Fuzzy Residual Statics Computation

The essential information needed for residual statics computation is the normal-moveout-corrected event times. Because of the noisy nature of seismic data, picking the event times is a difficult task. Our approach is to describe the event times implicitly in terms of fuzzy sets. As a result, we can delay picking of event times until a stage in which they are easier to determine. The benefits are that we minimize the chance of throwing out needed information and avoid making erroneous picks for later computations. We define a fuzzy averaging operation and extend a well-known back-projection algorithm in a fuzzy context that allows us to compute a set of fuzzy statics. We then defuzzify this set of fuzzy statics to crisp numbers and apply them to correct seismic data, Our results show the robustness of this algorithm for noisy data with large residual statics.