Velocity and event-slope analysis using a model-based common-diffraction-surface stack operator

Over the last two decades, scientists have introduced many ways to improve normal moveout velocity analysis by optimizing the resolution of the moveout velocity spectrum, a graph that displays a coherence value for every tested velocity traveltime pair. Almost all of these methods have failed to enhance resolution when faced with low-fold common-midpoint gathers, which might be caused by natural barriers or man-made obstacles. Another problem is that many approaches are derived from very simple model assumptions that quickly break down for complex structures and do not provide enough model flexibility for an iterative and interactive velocity analysis. In this paper, we present a new velocity analysis method based on the model-based common-diffraction-surface stack operator and apply it to two synthetic data sets, one with locally sparse common-midpoint coverage and one with a laterally variable complex geological structure. We generate velocity spectra by calculating the semblance along spatial operators obtained for all possible emergence angles and an entire range of velocity models. Comparing the resolution of such velocity spectra with those obtained with the classical normal moveout velocity analysis shows, in both two analysed cases, that the stacking velocity can be estimated much more precisely. The reasons for this are that the event dip is handled independently from the velocity and that the semblance is obtained, for each zero-offset sample, over a group of neighbouring common-midpoint gathers instead of just one.