The goal of processing seismic reflection data is to convert a recorded wave field into a structural or lithological image of the subsurface. Among the many steps in seismic processing, the imaging step, migration, not only positions, but also focuses reflector images. Migration requires a model of the wave propagation velocities of the subsurface, but obtaining this model is often the most difficult processing step in areas of complex structure.
In areas with structurally complex geology, conventional velocity analysis based on the stacking velocity Neidell and Taner (1971); Taner and Koehler (1969) often fails. Consequently a more accurate velocity estimation scheme such as seismic tomography is required. Seismic tomography is an iterative two-step process. First, traveltime errors are measured by comparing observed traveltimes with computed traveltimes through an assumed velocity model. Then the differences are projected back over the traced ray paths through the assumed velocity model to update the model.
There are many different algorithms in tomographic velocity analysis, which can be characterized according to the domains they used for traveltime error picking. Conventional traveltime tomography Bishop et al. (1985); Stork (1988) picks the traveltime errors in the prestack data. Perhaps the greatest drawback of traveltime tomography of this type is the necessity for large amounts of picking. Events in seismic data are generally complicated and variable wave patterns; reducing this information to isolated time picks can involve large amounts of human judgement and can be very time consuming. The picking process is subject to systematic errors caused by ambiguities in defining events or by incorrect assumptions about the wavelet phase, as well as random error. Automatic picking programs can work faster than people, but human judgement is usually better at avoiding egregious mispicks. To increase the reliability of the picking, Biondi 1990 used the measurement of moveouts in the beam stack domain.
In order to reduce the number, errors, and bias of picking, we can use the semblance velocity stack panel for picking Toldi (1985). Since a pick of the best stacking velocity corresponds to a pick of the best-fitting hyperbolic traveltime for an event in the common-midpoint (CMP) domain, it can be interpreted as a filtered version of prestack traveltime picking Fowler (1988).
The results of those two types of the time domain picking can be achieved similarly in the image domain after prestack migration by picking events for every offset van Trier (1990) or by picking the best residual moveout (RMO) velocity along the events in the stacked images Al-Yahya (1989); Etgen (1990). In contrast to transmission tomography, where ray endpoints are known, in reflection tomography the reflector positions are unknown, and an incorrect guess about them may lead to errors in velocity estimation. Picking in the image space, either event picking or RMO velocity picking, after prestack migration has the advantage of providing an accurate reflector location under the assumed velocity.
Tomographic velocity inversion constitutes a nonlinear inversion problem because both the velocity and ray paths are unknown. To solve such a nonlinear problem, we use a bootstrap approach. First, starting with an initial guess of the velocity model and the operator based on it, the traveltime errors are measured by comparing observed traveltimes with the computed traveltimes obtained through the assumed model. Next, the error in the assumed model is solved by inverting the measured traveltime errors and is used for updating the velocity model. We then iterate this linear inversion with the updated velocity model until it converges.
If we choose the RMO velocity analysis for traveltime error measure, a model-dependent RMO velocity analysis is required to compute accurate traveltime error. However, the measuring of the RMO velocity for a nonflat reflector is often difficult and not practical to implement because it requires a line search in a prestack migrated image cube Zhang (1990). To avoid such exhaustive searching, Etgen 1990 applied residual dip moveout (RDMO) before RMO velocity analysis so that the common reflection events could be lined up in the common surface location plane in the image cube.
This chapter describes a new way of measuring RMO velocity that reflects traveltime errors along the ray paths where the event has moved, with the help of plane wave synthesis imaging along irregular reflectors. First I review the basic traveltime tomography algorithm along with specific problems in reflection tomography. Then I explain how wavefront synthesis along irregular reflectors is used to generate reflector-oriented common reflection point (CRP) gathers, which provide accurate residual velocity. Finally, I summarize the entire algorithm for velocity estimation and present some examples. Since the algorithm presented in this chapter requires manual picking of reflectors that is the most tedious and time consuming process, a simple synthetic dataset with few reflectors was used to describe the algorithm instead of the Marmousi dataset that contains too many reflectors.