Two-dimensional velocity macro model estimation from seismic reflection data by local differential semblance optimization: applications to synthetic and real data sets

The quality of the migration/inversion in seismic reflection is directly re lated to the quality of the velocity macro model. We present here an extens ion of the differential semblance optimization method (DSO) for 2-D velocit y field estimation. DSO evaluates via local measurements (horizontal deriva tives) how flat events in common-image gathers are. Its major advantage wit h respect to the usual cost functions used in reflection seismic inverse pr oblems is that it is-at least in the 1-D case-unimodal and thus allows a lo cal (gradient) optimization process. Extension of DSO to three dimensions i n real cases involving a large number of inverted parameters thus appears m uch more feasible, because convergence might not require a random search pr ocess (global optimization). Our differential semblance function directly measures the quality of the co mmon-image gathers in the depth-migrated domain and does not involve de-mig ration. An example of inversion on a 2-D synthetic data set shows the abili ty of DSO to handle 2-D media with local optimization algorithms. The horiz ontal derivatives have to be carefully calculated for the inversion process . However, the computation of only a few common-image gathers is sufficient for a stable inversion. As a Kirchhoff scheme is used for migration, this undersampling largely reduces the computational cost. Finally, we present an application to a real North Sea marine data set. We prove with this example that DSO can provide velocity models for typical 2- D acquisition that improve the quality of the final pre-stack depth images when compared to the quality of images migrated with a velocity model obtai ned by a classical NMO/DMO analysis. Whilst random noise is not a real diff iculty for DSO, coherent noise, however, has to be carefully eliminated bef ore or during inversion for the success of the velocity estimation.