Ground-roll noise attenuation using a simple and effective approach based on local bandlimited orthogonalization

Example

The dataset that we use to demonstrate the effectiveness of our proposed denoising approach is an open-source dataset, which has been widely used in the geophysics community Yilmaz (1987); Yarham et al. (2006). This data is referred to as the OZ-25 dataset Yarham et al. (2006). One can easily download it either from the Seismic Unix (SU) website ( $http://www.cwp.mines.edu/cwpcodes/$ ) or from the Madagascar software website ( $www.ahay.org$ , Fomel et al. (2013)). The raw data in common shot domain is shown in Figure 2. The temporal sampling rate is 0.002s and the spatial sampling rate is 0.05km. The shot location is located at the middle of the receiver array, thus the shot record has a symmetric form. There are 81 traces (receivers) in the shot record and the offset ranges from -2km to 2km. The OZ-25 dataset is a typical dataset suitable for testing the ground-roll noise attenuation performance because of several reasons. First, there is a large amount of ground-roll noise contaminating this dataset. It is obvious that most of the primary reflections are covered by this coherent ground-roll noise. Secondly, the reflections are highly non-stationary. We can clearly see that the amplitudes of the reflections are variable in the range of the whole gather.

We locally orthogonalize the denoised section and noise section that come from the initial bandpass filtering using $fl=25$ Hz. The initial guess of the primary reflections and ground-roll noise are shown in Figures 3a and 3b. Figures 4a and 4b show the denoised section and noise section using the proposed approach. The denoised data using the proposed approach shows excellent result, because most of the ground-roll noise has been removed, but no primary reflections energy is damaged.

We also apply the widely used adaptive subtraction method to the field data and show its performance in Figures 4c and 4d. Figures 4c and 4d correspond to the denoised data and removed noise, respectively. It is obvious that there is some residual ground-roll noise remaining in the denoised data and that the noise section contains significant reflection energy, especially for the shallow part.

We zoom several parts from the denoised sections and noise sections and show them in Figures 5 and 6. Figure 5 shows the zoomed denoised sections for the frame box A, as shown in Figures 3a,3c, 4a, and 4c, respectively. We can see there is good primary reflection recovery using the proposed approach, by comparing Figures 5a and 5c. There is also an obvious decrease of noise using the proposed approach by comparing Figures 5b and 5c. It is more obvious that the adaptive subtraction method leaves some residual dipping ground-roll noise energy by comparing Figures 5c and 5d.

Figure 6 shows the zoomed noise sections for frame box B, as shown in Figures 3b, 3d, 4b, and 4d, respectively. Please note that there is a decrease of primary reflections using the proposed approach, comparing Figures 6a and 6c, and there is an increase of noise removal using the proposed approach, comparing Figures 6b and 6c. The proposed approach and the adaptive subtraction method are very similar in this selected region. There is a slight amount of useful energy in Figure 6c but hopefully not significant, considering the overall denoising performance. The ground-roll noise energy in Figure 6c, however, is a bit stronger than that in Figure 6d. These observations indicate that compared with bandpass filtering with $fl=25$ Hz, the proposed approach preserves much more useful energy, and compared with bandpass filtering with $fl=10$ Hz, the proposed method removes much more ground-roll noise. Compared with the traditional adaptive subtraction method, the proposed approach can obtain a generally better performance.

Figure 7 shows a comparison of the average spectrum of all the traces for different data. The black solid line denotes the average spectrum of raw data. The green line corresponds to the proposed approach. The red line corresponds to the high-pass filtering with $fl=25$ Hz. The pink line corresponds to the high-pass filtering with $fl=10$ Hz. Blue corresponds to the adaptive subtraction method. We can see obviously that there is a removal of ground-roll noise spectrum from the black and yellow lines to the green line. There is also a spectrum boost of the primary reflections between red and green. There exists several spectral notches for the blue spectrum, which indicates that there is still an overlap of reflections and ground-roll noise after applying the adaptive subtraction method.

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Figure 2. Raw OZ-25 field data, borrowed from Yarham et al. (2006).

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Figure 3. (a) Bandpass filtered data (fl=25 Hz). (b) Difference section corresponding to (a). (c) Bandpass filtered data (fl=10 Hz). (d) Difference section corresponding to (c).

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Figure 4. (a) Denoised data using the proposed approach. (b) Noise section corresponding to (a). (c) Denoised data using the adaptive subtraction approach. (d) Noise section corresponding to (c).

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Figure 5. (a)-(d) Zoomed denoised section comparisons for frame box A (as shown in Figures 3a,3c , 4a, and 4c, respectively). Note the primary reflections recovery from (a) to (c) and the noise decrease from (b) to (c). There is obvious residual ground-roll noise existing in (d).

zoomb-1,zoomb-2,zoomb-ortho,zoomb-3
Figure 6. (a)-(d) Zoomed noise section comparisons for frame box B (as shown in Figures 3b,3d, 4b, and 4d, respectively). Note the decrease of primary reflections from (a) to (c) and the increase of noise removal from (b) to (c). (c) and (d) are very similar in this zoomed region.

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Figure 7. Comparisons of the average spectrum of all the traces. The black line denotes the average spectrum of raw data. The green line corresponds to the proposed approach. The red line corresponds to $fl=25$ Hz. The pink line corresponds to $fl=10$ Hz. The blue line corresponds to the adaptive subtraction method. Note the removal of ground-roll noise spectrum from the black and pink lines to the green line, and the primary reflections spectrum boost from the red line to the green line. There exists several spectrum notches in the blue line, indicating a mixture of useful reflections and ground-roll noise after applying the adaptive subtraction method.

Ground-roll noise attenuation using a simple and effective approach based on local bandlimited orthogonalization