Reflection tomography is an inversion method that adjusts a velocity and reflector depth model to be consistent with the prestack time data. This tomography approach minimizes the misfit of the data and model in the premigrated domain. Generally, the data are represented by the traveltimes of reflection events, which has made the technique problematic and unpopular.Techniques generally known as "migration velocity analysis" have a similar objective but use the postmigrated domain. For a variety of practical reasons, this postmigrated domain has advantages over the premigrated domain. With slight modifications, the reflec-

Prestack velocity analysis in areas of complex structure is a coupled migration and transmission inversion problem that can be analyzed from a tomographic perspective. By making as few a priori assumptions about the solution as possible in parameterizing the inverse problem, generalized tomographic velocity analysis is applicable to a wide range of geologic cases. Constraints modify the method to the unique characteristics of each application. The ray trace/traveltime formulation for tomography, as proposed by Bishop et al. (1985), provides a conceptual tool for presenting features that are important to automated prestack velocity analysis in complex structure, such as (1) the coupling of the velocity field to the reflector positions, (2) the nonuniform coverage of the model by the data, (3) the ability to perform a controlled inversion of large matrices over a wide eigenvalue range, and (4) the implementation of constraints in the inversion. These features may impact other automated prestack velocity analysis methods for reflection seismology.

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Generalized prestack velocity analysis methods that use an automated approach to resolve laterally variable interval velocity fields are beset by a series of problems. The problem of resolving lateral velocity variations has inherent complications that prevent automated methods from being robust enough to be applied routinely to data from a variety of geologic provinces. The use of automated prestack velocity analysis methods will not eliminate the step of carefully producing an initial velocity model derived from regional geologic information and an interpretation of a conventionally processed section. For the methods to regularly produce useful additional information, the unique characteristics of each application must be input into the prestack velocity analysis with the use of inversion constraints. These constraints serve either to adapt the generalized prestack velocity analysis to a focused objective in a particular area or to provide iterative, interpretational tools that help the user produce a velocity model.