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Seismic random noise attenuation based on adaptive nonlocal median filter

Seismic random noise attenuation based on adaptive nonlocal median filter The accurate image of underground medium is determined by the quality of the seismic data, which can be improved by random noise attenuation and structural continuity enhancement. We proposed an adaptive nonlocal median filter that can protect geological structure while attenuating random noise. We combine the nonlocal idea with the weighted median filter and design the appropriate weights of the nonlocal median filter based on seismic data characteristics. The local structure is represented by the neighborhood around the center point. The directional difference of spatial vectors in the neighborhood is considered when computing the similarity. According to the local dip attribute of seismic data, the anisotropic Gaussian window is adaptively adjusted to increase the constraint along the structural direction. The proposed method can search more precisely for points with similar local structure to the filtered points and effectively attenuate seismic random noise. The continuity of events is enhanced while the goal of protecting fault information is achieved. The experimental results of the theoretical model and field data show that the adaptive nonlocal median filter can strike a balance between preserving structure information and attenuating seismic random noise. Keywords: random noise attenuation, nonlocal median filter, local similarity, anisotropic window, nonstationary seismic data 1. Introduction Seismic data is time-space variation manifested in the en- ergy and trace of seismic events, time-frequency spectrum The effective signals in seismic exploration are always in- and other characteristics that vary with time and space loca- evitably disturbed by random noise, especially in land explo- tion. Conventional denoising methods typically reduce the ration, which has a serious impact on the accurate imaging amplitude of curved and dipping events, affecting fault in- of the effective signals. The complex underground medium terpretation accuracy and complicating subsequent seismic easily causes the loss of effective information energy, and interpretation. There are numerous methods for suppress- random interferences caused by surface conditions result in ing random noise. The nonlocal mean filter is an effective the acquisition of low-quality data. The effective informa- method commonly used in image processing to suppress tion energy decreases with increasing detection depth, and Gaussian noise, which was first proposed by Buades et al. deep seismic data contain more random noise, resulting in (2005). The efficient nonlocal mean filter (Wang et al. 2006) lowsignal-to-noise ratio(SNR).Onlybyeffectivelyatten- and optimized spatial adaptive filter (Kervrann & Boulanger uating seismic random noise to improve the SNR can seis- 2006) have been proposed to accelerate speed and improve mic records more accurately reflect the subsurface geological the processing effect of the algorithm. Tasdizen ( 2009)sep- conditions. arated the noise components in the image information and © The Author(s) 2022. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute. This is an Open Access article distributed under the terms of 157 the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. improved the denoising ability of the filter. Bonar & Sac- median filter. The calculation method of the similarity co- chi (2012) first used the nonlocal mean filter to attenuate efficient is improved by combining the local cosine similar- random noise in seismic data. The adaptive nonlocal mean ity and the anisotropic Gaussian filter window. To improve (ABNLM) was proposed to address the issue of incorrect the weights along the structural direction, the window shapes filter parameter selection (Shang et al. 2013). Zhou et al. are adaptively adjusted based on the different dips of seismic (2016) combined nonlocal mean filter with sparse represen- events. The test results verify the effectiveness of the adaptive tation to suppress Gaussian noise and salt-pepper noise in im- nonlocal median filter that can attenuate the seismic random ages. Cao et al.(2018) proposed a more effective denoising noise and protect the valid signals from being filtered out. algorithm that combined the nonlocal mean filter with fuzzy edge compensation to preserve the detail structure of the 2. Theory image. 2.1. Local structure similarity The nonlocal mean filter has a good effect on suppressing seismic random noise, but it produces an excessive smooth- A neighborhood containing structural information is defined ing phenomenon during the filtering process. The median fil- as a comparison unit to quantitatively calculate the structural ter effectively suppresses the peak noise of the nonstation- similarity between the points i and j. There are numerous ary signals while protecting the edge information. The me- methods for measuring the local structure similarity. In the dian filter has been used in seismic data processing (Bed- traditional nonlocal mean filter, the Gaussian-weighted Eu- nar 1983; Duncan & Beresford 1995;Shi et al 2019). Wang clidean distance is used to represent the similarity. Consid- (2000) used correlation analysis to determine the best me- ering the influence of the distance from each point in the dian of median sequence in a range of apparent inclination neighborhood to the center point and the amplitude differ- as the effective signals. Liu et al.(2005)demonstratedthe ence of corresponding points between two neighborhoods, 2D multi-level median filtering technique and investigated the weight of each point is calculated as follows: the effects of the filter length and noise characteristics. The 2D multi-level median filter (Liu et al. 2006), time-varying w(i, j) = exp median filter (Liu et al. 2008), 3D adaptive median filter (Al- Z(i) ( ) Dossary 2014) and decision-based median filter (Bagheri & ∑ nl − [G (l)(d(N (l)) − d(N (l)))] a i j Riahi 2016) have been used to attenuate seismic random , (1) noise. Huo et al.(2017) used median filter along the princi- pal dip direction and processed the remaining principal dip signals in descending order by the iterative method. Wu et al. where d(N )and d(N ) are the neighborhoods of the points i i j (2018) proposed a 3D multi-directional vector median filter and j, respectively; G (l)isthe Gaussian kernel function and (Wang et al. 2020). Lyakhov et al.