Tomographic inversion of common image gathers

Interpretation of seismic reflection data in complex geological areas requires good seismic imaging which can only be pro- vided if the velocity field is known with high accuracy. In the presence of lateral velocity variations, pre-stack depth migra- tion (PSDM) is indispensable for obtaining the real depths and geometries of the structures. Stacking velocities are inad- equate to perform this step of the data processing, because they are evaluated supposing flat horizons and lateral con- stant velocity in each common depth point (Yilmaz, 2001). To avoid this problem, it is necessary to use a more accurate velocity analysis, such as the tomographic inversion tech- nique. The tomographic velocity field is usually used to obtain the travel time table to perform PSDM. A satisfactory migration result can provide information about the reliability of the velocity field. In fact, if the velocity field is correct, the reflected events in the common image gathers (CIGs), in the pre-stack depth domain, are flats. In particular, if we use a velocity field higher than the real velocity, the reflected events become deeper versus offset while, if the velocity is lower, the reflected events become shallower versus offset. In the last decade, many efforts have been developed to determine a more detailed velocity field by using the output of PSDM. In fact, as pointed out by Lafond and Levander (1993), pre-stack migration produces a wealth of data from which it is possible to extract velocity corrections. These can then in turn be used to improve the focusing of the reflectors. The method is based on a pre-stack layer-stripping Kirchhoff algorithm with geometrical ray tracing in heterogeneous media. In this way, they iteratively update the velocity model and depth focusing of the interfaces. The analysis of the sem- blance of the CIG is used to upgrade the depth velocity model, if the reflected events are not flat - see, for example, Liu (1995). This procedure has the same limitations as the stacking velocity analysis, because it assumes that the veloc- ity field is laterally constant inside the CIG. Kosloff et al. (1996) determined the velocity and the depth interface by using the tomography of migrated common reflecting point (CRP) gathers. This method is derived from the tomograph- ic principle that relates travel time change along a given ray to perturbations in slowness and layer depths. The tomo- graphic principle is used to convert depth errors in migrated CRP gathers to time errors along the CRP ray pair, and thus the conventional travel time tomography was used. This last method has the advantage that the migrated gathers are used at once as opposed to being analyzed at single stations. On the other hand, many PSDMs have to be performed to obtain the final model. For this reason, we developed a procedure to update the velocity field using a tomographic inversion of the picked reflected events in the CIGs which requires only one PSDM for each layer. The aim is to obtain a flatness of the picked events in every CIG at the end of our procedure. In this paper, we present the methodology, and a few applica- tions with both synthetic and real data.