Fast Ground-roll Attenuation in Time-frequency Domain

Ground roll or surface wave is a common type of interference wave in land seismic surveys, which is distinguished by high amplitudes and low frequencies. Time-frequency algorithms are effective for ground-roll attenuation (Elboth et al., 2010).

We first use an open-source OZ-25 dataset, which is a typical dataset suitable for testing the ground-roll noise attenuation performance and has been widely used in the geophysics community (Chen et al., 2015; Yilmaz, 1987; Tao et al., 2020; Yarham et al., 2006). Fig.5a shows the raw dataset in common-shot domain with 81 traces and 2000 samples per trace. The temporal and spatial sampling intervals are 0.002 s and 0.05 km, respectively. We use the proposed SLTFT to generate the $t$-$f$-$x$ spectrum coefficients (see Fig.5b). The noise energy is primarily concentrated within a triangular zone surrounding the near offset in low frequency band. We borrow a similar strategy from Liu and Fomel (2013) and design a filter mask to attenuate the noise energy cluster localized in both frequency and space (see Fig.5c). Then we use the inverse SLTFT to bring back the separated signal (see Fig.6e). The denoised dataset shows that the strong interference noise is well-attenuated and the reflection signals are preserved. We use bandpass filtering (see Fig.6a) and LTF decomposition (see Fig.6c) to compare the denoising performance. Fig.7 shows zoomed-in sections from the separated signals in Fig.6. Fig.7a and 7d show that the bandpass filtering fails to attenuate the overlapped noise. Compared to the denoised results of LTF decomposition in Fig.7b and 7e, the proposed SLTFT method brought more satisfactory results (see Fig.7c and 7f) with the strong interference noise is well-attenuated.

field,sltft,cmask
Figure 5. (a) Raw OZ-25 dataset, (b) the $t\textrm {-}f\textrm {-}x$ spectrum obtained by the SLTFT ( $\varepsilon =0.99$) and (c) the filter mask in $t\textrm {-}f\textrm {-}x$ domain.

bp,bp_err,iltft,iltft_err,isltft,isltft_err
Figure 6. Estimated signals and separated noise using (a) and (b) high-pass filter with $f_{\text {hi}}$=20 Hz, (c) and (d) LTF decomposition, (e) and (f) the proposed SLTFT.

bp_wig1,iltft_wig1,isltft_wig1,bp_wig2,iltft_wig2,isltft_wig2
Figure 7. Magnified sections of the denoised profile in Fig.6. (a), (b) and (c) correspond to the sections outlined by dashed rectangles in Figs. 6a, 6c, and 6e, respectively. (d), (e) and (f) correspond to the sections outlined by dashed rectangles in Figs. 6a, 6c, and 6e, respectively.

Next, we use another widely-used field dataset, the Saudi Arabia Dune dataset, to further test the performance of the proposed method. The field dataset contains strong ground-roll noise with hyperbolic moveout (see Fig.8a) and is popular as a benchmark dataset for ground-roll noise attenuation (Yang et al., 2024; Zheng et al., 2022; Fomel, 2002; Kaur et al., 2020). We use a mask filter in the $t\textrm {-}f\textrm {-}x$ domain (see Fig.8c) to suppress the ground-roll noise. The estimated signal by using the high-pass filter with 20-Hz cutoff frequency contains more low-level ground-roll noise (see Fig.9a). The denoised dataset obtained by the proposed SLTFT (see Fig.8b) shows that the proposed method achieved the separation goal that the underlying reflection events clearly appear in the estimated section, and the ground-roll noise is well suppressed.

Although the LTF decomposition can also produce a reasonable result (see Fig.6c and 9c), its computational cost is way too much. The proposed method demonstrates a significant reduction in time cost, for example, the computational time by the SLTFT is 7.77 s for the OZ-25 dataset and 1.90 s for the Dune dataset when compared with 62.37 s and 16.69 s needed from the LTF decomposition.

dat,sltft,cmask
Figure 8. (a) Raw Saudi Arabia Dune dataset, (b) the $t\textrm {-}f\textrm {-}x$ spectrum obtained by the SLTFT ( $\varepsilon =0.99$) and the filter mask in $t\textrm {-}f\textrm {-}x$ domain.

bpsign,bpnoiz,ltftsign,ltftnoiz,sltftsign,sltftnoiz
Figure 9. Estimated signals and separated noise using (a) and (b) high-pass filter with $f_{\text {hi}}$=24 Hz, (c) and (d) LTF decomposition, (e) and (f) the proposed SLTFT.