(2019)proposedanadap- Z(i) represents the normalizing factor. The parameter a con- tive median filter by combining the results of iterative image trols the local influence range of Gaussian kernel function. processing and median filtering. With an increase in parameter a,the rangeoflocalinfluence In the eld fi of image processing, some researchers have expands, the smoothness improves and the effect of structure combined the median filter and the nonlocal mean filter to information protection deteriorates. The constant h controls solve the problem where the nonlocal mean filter is not ideal the decay of the equation, and the smoothness increases as h for dealing with impulse noise. Lei (2015) proposed a non- increases. local average denoising algorithm based on median prefilter- Due to the different sampling rate of seismic data in time ing. A nonlocal median filter algorithm was proposed (Mat- and space direction, it is important to select appropriate suoka et al. 2015), which used the median of the data sorted weight coefficients based on the characteristics of the seis- by weight as the filtering result. Then the robustness of non- mic data. The traditional similarity coefficient only considers local median filter was enhanced by using weighted similarity the influences of distance and amplitude, which are related (Matsuoka et al. 2017). However, the nonlocal median filter to the coordinate position. It is more logical to treat the data withbetter edge protection abilityisrarelyusedinseismic as a vector eld fi rather than as an independent scalar field. data processing when compared to the classical median filter. Because the cosine correlation coefficient can measure the The nonlocal mean filter is an effective method for sup- difference in spatial vector directivity, it can be used to ex- pressing Gaussian noise, but it will excessively smooth fault press coherence between components, which is more consis- and structure information, reducing the accuracy of seismic tent with the essential characteristics of seismic data. In order interpretation. The weighted median filter can not only at- to effectively characterize the local variation of nonstation- tenuateseismic random noise,butitalsohas ahighability ary seismic data, we use a computationally efficient stream to protect local structure. We combine the weighted median algorithm to compute the local cosine similarity coefficient filter with a nonlocal idea to define a new adaptive nonlocal (Fomel 2007). The local cosine similarity coefficient can be 158 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. written as: conjugate gradient method is used to solve the least-squares 2 equation by adding the shaping regularization operator S: w = pq, (2) 2 2 ‖ ‖ ‖ ‖ −1 −1 T T T T 𝜎 ̂ =argmin D(𝜎 )d + S[𝜎 ] , (8) ‖ ‖ ‖ ‖ where p = (A A) (A b), q = (B B) (B a). a and b are 2 2 the vector forms of the signals a(i)and b(i), respectively. A where 𝜎 ̂ is the residual of the calculation and d consists of and B are diagonal matrices formed by elements of vectors multiple seismic traces. a and b, respectively. Since equation (2) is a mathematical Although the accuracy of the plane-wave method de- underdetermined problem that cannot be solved directly, a creases as the random noise intensity increases, the proposed streaming algorithm is used to constrain the local smoothing method has a low requirement for the accuracy of local dips, conditions (Zhou et al. 2021). The goal function of adding a which only uses the trend information to design the window local smoothing constraint in both time and space direction shape. The anisotropic Gaussian filter window is designed as is: follows: ( ( )) a a b ⎡ ⎤ ⎡ ⎤ i,j i,j i,j 2 2 d d ⎢ ⎥ ⎢ ⎥ 1 2 𝜆 p p ≈ , (3) t i−1,j t i,j G (x, y) =exp − + , (9) ⎢ ⎥ ⎢ ⎥ 2 2 a a 𝜆 p ⎣ ⎦ ⎣ ⎦ 1 2 x x i,j−1 where 𝜆 and 𝜆 are the constant scale parameters that con- where d = x cos 𝜎 + y sin 𝜎 , d = x cos 𝜎 − y sin 𝜎 and 𝜎 t x 1 2 strain the smoothness of p in time and space, respectively. is the local dip of the seismic event. a and a represent the 1 2 The least square solution of the equation (3) is: scale coefficients of the anisotropic Gaussian window, which can be selected according to the different local structural 2 2 characteristics of seismic data. When 𝜆 = = 1issatisefi d, a (a b ) + 𝜆 p̄ i,j i,j i,j i,j a p = , (4) i,j the anisotropic Gaussian filter window is converted to the tra- (a ) + 𝜆 i,j ditional isotropic Gaussian filter window. 2 2 𝜆 p + 𝜆 p i−1,j i,j−1 t x p̄ = , (5) i,j 𝜆 + 𝜆 2.3. Adaptive nonlocal median lt fi er 2 2 2 where the parameter 𝜆 is 𝜆 = 𝜆 + 𝜆 . Similarly, the vector Many similar image blocks are distributed throughout the t x q is calculated as: image in various positions, and the structural information 2 2 a (a b ) + 𝜆 q̄ surrounding each pixel can be represented by other pixels i,j i,j i,j i,j q = . (6) in the neighborhood. The nonlocal concept implies that the i,j (a ) + 𝜆 i,j similarity of the image itself can be used to search the points The local cosine similarity coefficient is with similar structural information to the filter point in the 2 global range. In comparison to other methods, such as the w̄ = p q . (7) i,j i,j i,j bilateral filter, the adaptive nonlocal median filter uses simi- According to the equation (7), we can get the cosine simi- larity between neighborhoods rather than similarity between laritycoecffi ientofeachpoint.Weusethedistancealgorithm points, which can better reflect local structural characteris- to measurethe distance andamplitudedifferences. Thesim- tics. The neighborhood is a square window with a side length ilarity coefficient algorithm is used to measure the difference of 2f + 1 in both time and space directions. To improve in spatial vector direction. calculation efficiency, we select a square window with the side length of 2t + 1 as the search window and calculate the weight of each point in the window. According to the char- 2.2. Anisotropic Gaussian lt fi er window acteristics of nonstationary seismic data, the local structure The traditional similarity calculation method uses an similarity is chosen as the weight to define the adaptive non- isotropic Gaussian filter window, which ignores the local median filter. anisotropic property of seismic events and results in ex- The local cosine similarity is combined with the Gaussian- cessive smoothing of structural information. Because the weighted Euclidean distance to describe the similarity be- anisotropic Gaussian filter window increases the weight tween each point in the search window and the center point. along the dip direction of the event when calculating the The local similarity equation (1) is changed as follows: ( ) similarity, the points with similar structures can be searched ∑ nl − [G (l)(d(N (l)) − d(N (l)))] a i j for more accurately. We design an anisotropic Gaussian filter l w(i, j) = exp window related to the local dip attribute of seismic data. h Z(i) Fomel (2010)calculatedthe dip 𝜎 by using a nonstationary nl plane-wave destruction filter D that can predict the adja- ⋅ w̄ , (10) i,j cent seismic trace according to the local seismic dip. The 159 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 1. Synthetic model test. (a) Model. (b) Noisy data. (c) Estimated data section by FXDECON. (d) Random noise separated by FXDECON. (e) Estimated data section by f-x RNA. (f) Random noise separated by f-x RNA. (g) Estimated data section by curvelet transform. (h) Random noise separated by curvelet transform. (i) Estimated data section by an adaptive nonlocal median filter. (j) Random noise separated by an adaptive nonlocal median filter. where w̄ denotes the cosine similarity coefficient of each follows: i,j ( ) nl point. Equation (10) is then combined with an anisotropic − [G (l)(d(N (l)) − d(N (l)))] 1 𝜎 i j Gaussian filter window, which can avoid edge and direc- w(i, j) = exp Z(i) tional structure blurring by reducing the weight of interfer- ( ) ence points in the neighborhood. The data in the window nl is the same as the neighborhood that can represent the lo- ⋅ G ⋅ w̄ , (11) i,j cal similarity of the center point. Equation (10) is changed as 160 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 1. Continued where the normalization factor is Z(i) = in ascending order sort[y(N)] and swap the positions of the nl ∑ − [G (l)(d(N (l))−d(N (l)))] ∑ 𝜎 i j nl weight coecffi ients sort[w ] and (iii) accumulate the weight l 2 (exp( ) ⋅ ( G ⋅ w̄ )). The j 2 𝜎 l i,j coecffi ients according to the rearranged sequence. The corre- weight is independent of its position and is only related to sponding data are used as the filtering result when the thresh- the local structural similarity of the calculated point neigh- old T is less than or equal to the accumulated number. borhood. The similarity coefficients calculated