The multiple attenuation is carried out in the shot domain. I display in Figure a near-offset section of the data. First, I estimate a weighting function for the filter estimation and a masking operator for the noise attenuation. For the masking operator, I manually picked the first surface-related multiple and applied a mute in the offset panel with the water velocity. Figure a shows a masking operator for one shot gather at location 4500 m. in Figure . The ones in Figure a show data points that are affected by the signal/noise separation. The zeros show data point that will be kept unchanged. For the noise and signal PEFs weighting operators, I first applied an AGC of 0.8 second (200 samples) on the shot gather for the data and the multiple model. From these gathers, I estimated a weighting function by dividing the gathers with AGC by the gathers without AGC, making sure that no division by zero would occur. Figure b displays the weighting function used for the noise PEFs estimation. Figure c shows the weighing function used for the signal PEFs estimation. Note that the weight for the signal PEFs is estimated from the data.
Having computed the masking and the weighting operators, we can proceed to the filter estimation and the multiple attenuation steps. The first step is to estimate the noise and signal PEFs, i.e., equation (11). Then, I estimate the signal, i.e. equation (7). I show the results of the multiple attenuation for three different locations in Figures , and . In Figure b, we notice that the multiple model has weak amplitudes at short offset. This comes from the acquisition geometry at short offset Dragoset and Jericevic (1998). It is interesting to notice that the weighing function in Figure b for the same location is boosting-up the short offset traces to balance this effect. The same problem in the multiple model can be seen in Figures b and b.
For each result in Figures , and I compare the estimated signal when 2-D and 3-D filters are utilized for the signal/noise separation. For every gather, the 3-D filters yield a better noise attenuation result. It is interesting to see that the 3-D filters can handle modeling errors and diffracted multiples very well (Figure d). Below the salt, e.g, Figure , the 3-D attenuation is very good at short and far offset. I show in Figure time slices of the time/offset/shot cube in which the multiple attenuation is performed. As expected, 3-D filters (Figure d) attenuate the noise much better than 2-D filters (Figure c). It is quite remarkable that 3-D filters perform so well in areas where the multiple model is known to be inaccurate. In particular, diffracted multiples and off-plane/3-D multiples are better attenuated (between offsets 2000 and 3000 m in Figure ).
Now, I show the stacked section of the input data, the estimated signal with 2-D and 3-D filters in Figures , and , respectively. The multiple attenuation with 3-D filters gives the best stacked results. With 3-D filters, most of the diffracted multiples are well attenuated, although they are not completely predicted in the multiple model. Therefore, having more dimensions for the filter greatly improves the multiple attenuation. It is also important to notice that as opposed to Liu et al. (2000), no internal mute or f-k filtering are necessary when the 3-D filters are utilized. Figure shows a close-up of the stacked sections for the data (Figure a), the estimated signal with 2-D filters (Figure b) and the estimated signal with 3-D filters (Figure c). The multiple attenuation with 3-D results clearly preserves the signal better than with 2-D filters.