Analysis of converted-wave extended images for migration velocity analysis

Converted-wave data have been recognized to have potential in complementing conventional compressional data. However, imaging for converted-waves is more difficult mainly due to the need for estimating shear-wave velocities, in addition to compressional-wave velocities. The common practice is to obtain the shear-wave velocity by registering PS and PP images. Despite its low cost, this procedure is prone to error due to the assumption of imaging simple structure and due to the high potential for cycle skipping. On the other hand, we could obtain S velocities by adapting wave-equation migration velocity analysis (MVA) tools for shear waves. We derive the moveout function for CIPs of converted-wave images and find that they present more complicated moveout than their pure-mode counterparts. We explore the applicability of differential semblance optimization (DSO) to the PP and PS CIP gathers to obtain objective functions, based on which we can construct optimal velocity models. We find that the objective functions for both PP and PS data are convex, which warrants their use for migration velocity analysis using efficient gradient-descent numerical optimization schemes.