by equation Buades et al. (2005) proposed a linear relationship be- (11) areusedasthe weightsofthe adaptive nonlocalmedian tween the constant h and the noise variance. When the noise filter. intensity is high, we select a larger value of the parameter The weighted median (Liu et al. 2011)ofeachpoint j in h that maintains the same order of magnitude as the root thesearchwindowisthe filteredresult d(i) of the point i, mean square (RMS) of the original seismic data. The neigh- which is defined as follows: borhood radius is chosen based on the amount of data to ̂ be denoised. The radius of the search window f and the d(i) = MEDIAN(w ♢d ,w ♢d , ⋯ ,w ♢d ), (12) i,1 1 i,2 2 i,N N neighborhood t have the relationship t = 2f + 1. As a result where d is a collection of samples [d d ⋯ d ]madeupof of the experiment, we have the following rules for selecting 1 2 N effective signals and random noise. ♢ denotes the replication the filter radius in table 1: operator, which means that x is copied w times. The value of i i the weight w between 0 and 1 represents the similarity, and i,j the sum of all weights in the search window equals 1. Table 1. Filtering radius selection regulation. The noninteger weighted median of the data within the search window are the filtering result of the adaptive non- Data size: d = n1 ∗ n2 d < 70∗70 70∗70 ≤ d ≤ 90∗90 d > 90∗90 local median filter, which is described as follows: (i) calcu- Neighborhood radius f 456 late the weight coefficients w in the search window and the Search window radius t 911 13 1 N threshold is T = w ;(ii)arrangetheraw data y(N) 0 i i=1 161 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 2. FK spectra of the synthetic model test. (a) FK spectra of model. (b) FK spectra of noisy data. (c) FK spectra of estimated data section by FXDECON. (d) FK spectra of random noise separated by FXDECON. I FK spectra of estimated data section by f-x RNA. (f) FK spectra of random noise separated by f-x RNA. (g) FK spectra of estimated data section by curvelet transform. (h) FK spectra of random noise separated by curvelet transform. (i) FK spectra of estimated data section by an adaptive nonlocal median filter. (j) FK spectra of random noise separated by an adaptive nonlocal median filter. 3. Discussion deep sinusoidal curved events, a fault and an unconformity (figure 1a). Figure 1b depicts the model data after adding 3.1. Synthetic model Gaussian and impulsive mixed random noise (SNR = The effectiveness of the adaptive nonlocal median filter was −1.104, RMS = 0.0022). The estimated data section by verified by a standard post-stack seismic data model (Claer- FXDECON (gfi ure 1c) shows that some noise has been bout 2008). The model size is 200 (time samples) × 200 suppressed (SNR = 4.243), but there are some artificial (space samples), including the shallow dipping events, the events.Thenoisesection (gfi ure 1d) demonstrates that the 162 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 2. Continued FXDECON cannot provide adequate protection for dip- some structural information is lost, particularly in curved ping and curved events, a portion of the effective signals events. When the filtering parameters are t = 13, f = 6 are filtered during the denoising process. We usually di- and h = 0.014, the estimated data section by the adaptive vide the data into small processing windows to satisfy the nonlocalmedianfilter is showninfigure 1i(SNR = 9.459). assumption that the event is linear in each subwindow. Note that theproposedmethodpreserves amoredetailed However, this method is faced with the problem of adap- structure and reveals a higher SNR while retaining con- tive window selection. The estimated data section by f-x struction information intact. When compared to gfi ure 1d, regularized nonstationary autoregressive (RNA) (gfi ure 1e) f and h, the noise section (gfi ure 1j) demonstrates that the shows a better filtering effect and a relatively high SNR proposed method recovers the valid information in the non- (SNR = 7.427). The noise section (gfi ure 1f) shows that stationary seismic data reasonably, such as the fault and the the f-x RNA can better protect the structure information unconformity. of curved events than FXDECON. Although f-x domain We calculated the FK spectra of the synthetic model and prediction filtering methods can suppress random noise, processing results in gfi ure 1 to further validate the effective- effective information cannot be accurately estimated. When ness of the adaptive nonlocal median filter. Figure 2ashows dealing with nonstationary seismic data, more structure the FK spectra of the original signals, which corresponds information is filtered. The random noise is then attenuated well to the synthetic model. The signals with higher energy using the second generation curvelet transform (Candès on both sides correspond to the sinusoidal curved events in et al. 2006). Figure 1 parts g (SNR = 7.598) and h are the the deep layer, while the signals with the steeper slope on denoised result and the noise section by the curvelet trans- the right side correspond to the dipping events in the shal- form, respectively. We can see that the noise is effectively low layer. Figure 2b shows the FK spectra of the noisy data. removed and the denoised data are smoother than that of f-x Note that the distribution of random noise in FK domain prediction filter. However, there are unwanted nonsmooth is also random. The FK spectra of the data processed by artifacts near the discontinuous region. Figure 1hshows that FXDECON, f-x RNA, curvelet transform and the adaptive 163 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. similar to the original theoretical model. Figure 2 parts d, f, h and j show the FK spectra of removed noise sections, re- spectively. The adaptive nonlocal median filter outperforms the traditional methods in terms of random noise attenuation and structure protection. 3.2. Field data Theadaptivenonlocalmedianfilter wasapplied to a3D field data containing faults, nonstationary events and ran- dom noise. Thedatasizeis200 (timesamples) × 200 (x samples) × 200 (y samples), and the sampling interval is 4 ms (gfi ure 3). Figure 4 parts a and b show the estimated data section and the separated random noise produced by Figure 3. The3Dfielddata. the FXDECON at the same clip value. Although the SNR of the estimated data is increased, the method has a signif- nonlocal median filter are shown in gfi ure 2 partsc,e,gandi, icant leakage of effective signal energy. These results show respectively. These results show that the filtering effect of that the FXDECON has a poor signal protection effect on theproposedmethodisbetter, alarge amount of noiseisre- nonstationary seismic data. The denoising results and the moved, and the spectral characteristics after filtering are more separated noise using the f-x-y RNA (Wang 1999)are shown Figure 4. The 3D eld fi data test. (a) Estimated data section by FXDECON. (b) Random noise separated by FXDECON. (c) Estimated data section by f-x-yRNA.(d) Random noiseseparated by f-x-yRNA.(e) Estimateddata section by curvelet transform. (f) Random noise separated by curvelet transform. (g) Estimated data section by an adaptive nonlocal median filter. (h) Random noise separated by an adaptive nonlocal median filter. 