Abstract:Noise suppression is a crucial step for seismic data processing. In recent years, with the rapid development of deep learning, its application in seismic data denoising has achieved significant effects. For practical application, since it is difficult to collect a large number of labeled seismic data(noise-free data), this paper proposes to suppress the random noise in two-dimensional(2D) seismic data based on the unsupervised deep image prior(DIP) framework. Firstly, the influence of skip connection on network denoising performance is explored, and the network architecture is determined. Secondly, the weighted total variation(WTV) regularization term is added to the loss function. Different from that of the traditional total variation(TV) regularization term, the weight coefficient of the WTV regularization term is no longer a fixed hyper parameter but a learnable parameter related to the spatial structure of data. Finally, the alternating direction method of multipliers(ADMM) is used to solve the optimization problem. Synthetic and real data experiments show that the DIP method combining WTV regularization term and ADMM can reduce the effective signal loss while suppressing random noise in seismic data and has better denoising stability than DIP;the peak signal-to-noise ratio fluctuation of adjacent iterations is small, and it is easier to develop early stopping criteria and applied.
王婧, 陈睿, 马小琴, 吴帮玉. 加权全变分正则化与ADMM求解的无监督地震数据随机噪声压制方法[J]. 石油地球物理勘探, 2023, 58(4): 766-779,800.
WANG Jing, CHEN Rui, MA Xiaoqin, WU Bangyu. Unsupervised seismic data random noise suppression method based on weighted total variation regularization and ADMM solution. Oil Geophysical Prospecting, 2023, 58(4): 766-779,800.
朱跃飞, 曹静杰, 殷晗钧. 一种自动判定保留的奇异值个数的地震随机噪声压制算法[J]. 石油地球物理勘探, 2022, 57(3):570-581.ZHU Yuefei, CAO Jingjie, YIN Hanjun. Seismic random noise suppression algorithm with automatic determination of the number of retained singular values[J]. Oil Geophysical Prospecting, 2022, 57(3):570-581.
[2]
GÜLÜNAY N. Signal leakage in f-x deconvolution algorithms[J]. Geophysics, 2017, 82(5):W31-W45.
[3]
ABMA R, CLAERBOUT J. Lateral prediction for noise attenuation by t-x and f-x techniques[J]. Geophysics, 1997, 60(6):1887-1896.
[4]
李志娜, 李振春, 王鹏, 等. 地震资料F-K滤波去除相干噪声综合性实验[J]. 实验技术与管理, 2022, 39(1):66-71.LI Zhina, LI Zhenchun, WANG Peng, et al. Comprehensive experiment on coherent noise removal by F-K filtering in seismic data[J]. Experimental Technology and Management, 2022, 39(1):66-71.
[5]
TAO R, DENG B, WANG Y. Research progress of the fractional Fourier transform in signal processing[J]. Science in China, Series F, 2006, 49(1):1-25.
[6]
CHEN Y, LIU T, CHEN X, et al. Time-frequency analysis of seismic data using synchrosqueezing wavelet transform[J]. Journal of Seismic Exploration, 2014, 23(4):303-312.
[7]
HENNENFENT G, HERRMANN F J. Seismic denoising with nonuniformly sampled curvelets[J]. Computing in Science & Engineering, 2006, 8(3):16-25.
[8]
TRAD D, ULRYCH T, SACCHI M. Latest views of the sparse Radon transform[J]. Geophysics, 2003, 68(1):386-399.
[9]
OROPEZA V, SACCHI M. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis[J]. Geophysics, 2011, 76(3):V25-V32.
[10]
KENDALL R, JIN S, RONEN S, et al. An SVD-polarization filter for ground roll attenuation on multicom-ponent data[C]. SEG Technical Program Expanded Abstracts, 2005, 24:928-931.
[11]
GÓMEZ J L, VELIS D R. A simple method inspired by empirical mode decomposition for denoising seismic data[J]. Geophysics, 2016, 81(6):403-413.
[12]
MA H, YAN J, LI Y. Low-frequency noise suppression of desert seismic data based on variational mode decomposition and low-rank component extraction[J]. IEEE Geoscience and Remote Sensing Letters, 2019, 17(2):337-341.
[13]
MOUSAVI S M, BEROZA G C. Deep-learning seismology[J]. Science, 2022, 377(6607):EABM4470.
[14]
WU B, MENG D, WANG L, et al. Seismic impedance inversion using fully convolutional residual network and transfer learning[J]. IEEE Geoscience and Remote Sensing Letters, 2020, 17(12):2140-2144.
