where is the optimal time shift for th trace in the processing window, denotes the number of time samples in the processing window and denotes the th sample of the reference trace and denotes the data value in th sample and th trace. corresponds to shifting trace downward with respect to the reference trace, and corresponds to shifting trace upward.

As can be seen from the equation 5, the selection of reference trace is crucial for the effectiveness of LSVD. It can be chosen as random trace in the processing window if the noise level is not high, or can be chosen as a stacked trace after normal-moveout (NMO) of common-midpoint gathers. Bekara and van der Baan (2007) proposed an iterative strategy for selecting the optimal reference trace stating that the resulting shifted traces are stacked after each cross-correlation pass for updating the new reference traces and the process of cross-correlation, shifting, and stacking is repeated until the process converges. Figure 1 shows a demonstration for dip steering and the processes of LSVD. Figure 1a is the original noisy dipping event. Figure 1b denotes the flattened event after forward dip steering. Figure 1c shows the LSVD denoised result by choosing only one singular value. The final denoised result after inverse dip steering on Figure 1c is shown in Figure 1d. The time shifts after the optimizing equation 5 are shown in Figure 2. The reference trace is simply chosen as the first trace of the original data, as shown in Figure 1a.

dn,dh,dhc,dc
Demonstration for dip steering and LSVD. (a) Noisy dip reflector. (b) Flattened event using dip steering. (c) SVD denoised result by selecting only one eigen-image. (d) Denoised data after inverse dip steering.
Figure 1. |
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shift
Time shifts for each trace for the forward dip steering as shown in Figure 1 (reference trace selected as the left trace in Figure 1a).
Figure 2. |
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2020-03-09