Determination of velocity smoothing operator for prestack Kirchhoff depth migration by Common Scatter Point Gathers
Hassan Khaniani, John C. Bancroft
Optimum smoothing is required in ray based prestack Kirchhoff depth migration to handle complex velocity models. It ensures numerical consistency and validity of modeling of finite difference data using ray tracing methods. Conventional approaches to find an optimum smoothing operator for the velocity field are based on visual inspection of final migrated image which is a time consuming and an expensive operation. In this work, to find an optimum smoothing operator, we propose to compare the modeled Common Scatter Point (CSP) data computed from ray tracing method with corresponding CSP gathers from real data. For numerical analysis, we applied this approach for a scatterpoint within a highly complex structure of Marmousi 2-D synthetic dataset that were considered as the real data. For CSP modeling, the velocity of the Marmousi model was smoothed with four different smoothing operators (i.e., smoothing length of 50m, 150m, 250m and 500m). Then for each smoothed velocity, scatterpoint response from the coordination of (5500, 2450) m of the model were simulated by ray tracing. Comparing the ray tracing CSP gather with the real data showed that the smoothing length of 250 m had the most optimum fit among other smoothing lengths. Our modeling results are consistent with the optimum smoothing operator length published by Gray (2000) (i.e., 100 m-200 m) that were obtained based on visual inspection of the final depth migrated section.