Prestack depth migration algorithms are based on approximate models of elastic wave propagation in the subsurface. One of such approximations consists in the assumption that the earth response is isotropic. In fact, in some areas it has been observed that the depth of reflectors determined from surface seismic data are often deeper than well log depths. These misties have been correlated with the presence of VTI anisotropy due to shales. Moreover, it is a common experience that VTI anisotropy induces lateral mispositioning and defocusing in conventional isotropic depth migration. These limitations can be overcome by taking VTI anisotropy into account during migration. This paper discusses the VTI extension of a proprietary Isotropic 3D Prestack Kirchhoff Depth Migration algorithm. This extension impacts mainly the ray tracing algorithm underlying Kirchhoff migration. The anisotropic ray tracer exploits a parsimonious acoustic approximation of VTI anisotropy such that only P-wave traveltimes are computed. This approximation is reasonable for weak anisotropy since in this case mode conversions are negligible. Comparisons are shown from isotropic and anisotropic depth migrations results, for both synthetic and field data, showing the improvements gained by taking anisotropy into account.
Several prestack depth migration algorithms are available. Each of them has its own efficiency, applicability advantages and of course limitations. One popular and commonly used prestack migration method is the Kirchhoff approach, that has become the industrial workhorse for depth imaging due to its flexibility and relative efficiency. No other prestack migration method can properly handle inhomogeneous media, as well as provide the flexibility to focus arbitrary small portions of the data, as does the Kirchhoff method. These features are particularly important for purposes of prestack migration velocity analysis.
Prestack Kirchhoff migration consists of two main steps. The first step is the calculation of wavefront traveltimes, that can be obtained from the eikonal equation (which is an asymptotic approximation of the wave equation). The eikonal equation can be integrated directly or solved indirectly by using ray tracing. If proper amplitude treatment is desired, we also need to solve the transport equation or the equivalent dynamic raytracing equations. The second step uses these traveltimes to backpropagate backscattered energy to their true reflection points and then applies the Kirchhoff summation to produce the final image . Anisotropy impacts only the first step of Kirchhoff migration, that is traveltime computation, leaving the imaging summation unaffected.