Attenuation of ground-roll

The first test aims to attenuate severely aliased hyperbolic ground-roll. The shot gather in Figure 1a comes from a 3-D land acquisition survey in Saudi Arabia. This shot gather has been previously used by Brown et al. (1999) and Fomel (2000). With this field example, because the noise and the signal span distinct frequency bandwiths, the ground-roll may be attenuated by applying a high-pass filter. However, Fomel (2000) shows that the separation in that case is far from optimal. Nonetheless, a low-pass filtering of the data gives an excellent ground-roll model that can be later used for the coherent noise attenuation. Figure 1b shows the noise model obtained with a bandpass filter. We added random noise to the noise model in order to stabilize the PEF inversion. We then estimated the noise PEFs N from this model.

After building the noise model, we performed the coherent noise attenuation using the two preceding schemes (equations (2) and (4)). The PEF and patch sizes are different in the two cases. With this dataset, we noticed that a larger PEF was needed in the subtraction scheme. The number of iterations needed in the PEF estimation and in the final inversion is the same for both methods. The parameters used in the Wiener-like technique are directly taken from Brown et al. (1999) and correspond to the best possible combination of parameters for an optimal separation of the noise from the signal.

Figure 2 shows the result of the noise attenuation for both methods. The two panels look similar and both show that the ground-roll has been correctly separated from the signal. Figure 3 shows the estimated noise computed by subtracting the signal in Figure 2 from the input data in Figure 1a. We see that the subtraction did a better job at preserving the signal because few coherent events remain outside the ground-roll cone in the estimated noise panel in Figure 3a.

 

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Figure 1 (a) Ground-roll contaminated shot gather. (b) The ground-roll model used to compute the noise PEF N (low pass filter of a, plus random noise).

 

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Figure 2 (a) The estimated signal using the subtraction scheme. (b) The estimated signal using the Wiener-like method. Both results are very similar.

 

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Figure 3 (a) The estimated noise using the subtraction scheme. (b) The estimated signal using the Wiener-like method. Less coherent noise is left outside the ground-roll cone for the subtraction method.