Hough transform based multiple removal in the XT domain

The proposed method for multiple reflection attenuation is based on a two-step procedure for the construction of optimized model traces. Statistical optimization of the model traces at each offset (step 1) is followed by a Hough transform based scaling (step 2) which further reduces the non-multiple energy in the model traces. The major advantage is the substantial enhancement of the non-multiple/multiple energy ratio in the near offset, obtained through the Hough transform scaling. We apply the method to CMP gathers corrected for the NMO of the multiples. The multiple reject zone is defined by the analyst in the velocity analysis phase. At the present state of implementation the proposed method is effective in the removal of horizontally aligned events. The first step is separately carried out for each multiple reflection, thus resulting in a time-variant and offset-variant number of traces which contribute to the model-trace construction. A measure of the coherence obtained in the multiple reject window, as a function of the number of adjacent traces considered, is used to determine the optimum number of traces to be summed for the construction of the individual model traces at each offset. A scaling function is calculated from the input data which is applied to the model traces in order to minimize the non-multiple energy. A single scaling function for all the offsets is calculated from the NMO corrected CMP gather by applying a shape detection algorithm based on the Hough transform. Maximum values of the scaling function are obtained where the algorithm detects the presence of horizontal alignments, corresponding to multiple reflections in the input data. The scaled model traces are subtracted from the data. The method was tested on real data from the Ross Sea (Antarctica) and from the Rockall Trough (offshore U.K., courtesy of BIRPS). The results indicate that the method provides superior multiple attenuation and preservation of the primary signal in most cases when compared with conventional techniques, such as filtering in the FK and τp domains. The present implementation of the algorithm carries out in parallel model trace and scaling function computation. The CPU time requested for a complete run of the proposed algorithm is approximately one tenth of that requested by conventional FK filtering.