Simultaneous Estimation of Statics and Velocity

Where subsurface is complex, reflection data from land seismic surveys often suffer triply – from statics variations, the presence of various types of noise, and imperfect moveout correction due to crossing events and non-hyperbolic movement that varies rapidly with midpoint. For such data, velocity analysis, already difficult due to the non-hyperbolic movement and crossing events, is further complicated by anomalies due to variations in the near-surface. Conversely, accurate statics estimation requires some accuracy in the velocity model. Because the velocity and statics problems are intertwined for data from structurally complex areas, it is ideal to treat the velocity and statics problems as one.

Modern practice for data from structurally complex areas bases velocity analysis on iterative use of prestack depth migration, in conjunction with some process such as depth-focussing analysis. The hope is that the iterations will converge to an acceptable velocity model. We propose to incorporate into this iterative velocity analysis a statics-estimation procedure that also utilizes prestack migration. When applied to statics-contaminated data, the prestack depth migration will correct the data for non-hyperbolic moveout, dipping and crossing events, provided that the velocity model is sufficiently accurate. These prestack migrated data are then stacked, and the stacked traces are input to a multi-offset modeling that generates a reference trace for each of the traces in the unstacked data. Cross-correlation of each data trace with its associated reference trace gives the time shift for that data trace. The derived shifts are then used in a conventional statics-estimation procedure under the familiar assumption of surface consistency.

Although the correct velocity model is not known at the outset of the procedure, tests with statics-contaminated, Marmousi model data show that even where the initial velocity model is poorly known, the migration-based method produces acceptable initial-stage statics estimates. After applying the method iteratively in conjunction with a migration velocity analysis, alternating between velocity and statics estimation, both velocity and statics solutions are improved, producing a good statics solution in the Marmousi data after just a few iterations. Further iterations can then be directed solely towards improvement of the velocity model.