[15]
ZHENG X, WU B, ZHU X. Multi-task deep learning seismic impedance inversion optimization based on homoscedastic uncertainty[J]. Applied Sciences, 2022, 12(3):1200.
[16]
WU B, MENG D, ZHAO H. Semi-supervised learning for seismic impedance inversion using generative adversarial networks[J]. Remote Sensing, 2021, 13(5):909.
[17]
WANG L, MENG D, WU B. Seismic inversion via closed-loop fully convolutional residual network and transfer learning[J]. Geophysics, 2021, 86(5):R671-R683.
[18]
YU J, WU B. Attention and hybrid loss guided deep learning for consecutively missing seismic data reconstruction[J]. IEEE Transactions on Geoscience and Remote Sensing, 2022, 60:1-8.
[19]
LI X, WU B, ZHU X, et al. Consecutively missing seismic data interpolation based on coordinate attention attention UNET[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19:1-5.
[20]
HE T, WU B, ZHU X. Seismic data consecutively missing trace interpolation based on multistage neural network training process[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19:1-5.
[21]
HUANG W, GAO F, LIAO J, et al. A deep learning network for estimation of seismic local slopes[J]. Petroleum Science, 2021, 18(1):92-105.
[22]
WANG Z, LI B, LIU N, et al. Distilling knowledge from an ensemble of convolutional neural networks for seismic fault detection[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19:1-5.
[23]
LIU N, HE T, TIAN Y, et al. Common-azimuth seismic data fault analysis using residual UNet[J]. Interpretation, 2020, 8(3):SM25-SM37.
[24]
宋辉, 高洋, 陈伟, 等. 基于卷积降噪自编码器的地震数据去噪[J]. 石油地球物理勘探, 2020, 55(6):1210-1219.SONG Hui, GAO Yang, CHEN Wei, et al. Seismic noise suppression based on convolutional denoising autoencoders[J]. Oil Geophysical Prospecting, 2020, 55(6):1210-1219.
[25]
WANG F, CHEN S. Residual learning of deep convolutional neural network for seismic random noise attenuation[J]. IEEE Geoscience and Remote Sensing Letters, 2019, 16(8):1314-1318.
[26]
韩卫雪, 周亚同, 池越. 基于深度学习卷积神经网络的地震数据随机噪声去除[J]. 石油物探, 2018, 57(6):862-869, 877.HAN Weixue, ZHOU Yatong, CHI Yue. Deep learning convolutional neural networks for random noise attenuation in seismic data[J]. Geophysical Prospecting for Petroleum, 2018, 57(6):862-869, 877.
[27]
王钰清, 陆文凯, 刘金林, 等. 基于数据增广和CNN的地震随机噪声压制[J]. 地球物理学报, 2019, 62(1):421-433.WANG Yuqing, LU Wenkai, LIU Jinlin, et al. Random seismic noise attenuation based on data augmentation and CNN[J]. Chinese Journal of Geophysics, 2019, 62(1):421-433.
[28]
方文倩, 李志明. 基于双重残差网络的地震数据随机噪声压制[J]. 工程地球物理学报, 2021, 18(1):44-50.FANG Wenqian, LI Zhiming. Random noise attenuation in seismic data based on dual residual networks[J]. Chinese Journal of Engineering Geophysics, 2021, 18(1):44-50.
[29]
刘小舟, 胡天跃, 刘韬, 等. 数据增广的编解码卷积网络地震层间多次波压制方法[J]. 石油地球物理勘探, 2022, 57(4):757-767.LIU Xiaozhou, HU Tianyue, LIU Tao, et al. Seismic internal multiple suppression method with encoder-decoder convolutional network based on data augmentation[J]. Oil Geophysical Prospecting, 2022, 57(4):757-767.
[30]
张猛. 基于自注意力机制的卷积自编码器多次波压制方法[J]. 石油物探, 2022, 61(3):454-462.ZHANG Meng. A multiple suppression method based on self-attention convolutional auto-encoder[J]. Geophysical Prospecting for Petroleum, 2022, 61(3):454-462.
[31]
张岩, 李新月, 王斌, 等. 基于深度学习的鲁棒地震数据去噪[J]. 石油地球物理勘探, 2022, 57(1):12-25.ZHANG Yan, LI Xinyue, WANG Bin, et al. Robust seismic data denoising based on deep learning[J]. Oil Geophysical Prospecting, 2022, 57(1):12-25.
[32]
徐彦凯, 刘曾梅, 薛亚茹, 等. 应用双通道卷积神经网络的地震随机噪声压制方法[J]. 石油地球物理勘探, 2022, 57(4):747-756.XU Yankai, LIU Zengmei, XUE Yaru, et al. Suppression of seismic random noise using dual-channel convolutional neural network[J]. Oil Geophysical Prospecting, 2022, 57(4):747-756.