164 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 4. Continued in the gfi ure 4 parts c and d, respectively. The overall clarity 4. Conclusions of the profile has improved, but there are still some dipping We introduced an adaptive nonlocal median filter to suppress and curved events in the noise section. Then we use the seismic random noise in this paper. The proposed method se- curvelet transform and the adaptive nonlocal median filter lected the appropriate similarity coefficient according to the to suppress random noise for each slice along the time direc- characteristics of seismic data to find the points with simi- tion. The denoised data by the curvelet transform are shown lar structures, and used the weighted median filter to select in gfi ure 4e, indicating the ability of the algorithm in accu- the data with higher local similarity. The traditional method rately recovering theseismic events.Wecan noticeaportion of calculating the similarity coefficient only considers the in- of the structure information has been filtered out, which fluence of distance and amplitude; we combined the cosine appears clearly in the noise section (figure 4f). Because the correlation coefficient that can represent the direction of the RMS of the field data is 3132.04, we chose the parameters space vector and designed an anisotropic Gaussian filter win- t = 13, f = 6and h = 9000. The estimated data section by dow to enhance the weight of the structural direction. The the adaptive nonlocal median filter is shown in gfi ure 4g. window shape was adaptively adjusted according to the lo- Note that the SNR and local structural characteristics of cal dip attributes of seismic data so that the similarity coef- the seismic data have been improved, effective signal energy ficient was more consistent with the characteristics of seis- becomescontinuousandtheshapesofreflection eventshave mic data and more suitable for nonstationary seismic data been well restored. Compared with figure 4 b, d and f, the processing. random noise is effectively suppressed with almost no noise When compared to traditional methods such as the in- energy present, implying that the proposed method can suc- dustry standard FXDECON, f-x-y RNA and curvelet trans- cessfully separate signals and noise (gfi ure 4h). Furthermore, form, the relationship of effective signal protection and the relationship between random noise attenuation and SNR enhancement could be well balanced by our proposed effective signal protection can be changed by adjusting the method. The numerical experiment results showed that the parameter h. 165 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. adaptive nonlocal median filter has advantages in structural Liu, C., Liu, Y., Yang, B.J., Wang, D. & Sun, J.G., 2006. A 2D multistage median filter to reduce random seismic noise, Geophysics, 71, V105– detail protection and can produce a more reasonable filtering V110. result. Liu, C., Wang, D., Liu, Y., Wang, P.M. & Li, Q.X., 2005. Preliminary study of using 2D multi-level median filtering technique to eliminate random noises, Oil Geophysical Prospecting, 40, 163–167. Acknowledgements Liu, Y., Liu, C., Wang, D., Li, Q.X., Feng, X. & Wang, J.M., 2008. Applica- This work is supported by National Natural Science Foundation of tion of time-variant median filtering technique to attenuation of seismic random noises, Oil Geophysical Prospecting, 43, 327–332. China (grant nos. 41874125, 41974134 and 41774127) and Na- Liu, Y., Wang, D., Liu, C. & Feng, X., 2011. Weighted median filter based tional key Research and Development Program of China (grant no. on local correlation and its application to poststack random noise atten- 2018YFC0603701). uation, Chinese Journal of Geophysics, 54, 358–367. Lyakhov, P.A., Orazaev, A.R., Chervyakov, N.I. & Kaplun, D.I., 2019. A Conflict of interest statement: None declared. new method for adaptive median filtering of images, 2019 IEEE Confer- ence of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), pp. 1197–1201. References Matsuoka, J., Koqa, T., Suetake, N. & Uchino, E., 2015. Switching non-local Al-Dossary, S., 2014. Random noise cancellation in seismic data using a median filter, Optical Review, 22, 448–458. 3D adaptive median filter, SEG Technical Program Expanded Abstracts, Matsuoka, J., Koqa, T., Suetake, N. & Uchino, E., 2017. Robust non-local pp. 2512–2516. median filter, Optical Review, 24, 87–96. Bagheri, M. & Riahi, M.A., 2016. Seismic data random noise attenuation Shang, S., Han, L.G., Lü, Q.T. & Tan, C.Q., 2013. Seismic random noise using DBM filtering, Bolletion DIG, 57, 1–11. suppression using an adaptive nonlocal means algorithm, Applied Geo- Bednar, J.B., 1983. Applications of median filtering to deconvolution, pulse physics, 10, 33–40. estimation, and statistical editing of seismic data, Geophysics, 48, 1598– Shi, Y., Zhang, W. & Wang, Y., 2019. Seismic elastic RTM with vector- wavefield decomposition, Journal of Geophysics and Engineering, 16, Bonar, D. & Sacchi, M., 2012. Denoising seismic data using the nonlocal 509–524. means algorithm, Geophysics, 77,A5–A8. Tasdizen, T., 2009. Principal neighborhood dictionaries for nonlocal Buades, A., Coll, B. & Morel, J.M., 2005. A non-local algorithm for image means image denosing, IEEE Transactions on Image Processing, 18, denoising, IEEE Computer Society Conference on Computer Vision and 2649–2660. Pattern Recognition, 2, 60–65. Wang, J., Guo, Y., Ying, Y., Liu, Y.L. & Peng, Q.S., 2006. Fast nonlocal algo- Candès, E., Demanet, L., Donoho, D. & Ying, L. X., 2006. Fast discrete rithm for image denoising, IEEE International Conference on Image Pro- curvelet transforms, Multiscale Model. Simul., 5, 861–899. cessing, pp. 1429–1432. Cao, S., Huang, L.P., Hou, B.B. & Gang, C., 2018. Self-adaptive non-local Wang, W.H., 2000. Coherent signal prediction using mid-value correlative means image denoising algorithm based on fuzzy edge complement, filtering, Oil Geophysical Prospecting, 35, 273–282. Laser & Optoelectronics Progress, 55, 213–218. Wang, Y., 1999. Random noise attenuation using forward-backward linear Claerbout, J.F., 2008. Basic earth imaging. Standford Exploration Project, prediction, JournalofSeismic Exploration, 8, 133–142. http://sepwww.standford.edu/sep/prof/. Wang, Y., Liu, X., Gao, F. & Rao, Y., 2020. Robust vector median filter- Duncan, G. & Beresford, G., 1995. Some analyses of 2-D median f-k filters, ing with a structure-adaptive implementation, Geophysics, 85, V407– Geophysics, 60, 1157–1168. V414. Fomel, S., 2007. Local seismic attributes, Geophysics, 72, A29–A33. Wu, S.J., Wang, Y.B., Di, Z.X. & Chang, X., 2018. Random noise attenua- Fomel, S., 2010. Predictive painting of 3-D seismic volumes, Geophysics, tion by 3D multi-directional vector median filter, JournalofApplied Geo- 75, A25–A30. physics, 159, 277–284. Huo, S.D., Zhu, W.H. & Shi, T.K., 2017. Iterative dip-steering median filter, Zhou, Y.Y., Lin, M.S., Xu, S., Zhang, H.B., He, H.S., Li, Q. & Guo, J., Journal of Applied Geophysics, 144, 151–156. 2016. An image denoising algorithm for mixed noise combining non- Kervrann, C. & Boulanger, J., 2006. Optimal spatial adaptation for patch- local means filter and sparse representation technique, Journal of Visual based image denoising, IEEE Transactions on Image Processing, 15, Communication and Image Representation, 41, 74–86. 2866–2878. Zhou, Z.Y., Liu, Y., Liu, C., Wang, Q.H. & Zheng, Z.S., 2021. Local cosine Lei, Y., 2015. Research of image denoising algorithm based on non-local similarity attribute based on fast-streaming computation, SEG Technical priori constraints, Microelectronics & Computer, 32, 138–142. Program Expanded Abstracts,1–4. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Geophysics and Engineering Oxford University Press

Seismic random noise attenuation based on adaptive nonlocal median filter

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Oxford University Press
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© The Author(s) 2022. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute.
