The multiple model was calculated in the shot domain using a non-recursive version of the SRME technique developed by Delft Verschuur et al. (1992). We describe how we created the multiple model in the appendix A [equation (16)]. In few words, the goal of our modeling algorithm is to generate a kinematically correct multiple field. Therefore, there is no attempt to compensate for source signature effects. Indeed, our hope is that the attenuation scheme is robust enough to cope with significant amplitude errors in the multiple model.
Figure 5 shows a comparison between one recorded shot gather on the right, and the multiple model for the same shot location on the left. This shot is taken at the vertical of the salt body. The kinematics of the input data, displayed in the right-hand panel of Figure 5, are accurately reproduced in the multiple model (left-hand panel of Figure 5). The missing energy at near offset in the multiple model results from the lack of short offset traces. Out-of-plane effects might affect the accuracy of the model considerably. In addition, the limited aperture of the recording geometry may cause modeling problems when dipping beds are present in the subsurface Guitton (1999).
The multiple prediction is done in the shot domain, but our multiple attenuation scheme was tested in the CMP domain. The next two sections present multiple attenuation results for one CMP gather outside the salt boundaries and one over the salt body.
Figure 6a shows a CMP gather extracted from the Gulf of Mexico dataset, outside the salt boundaries, and infested with multiples. Figure 6b shows the multiple model at the same location. The main patterns are accurately modeled but the relative amplitudes of high-order multiples are not preserved. The multiple attenuation starts by estimating the PEF for the data and the noise model. The PEF coefficients are then smoothed along radial directions to stabilize their inversion Clapp et al. (1999). Then, the noise attenuation begins with either equation (2), for the Wiener-like method, or equation (4), for the subtraction scheme. Figure 7 displays the result of the multiple attenuation using both methods. The multiples have been correctly attenuated in the two cases. Figure 8 shows the difference between the input data and the multiple-free gather using both methods. The two noise attenuation schemes lead to very similar results.
For the last multiple attenuation result of this paper, we extracted a CMP gather over the salt body. Multiple attenuation becomes more challenging because the salt body generates strong internal multiples, diffractions and shadow zones that are difficult to incorporate in the noise model. Figure 9 shows the selected CMP gather inside the salt boundaries with the corresponding multiple model. Despite the inherent difficulty of modeling subsalt multiples, the kinematics of the multiples in Figure 9a look similar to those in Figure 9b. Figure 10 shows the estimated signal. As expected, the remaining signal is less coherent inside the salt boundaries than outside. Nonetheless, the two schemes reveal hidden information in a similar way. Figure 11 proves that once again, the coherent noise attenuation is comparable for both methods.