[33]
杨翠倩, 周亚同, 何昊, 等. 基于全局上下文和注意力机制深度卷积神经网络的地震数据去噪[J]. 石油物探, 2021, 60(5):751-762, 855.YANG Cuiqian, ZHOU Yatong, HE Hao, et al. Global context and attention-based deep convolutional neural network for seismic data denoising[J]. Geophysical Prospecting for Petroleum, 2021, 60(5):751-762, 855.
[34]
董新桐, 钟铁, 王洪洲, 等. 基于卷积对抗降噪网络的塔里木盆地沙漠地震资料消噪方法研究[J]. 地球物理学报, 2022, 65(7):2661-2672.DONG Xintong, ZHONG Tie, WANG Hongzhou, et al. The denoising of desert seismic data acquired from Tarim Basin based on convolutional adversarial denoising network[J]. Chinese Journal of Geophysics, 2022, 65(7):2661-2672.
[35]
买皓. 基于深度残差网络的地震数据去噪研究[D]. 北京:中国石油大学(北京), 2019.MAI Hao. Seismic Data Noise Attenuation Based on Deep Residual Network[D]. China University of Petroleum (Beijing), Beijing, 2019.
[36]
高好天, 孙宁娜, 孙可奕, 等. DnCNN和U-Net对地震随机噪声压制的对比分析[J]. 地球物理学进展, 2021, 36(6):2441-2453.GAO Haotian, SUN Ningna, SUN Keyi, et al. Comparative analysis of DnCNN and U-Net on suppression of seismic random noise[J]. Progress in Geophysics, 2021, 36(6):2441-2453.
[37]
罗仁泽, 李阳阳. 一种基于RUnet卷积神经网络的地震资料随机噪声压制方法[J]. 石油物探, 2020, 59(1):51-59.LUO Renze, LI Yangyang. Random seismic noise attenuation based on RUnet convolutional neural network[J]. Geophysical Prospecting for Petroleum, 2020, 59(1):51-59.
[38]
LEMPITSKY V, VEDALDI A, ULYANOV D. Deep image prior[C]. 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, 9446-9454.
[39]
LEHTINEN J, MUNKBERG J, HASSELGREN J, et al. Noise2Noise:learning image restoration without clean data[C]. Proceedings of the 35th International Conference on Machine Learning, 2018, 2965-2974.
[40]
KRULL A, BUCHHOLZ T O, JUG F. Noise2Void-learning denoising from single noisy images[C]. 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, 2124-2132.
[41]
MORAN N, SCHMIDT D, ZHONG Y, et al. Noisier2Noise:learning to denoise from unpaired noisy data[C]. 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020, 12061-12069.
[42]
HUANG T, LI S, JIA X, et al. Neighbor2neighbor:self-supervised denoising from single noisy images[C]. 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, 14776-14785.
[43]
LIU J, SUN Y, XU X, et al. Image restoration using total variation regularized deep image prior[C]. 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, 7715-7719.
[44]
CALATRONI L, LANZA A, PRAGLIOLA M, et al. Adaptive parameter selection for weighted-TV image reconstruction problems[J]. Journal of Physics:Conference Series, 2020, 1476:012003.
[45]
WANG Y, YIN W, ZENG J. Global convergence of ADMM in nonconvex nonsmooth optimization[J]. Journal of Scientific Computing, 2019, 78(1):29-63.
[46]
宋洁, 陈平, 潘晋孝. 实现稀疏角度下的精确CT重建:利用ADMM-LP算法求解非凸模型[J]. 中国组织工程研究, 2018, 22(31):4998-5002.SONG Jie, CHEN Ping, PAN Jinxiao. Reconstruction accuracy of sparse angle CT imaging:ADMM-CT algorithm based on LP-norm[J]. Chinese Journal of Tissue Engineering Research, 2018, 22(31):4998-5002.
[47]
CASCARANO P, SEBASTIANI A, COMES M C, et al. Combining weighted total variation and deep image prior for natural and medical image restoration via ADMM[C]. 202121st International Conference on Computational Science and Its Applications (ICCSA), 2021, 39-46.
[48]
QIU C, WU B, LIU N, et al. Deep learning prior model for unsupervised seismic data random noise attenuation[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19:1-5.
[49]
JO Y, CHUN S Y, CHOI J. Rethinking deep image prior for denoising[C]. 2021 IEEE/CVF International Conference on Computer Vision (ICCV), 2021, 5067-5076.