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Abstract

The accurate image of underground medium is determined by the quality of the seismic data, which can be improved by random noise attenuation and structural continuity enhancement. We proposed an adaptive nonlocal median filter that can protect geological structure while attenuating random noise. We combine the nonlocal idea with the weighted median filter and design the appropriate weights of the nonlocal median filter based on seismic data characteristics. The local structure is represented by the neighborhood around the center point. The directional difference of spatial vectors in the neighborhood is considered when computing the similarity. According to the local dip attribute of seismic data, the anisotropic Gaussian window is adaptively adjusted to increase the constraint along the structural direction. The proposed method can search more precisely for points with similar local structure to the filtered points and effectively attenuate seismic random noise. The continuity of events is enhanced while the goal of protecting fault information is achieved. The experimental results of the theoretical model and field data show that the adaptive nonlocal median filter can strike a balance between preserving structure information and attenuating seismic random noise. Keywords: random noise attenuation, nonlocal median filter, local similarity, anisotropic window, nonstationary seismic data 1. Introduction Seismic data is time-space variation manifested in the en- ergy and trace of seismic events, time-frequency spectrum The effective signals in seismic exploration are always in- and other characteristics that vary with time and space loca- evitably disturbed by random noise, especially in land explo- tion. Conventional denoising methods typically reduce the ration, which has a serious impact on the accurate imaging amplitude of curved and dipping events, affecting fault in- of the effective signals. The complex underground medium terpretation accuracy and complicating subsequent seismic easily causes the loss of effective information energy, and interpretation. There are numerous methods for suppress- random interferences caused by surface conditions result in ing random noise. The nonlocal mean filter is an effective the acquisition of low-quality data. The effective informa- method commonly used in image processing to suppress tion energy decreases with increasing detection depth, and Gaussian noise, which was first proposed by Buades et al. deep seismic data contain more random noise, resulting in (2005). The efficient nonlocal mean filter (Wang et al. 2006) lowsignal-to-noise ratio(SNR).Onlybyeffectivelyatten- and optimized spatial adaptive filter (Kervrann & Boulanger uating seismic random noise to improve the SNR can seis- 2006) have been proposed to accelerate speed and improve mic records more accurately reflect the subsurface geological the processing effect of the algorithm. Tasdizen ( 2009)sep- conditions. arated the noise components in the image information and © The Author(s) 2022. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute. This is an Open Access article distributed under the terms of 157 the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. improved the denoising ability of the filter. Bonar & Sac- median filter. The calculation method of the similarity co- chi (2012) first used the nonlocal mean filter to attenuate efficient is improved by combining the local cosine similar- random noise in seismic data. The adaptive nonlocal mean ity and the anisotropic Gaussian filter window. To improve (ABNLM) was proposed to address the issue of incorrect the weights along the structural direction, the window shapes filter parameter selection (Shang et al. 2013). Zhou et al. are adaptively adjusted based on the different dips of seismic (2016) combined nonlocal mean filter with sparse represen- events. The test results verify the effectiveness of the adaptive tation to suppress Gaussian noise and salt-pepper noise in im- nonlocal median filter that can attenuate the seismic random ages. Cao et al.(2018) proposed a more effective denoising noise and protect the valid signals from being filtered out. algorithm that combined the nonlocal mean filter with fuzzy edge compensation to preserve the detail structure of the 2. Theory image. 2.1. Local structure similarity The nonlocal mean filter has a good effect on suppressing seismic random noise, but it produces an excessive smooth- A neighborhood containing structural information is defined ing phenomenon during the filtering process. The median fil- as a comparison unit to quantitatively calculate the structural ter effectively suppresses the peak noise of the nonstation- similarity between the points i and j. There are numerous ary signals while protecting the edge information. The me- methods for measuring the local structure similarity. In the dian filter has been used in seismic data processing (Bed- traditional nonlocal mean filter, the Gaussian-weighted Eu- nar 1983; Duncan & Beresford 1995;Shi et al 2019). Wang clidean distance is used to represent the similarity. Consid- (2000) used correlation analysis to determine the best me- ering the influence of the distance from each point in the dian of median sequence in a range of apparent inclination neighborhood to the center point and the amplitude differ- as the effective signals. Liu et al.(2005)demonstratedthe ence of corresponding points between two neighborhoods, 2D multi-level median filtering technique and investigated the weight of each point is calculated as follows: the effects of the filter length and noise characteristics. The 2D multi-level median filter (Liu et al. 2006), time-varying w(i, j) = exp median filter (Liu et al. 2008), 3D adaptive median filter (Al- Z(i) ( ) Dossary 2014) and decision-based median filter (Bagheri & ∑ nl − [G (l)(d(N (l)) − d(N (l)))] a i j Riahi 2016) have been used to attenuate seismic random , (1) noise. Huo et al.(2017) used median filter along the princi- pal dip direction and processed the remaining principal dip signals in descending order by the iterative method. Wu et al. where d(N )and d(N ) are the neighborhoods of the points i i j (2018) proposed a 3D multi-directional vector median filter and j, respectively; G (l)isthe Gaussian kernel function and (Wang et al. 2020). Lyakhov et al.(2019)proposedanadap- Z(i) represents the normalizing factor. The parameter a con- tive median filter by combining the results of iterative image trols the local influence range of Gaussian kernel function. processing and median filtering. With an increase in parameter a,the rangeoflocalinfluence In the eld fi of image processing, some researchers have expands, the smoothness improves and the effect of structure combined the median filter and the nonlocal mean filter to information protection deteriorates. The constant h controls solve the problem where the nonlocal mean filter is not ideal the decay of the equation, and the smoothness increases as h for dealing with impulse noise. Lei (2015) proposed a non- increases. local average denoising algorithm based on median prefilter- Due to the different sampling rate of seismic data in time ing. A nonlocal median filter algorithm was proposed (Mat- and space direction, it is important to select appropriate suoka et al. 2015), which used the median of the data sorted weight coefficients based on the characteristics of the seis- by weight as the filtering result. Then the robustness of non- mic data. The traditional similarity coefficient only considers local median