different choices of angle parameters can yield nearly identical data. In the worst case, there can be a complete loss of a degree of freedom, making it difficult to invert for important model parameters such as fracture orientation. Quaternions provide an alternative representation for 3D rotations that avoid these inversion problems. Quaternions also provide efficient and well-behaved interpolation of rotation angles, as well as differentials of data with respect to rotation parameters.

Current commercial seismic imaging techniques routinely handle wave propagation in transversely isotropic media with vertical symmetry axis (VTI). VTI anisotropy is ubiquitous in sedimentary basins because lithification generally occurs in a stress environment dominated by the vertically oriented gravitational gradient. Tectonic stresses can rotate the symmetry axis away from vertical, requiring compensation for tilted transverse isotropy (TTI) effects as well. Tectonic stresses can also induce fracturing in rocks, which can further lower the symmetry class describing wave propagation. The next lower symmetry class of importance for describing seismic waves is orthorhombic, which incorporates not just layering effects but also perpendicular fracturing.

SUMMARY We propose a new approximate partial differential equation for qP-waves in transverse isotropy with a vertical symmetry axis (VTI) media. We analyse its relationship to two other published "pseudo-acoustic" VTI equations. All three pseudo-acoustic VTI wave equations are coupled systems of second-order PDEs in time, derived from the same dispersion relation for qP waves by introducing different auxiliary functions. The new method combines efficient implementation and low artifacts. Modeling and reversetime migration are shown to validate the wave equation.

Two-way migration methods require significantly greater computational resources than one-way migration methods. However, their advantage is that they can not only handle multiarrivals, but have virtually no dip limitation, enabling imaging of overturned reflections. Reverse time migration, a wave equation technique using two-way propagation, correctly handles both multiarrivals and the phase changes due to caustics, but by using two-way propagation, does not suffer from dip limitation like one-way downward continuation techniques. Although one-way wave equation techniques can be implemented and classified as true-amplitude migrations, reverse time migration makes no approximations that must be corrected to control amplitude.

The importance of including anisotropy and turning waves in depth imaging is generally recognized; however, in time imaging, these effects are often handled with approximations that unnecessarily limit the quality of the migrated result. Here we show that Kirchhoff prestack time migration can accurately image steep or overturned events with little additional cost, provided turning rays and anisotropy are taken into account. High-accuracy anisotropic turning-ray migration can also offer many other additional benefits, including improved lateral resolution, improved vertical (stratigraphic) resolution, better velocity resolution, and better AVA parameter estimation.

Summary In processing converted-wave data, one of the key points is the correct binning of data with asymmetric raypaths. In the past, this was routinely done through separate CCP binning, moveout correction and PS-DMO. Extracting correct parameters was difficult and time-consuming and the results often unsatisfactory. Kirchhoff prestack time migration offers a consistent way to handle moveout, binning, and dip at the same time. When using accurate ray-tracing methods and the inclusion of polar anisotropy in the traveltime calculation, we have seen significant improvements in imaging of the converted waves in multicomponent data sets. In this paper, we will present the anisotropic velocity model building methodology for multicomponent data and the results from applying Kirchhoff prestack time migration on several datasets.

Kirchhoff prestack time migration is routinely used with good results in conventional data processing and has also recently become popular in the processing of multicomponent data. We have seen that accurate raytracing methods and inclusion of anisotropy are giving further improvement in imaging and are particularly important for handling the converted waves in multicomponent data sets. In this paper, we will present the anisotropic velocity model building for multicomponent data and the results from applying Kirchhoff prestack time migration on several data sets.

Obtaining optimal migrated images from land data acquired in rugged terrain requires accurate correction for topographic relief. Wave-equation datuming to a flat reference surface before migration is significantly more accurate than static time shifting. Since the replacement velocity used for topographic datuming is usually laterally invariant, it is possible to design hybrid datuming algorithms that are both highly accurate and efficient. These datuming schemes can also be used for marine water-layer replacement.