filter was enhanced by using weighted similarity the influences of distance and amplitude, which are related (Matsuoka et al. 2017). However, the nonlocal median filter to the coordinate position. It is more logical to treat the data withbetter edge protection abilityisrarelyusedinseismic as a vector eld fi rather than as an independent scalar field. data processing when compared to the classical median filter. Because the cosine correlation coefficient can measure the The nonlocal mean filter is an effective method for sup- difference in spatial vector directivity, it can be used to ex- pressing Gaussian noise, but it will excessively smooth fault press coherence between components, which is more consis- and structure information, reducing the accuracy of seismic tent with the essential characteristics of seismic data. In order interpretation. The weighted median filter can not only at- to effectively characterize the local variation of nonstation- tenuateseismic random noise,butitalsohas ahighability ary seismic data, we use a computationally efficient stream to protect local structure. We combine the weighted median algorithm to compute the local cosine similarity coefficient filter with a nonlocal idea to define a new adaptive nonlocal (Fomel 2007). The local cosine similarity coefficient can be 158 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. written as: conjugate gradient method is used to solve the least-squares 2 equation by adding the shaping regularization operator S: w = pq, (2) 2 2 ‖ ‖ ‖ ‖ −1 −1 T T T T 𝜎 ̂ =argmin D(𝜎 )d + S[𝜎 ] , (8) ‖ ‖ ‖ ‖ where p = (A A) (A b), q = (B B) (B a). a and b are 2 2 the vector forms of the signals a(i)and b(i), respectively. A where 𝜎 ̂ is the residual of the calculation and d consists of and B are diagonal matrices formed by elements of vectors multiple seismic traces. a and b, respectively. Since equation (2) is a mathematical Although the accuracy of the plane-wave method de- underdetermined problem that cannot be solved directly, a creases as the random noise intensity increases, the proposed streaming algorithm is used to constrain the local smoothing method has a low requirement for the accuracy of local dips, conditions (Zhou et al. 2021). The goal function of adding a which only uses the trend information to design the window local smoothing constraint in both time and space direction shape. The anisotropic Gaussian filter window is designed as is: follows: ( ( )) a a b ⎡ ⎤ ⎡ ⎤ i,j i,j i,j 2 2 d d ⎢ ⎥ ⎢ ⎥ 1 2 𝜆 p p ≈ , (3) t i−1,j t i,j G (x, y) =exp − + , (9) ⎢ ⎥ ⎢ ⎥ 2 2 a a 𝜆 p ⎣ ⎦ ⎣ ⎦ 1 2 x x i,j−1 where 𝜆 and 𝜆 are the constant scale parameters that con- where d = x cos 𝜎 + y sin 𝜎 , d = x cos 𝜎 − y sin 𝜎 and 𝜎 t x 1 2 strain the smoothness of p in time and space, respectively. is the local dip of the seismic event. a and a represent the 1 2 The least square solution of the equation (3) is: scale coefficients of the anisotropic Gaussian window, which can be selected according to the different local structural 2 2 characteristics of seismic data. When 𝜆 = = 1issatisefi d, a (a b ) + 𝜆 p̄ i,j i,j i,j i,j a p = , (4) i,j the anisotropic Gaussian filter window is converted to the tra- (a ) + 𝜆 i,j ditional isotropic Gaussian filter window. 2 2 𝜆 p + 𝜆 p i−1,j i,j−1 t x p̄ = , (5) i,j 𝜆 + 𝜆 2.3. Adaptive nonlocal median lt fi er 2 2 2 where the parameter 𝜆 is 𝜆 = 𝜆 + 𝜆 . Similarly, the vector Many similar image blocks are distributed throughout the t x q is calculated as: image in various positions, and the structural information 2 2 a (a b ) + 𝜆 q̄ surrounding each pixel can be represented by other pixels i,j i,j i,j i,j q = . (6) in the neighborhood. The nonlocal concept implies that the i,j (a ) + 𝜆 i,j similarity of the image itself can be used to search the points The local cosine similarity coefficient is with similar structural information to the filter point in the 2 global range. In comparison to other methods, such as the w̄ = p q . (7) i,j i,j i,j bilateral filter, the adaptive nonlocal median filter uses simi- According to the equation (7), we can get the cosine simi- larity between neighborhoods rather than similarity between laritycoecffi ientofeachpoint.Weusethedistancealgorithm points, which can better reflect local structural characteris- to measurethe distance andamplitudedifferences. Thesim- tics. The neighborhood is a square window with a side length ilarity coefficient algorithm is used to measure the difference of 2f + 1 in both time and space directions. To improve in spatial vector direction. calculation efficiency, we select a square window with the side length of 2t + 1 as the search window and calculate the weight of each point in the window. According to the char- 2.2. Anisotropic Gaussian lt fi er window acteristics of nonstationary seismic data, the local structure The traditional similarity calculation method uses an similarity is chosen as the weight to define the adaptive non- isotropic Gaussian filter window, which ignores the local median filter. anisotropic property of seismic events and results in ex- The local cosine similarity is combined with the Gaussian- cessive smoothing of structural information. Because the weighted Euclidean distance to describe the similarity be- anisotropic Gaussian filter window increases the weight tween each point in the search window and the center point. along the dip direction of the event when calculating the The local similarity equation (1) is changed as follows: ( ) similarity, the points with similar structures can be searched ∑ nl − [G (l)(d(N (l)) − d(N (l)))] a i j for more accurately. We design an anisotropic Gaussian filter l w(i, j) = exp window related to the local dip attribute of seismic data. h Z(i) Fomel (2010)calculatedthe dip 𝜎 by using a nonstationary nl plane-wave destruction filter D that can predict the adja- ⋅ w̄ , (10) i,j cent seismic trace according to the local seismic dip. The 159 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 1. Synthetic model test. (a) Model. (b) Noisy data. (c) Estimated data section by FXDECON. (d) Random noise separated by FXDECON. (e) Estimated data section by f-x RNA. (f) Random noise separated by f-x RNA. (g) Estimated data section by curvelet transform. (h) Random noise separated by curvelet transform. (i) Estimated data section by an adaptive nonlocal median filter. (j) Random noise separated by an adaptive nonlocal median filter. where w̄ denotes the cosine similarity coefficient of each follows: i,j ( ) nl point. Equation (10) is then combined with an anisotropic − [G (l)(d(N (l)) − d(N (l)))] 1 𝜎 i j Gaussian filter window, which can avoid edge and direc- w(i, j) = exp Z(i) tional structure blurring by reducing the weight of interfer- ( ) ence points in the neighborhood. The data in the window nl is the same as the neighborhood that can represent the lo- ⋅ G ⋅ w̄ , (11) i,j cal similarity of the center point. Equation (10) is changed as 160 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 1. Continued where the normalization factor is Z(i) = in ascending order sort[y(N)] and swap the positions of the nl ∑ − [G (l)(d(N (l))−d(N (l)))] ∑ 𝜎 i j nl weight coecffi ients sort[w ] and (iii) accumulate the weight l 2 (exp( ) ⋅ ( G ⋅ w̄ )). The j 2 𝜎 l i,j coecffi ients according to the rearranged sequence. The corre- weight is independent of its position and is only related to sponding data are used as the filtering result when the thresh- the local structural similarity of the calculated point neigh- old T is less than or equal to the accumulated number. borhood. The similarity coefficients calculated by equation Buades et al. (2005) proposed a linear relationship be- (11) areusedasthe weightsofthe adaptive nonlocalmedian tween the constant h and the noise variance. When the noise filter. intensity is high, we select a larger value of the parameter The weighted median (Liu et al. 2011)ofeachpoint j in h that maintains the same order of magnitude as the root thesearchwindowisthe filteredresult d(i) of the point i, mean square (RMS) of the original seismic data. The neigh- which is defined as follows: borhood radius is chosen based on the amount of data to ̂ be denoised. The radius of the search window f and the d(i) = MEDIAN(w ♢d ,w ♢d , ⋯ ,w ♢d ), (12) i,1 1 i,2 2 i,N N neighborhood t have the relationship t = 2f + 1. As a result where d is a collection of samples [d d ⋯ d ]madeupof of the experiment, we have the following rules for selecting 1 2 N effective signals and random noise. ♢ denotes the replication the filter radius in table 1: operator, which means that x is copied w times. The value of i i the weight w between 0 and 1 represents the similarity, and i,j the sum of all weights in the search window equals 1. Table 1. Filtering radius selection regulation. The noninteger weighted median of the data within the search window are the filtering result of the adaptive non- Data size: d = n1 ∗ n2 d < 70∗70 70∗70 ≤ d ≤ 90∗90 d > 90∗90 local median filter, which is described as follows: (i) calcu- Neighborhood radius f 456 late the weight coefficients w in the search window and the Search window radius t 911 13 1 N threshold is T = w ;(ii)arrangetheraw data y(N) 0 i i=1 161 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 2. FK spectra of the synthetic model test. (a) FK spectra of model. (b) FK spectra of noisy data. (c) FK spectra of estimated data section by FXDECON. (d) FK spectra of random noise separated by FXDECON. I FK spectra of estimated data section by f-x RNA. (f) FK spectra of random noise separated by f-x RNA. (g) FK spectra of estimated data section by curvelet transform. (h) FK spectra of random noise separated by curvelet transform. (i) FK spectra of estimated data section by an adaptive nonlocal median filter. (j) FK spectra of random noise separated by an adaptive nonlocal median filter. 3. Discussion deep sinusoidal curved events, a fault and an unconformity (figure 1a). Figure 1b depicts the model data after adding 3.1. Synthetic model Gaussian and impulsive mixed random noise (SNR = The effectiveness of the adaptive nonlocal median filter was −1.104, RMS = 0.0022). The estimated data section by verified by a standard post-stack seismic data model (Claer- FXDECON (gfi ure 1c) shows that some noise has been bout 2008). The model size is 200 (time samples) × 200 suppressed (SNR = 4.243), but there are some artificial (space samples), including the shallow dipping events, the events.Thenoisesection (gfi ure 1d) demonstrates that the 162 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 2. Continued FXDECON cannot provide adequate protection for dip- some structural information is lost, particularly in curved ping and curved events, a portion of the effective signals events. When the filtering parameters are t = 13, f = 6 are filtered during the denoising process. We usually di- and h = 0.014, the estimated data section by the adaptive vide the data into small processing windows to satisfy the nonlocalmedianfilter is showninfigure 1i(SNR = 9.459). assumption that the event is linear in each subwindow. Note that theproposedmethodpreserves amoredetailed However, this method is faced with the problem of adap- structure and reveals a higher SNR while retaining con- tive window selection. The estimated data section by f-x struction information intact. When compared to gfi ure 1d, regularized nonstationary autoregressive (RNA) (gfi ure 1e) f and h, the noise section (gfi ure 1j) demonstrates that the shows a better filtering effect and a relatively high SNR proposed method recovers the valid information in the non- (SNR = 7.427). The noise section (gfi ure 1f) shows that stationary seismic data reasonably, such as the fault and the the f-x RNA can better protect the structure information unconformity. of curved events than FXDECON. Although f-x domain We calculated the FK spectra of the synthetic model and prediction filtering methods can suppress random noise, processing results in gfi ure 1 to further validate the effective- effective information cannot be accurately estimated. When ness of the adaptive nonlocal median filter. Figure 2ashows dealing with nonstationary seismic data, more structure the FK spectra of the original signals, which corresponds information is filtered. The random noise is then attenuated well to the synthetic model. The signals with higher energy using the second generation curvelet transform (Candès on both sides correspond to the sinusoidal curved events in et al. 2006). Figure 1 parts g (SNR = 7.598) and h are the the deep layer, while the signals with the steeper slope on denoised result and the noise section by the curvelet trans- the right side correspond to the dipping events in the shal- form, respectively. We can see that the noise is effectively low layer. Figure 2b shows the FK spectra of the noisy data. removed and the denoised data are smoother than that of f-x Note that the distribution of random noise in FK domain prediction filter. However, there are unwanted nonsmooth is also random. The FK spectra of the data processed by artifacts near the discontinuous region. Figure 1hshows that FXDECON, f-x RNA, curvelet transform and the adaptive 163 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. similar to the original theoretical model. Figure 2 parts d, f, h and j show the FK spectra of removed noise sections, re- spectively. The adaptive nonlocal median filter outperforms the traditional methods in terms of random noise attenuation and structure protection. 3.2. Field data Theadaptivenonlocalmedianfilter wasapplied to a3D field data containing faults, nonstationary events and ran- dom noise. Thedatasizeis200 (timesamples) × 200 (x samples) × 200 (y samples), and the sampling interval is 4 ms (gfi ure 3). Figure 4 parts a and b show the estimated data section and the separated random noise produced by Figure 3. The3Dfielddata. the FXDECON at the same clip value. Although the SNR of the estimated data is increased, the method has a signif- nonlocal median filter are shown in gfi ure 2 partsc,e,gandi, icant leakage of effective signal energy. These results show respectively. These results show that the filtering effect of that the FXDECON has a poor signal protection effect on theproposedmethodisbetter, alarge amount of noiseisre- nonstationary seismic data. The denoising results and the moved, and the spectral characteristics after filtering are more separated noise using the f-x-y RNA (Wang 1999)are shown Figure 4. The 3D eld fi data test. (a) Estimated data section by FXDECON. (b) Random noise separated by FXDECON. (c) Estimated data section by f-x-yRNA.(d) Random noiseseparated by f-x-yRNA.(e) Estimateddata section by curvelet transform. (f) Random noise separated by curvelet transform. (g) Estimated data section by an adaptive nonlocal median filter. (h) Random noise separated by an adaptive nonlocal median filter. 164 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. Figure 4. Continued in the gfi ure 4 parts c and d, respectively. The overall clarity 4. Conclusions of the profile has improved, but there are still some dipping We introduced an adaptive nonlocal median filter to suppress and curved events in the noise section. Then we use the seismic random noise in this paper. The proposed method se- curvelet transform and the adaptive nonlocal median filter lected the appropriate similarity coefficient according to the to suppress random noise for each slice along the time direc- characteristics of seismic data to find the points with simi- tion. The denoised data by the curvelet transform are shown lar structures, and used the weighted median filter to select in gfi ure 4e, indicating the ability of the algorithm in accu- the data with higher local similarity. The traditional method rately recovering theseismic events.Wecan noticeaportion of calculating the similarity coefficient only considers the in- of the structure information has been filtered out, which fluence of distance and amplitude; we combined the cosine appears clearly in the noise section (figure 4f). Because the correlation coefficient that can represent the direction of the RMS of the field data is 3132.04, we chose the parameters space vector and designed an anisotropic Gaussian filter win- t = 13, f = 6and h = 9000. The estimated data section by dow to enhance the weight of the structural direction. The the adaptive nonlocal median filter is shown in gfi ure 4g. window shape was adaptively adjusted according to the lo- Note that the SNR and local structural characteristics of cal dip attributes of seismic data so that the similarity coef- the seismic data have been improved, effective signal energy ficient was more consistent with the characteristics of seis- becomescontinuousandtheshapesofreflection eventshave mic data and more suitable for nonstationary seismic data been well restored. Compared with figure 4 b, d and f, the processing. random noise is effectively suppressed with almost no noise When compared to traditional methods such as the in- energy present, implying that the proposed method can suc- dustry standard FXDECON, f-x-y RNA and curvelet trans- cessfully separate signals and noise (gfi ure 4h). Furthermore, form, the relationship of effective signal protection and the relationship between random noise attenuation and SNR enhancement could be well balanced by our proposed effective signal protection can be changed by adjusting the method. The numerical experiment results showed that the parameter h. 165 JournalofGeophysicsand Engineering (2022) 19, 157–166 Liu et al. adaptive nonlocal median filter has advantages in structural Liu, C., Liu, Y., Yang, B.J., Wang, D. & Sun, J.G., 2006. A 2D multistage median filter to reduce random seismic noise, Geophysics, 71, V105– detail protection and can produce a more reasonable filtering V110. result. Liu, C., Wang, D., Liu, Y., Wang, P.M. & Li, Q.X., 2005. Preliminary study of using 2D multi-level median filtering technique to eliminate random noises, Oil Geophysical Prospecting, 40, 163–167. Acknowledgements Liu, Y., Liu, C., Wang, D., Li, Q.X., Feng, X. & Wang, J.M., 2008. Applica- This work is supported by National Natural Science Foundation of tion of time-variant median filtering technique to attenuation of seismic random noises, Oil Geophysical Prospecting, 43, 327–332. China (grant nos. 41874125, 41974134 and 41774127) and Na- Liu, Y., Wang, D., Liu, C. & Feng, X., 2011. Weighted median filter based tional key Research and Development Program of China (grant no. on local correlation and its application to poststack random noise atten- 2018YFC0603701). uation, Chinese Journal of Geophysics, 54, 358–367. Lyakhov, P.A., Orazaev, A.R., Chervyakov, N.I. & Kaplun, D.I., 2019. A Conflict of interest statement: None declared. new method for adaptive median filtering of images, 2019 IEEE Confer- ence of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), pp. 1197–1201. References Matsuoka, J., Koqa, T., Suetake, N. & Uchino, E., 2015. Switching non-local Al-Dossary, S., 2014. Random noise cancellation in seismic data using a median filter, Optical Review, 22, 448–458. 3D adaptive median filter, SEG Technical Program Expanded Abstracts, Matsuoka, J., Koqa, T., Suetake, N. & Uchino, E., 2017. Robust non-local pp. 2512–2516. median filter, Optical Review, 24, 87–96. Bagheri, M. & Riahi, M.A., 2016. Seismic data random noise attenuation Shang, S., Han, L.G., Lü, Q.T. & Tan, C.Q., 2013. Seismic random noise using DBM filtering, Bolletion DIG, 57, 1–11. suppression using an adaptive nonlocal means algorithm, Applied Geo- Bednar, J.B., 1983. Applications of median filtering to deconvolution, pulse physics, 10, 33–40. estimation, and statistical editing of seismic data, Geophysics, 48, 1598– Shi, Y., Zhang, W. & Wang, Y., 2019. Seismic elastic RTM with vector- wavefield decomposition, Journal of Geophysics and Engineering, 16, Bonar, D. & Sacchi, M., 2012. Denoising seismic data using the nonlocal 509–524. means algorithm, Geophysics, 77,A5–A8. Tasdizen, T., 2009. Principal neighborhood dictionaries for nonlocal Buades, A., Coll, B. & Morel, J.M., 2005. A non-local algorithm for image means image denosing, IEEE Transactions on Image Processing, 18, denoising, IEEE Computer Society Conference on Computer Vision and 2649–2660. Pattern Recognition, 2, 60–65. Wang, J., Guo, Y., Ying, Y., Liu, Y.L. & Peng, Q.S., 2006. Fast nonlocal algo- Candès, E., Demanet, L., Donoho, D. & Ying, L. X., 2006. Fast discrete rithm for image denoising, IEEE International Conference on Image Pro- curvelet transforms, Multiscale Model. Simul., 5, 861–899. cessing, pp. 1429–1432. Cao, S., Huang, L.P., Hou, B.B. & Gang, C., 2018. Self-adaptive non-local Wang, W.H., 2000. Coherent signal prediction using mid-value correlative means image denoising algorithm based on fuzzy edge complement, filtering, Oil Geophysical Prospecting, 35, 273–282. Laser & Optoelectronics Progress, 55, 213–218. Wang, Y., 1999. Random noise attenuation using forward-backward linear Claerbout, J.F., 2008. Basic earth imaging. Standford Exploration Project, prediction, JournalofSeismic Exploration, 8, 133–142. http://sepwww.standford.edu/sep/prof/. Wang, Y., Liu, X., Gao, F. & Rao, Y., 2020. Robust vector median filter- Duncan, G. & Beresford, G., 1995. Some analyses of 2-D median f-k filters, ing with a structure-adaptive implementation, Geophysics, 85, V407– Geophysics, 60, 1157–1168. V414. Fomel, S., 2007. Local seismic attributes, Geophysics, 72, A29–A33. Wu, S.J., Wang, Y.B., Di, Z.X. & Chang, X., 2018. Random noise attenua- Fomel, S., 2010. Predictive painting of 3-D seismic volumes, Geophysics, tion by 3D multi-directional vector median filter, JournalofApplied Geo- 75, A25–A30. physics, 159, 277–284. Huo, S.D., Zhu, W.H. & Shi, T.K., 2017. Iterative dip-steering median filter, Zhou, Y.Y., Lin, M.S., Xu, S., Zhang, H.B., He, H.S., Li, Q. & Guo, J., Journal of Applied Geophysics, 144, 151–156. 2016. An image denoising algorithm for mixed noise combining non- Kervrann, C. & Boulanger, J., 2006. Optimal spatial adaptation for patch- local means filter and sparse representation technique, Journal of Visual based image denoising, IEEE Transactions on Image Processing, 15, Communication and Image Representation, 41, 74–86. 2866–2878. Zhou, Z.Y., Liu, Y., Liu, C., Wang, Q.H. & Zheng, Z.S., 2021. Local cosine Lei, Y., 2015. Research of image denoising algorithm based on non-local similarity attribute based on fast-streaming computation, SEG Technical priori constraints, Microelectronics & Computer, 32, 138–142. Program Expanded Abstracts,1–4.

Journal

Journal of Geophysics and Engineering – Oxford University Press

Published: Apr 1, 2022

Keywords: random noise attenuation; nonlocal median filter; local similarity; anisotropic window; nonstationary seismic data

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