Seismic data regularization based on deep learning combining wavelet domain
ZHANG Yan1, LI Jie1, WANG Bin1, LI Xinyue1, DONG Hongli2,3
1. School of Computer & Information Technology, Northeast Petroleum University, Daqing, Heilongjiang 163318, China;
2. Artificial Intelligence Energy Research Institute, Northeast Petroleum University, Daqing, Heilongjiang 163318, China;
3. Heilongjiang Provincial Key Laboratory of Networking and Intelligent Control, Daqing, Heilongjiang 163318, China
Abstract：Data regularization is a fundamental step in seismic data processing,and the conventional method based on physical modeling requires massive computations and is not widely in use. At present,the regularization methods of seismic data based on convolutional neural networks (CNNs) are usually limited in the time domain,which leads to the problems of the excessively smooth reconstructed data and severe loss of texture details,especially at a low sampling rate. Wavelet analysis has the characteristics of multiple scales and multiple directions,which is more suitable to represent the texture characteristics of two-dimensional data and can focus on the details of seismic data signals. Therefore,a CNN model combining the wavelet domain is proposed to learn the joint distribution characteristics of seismic data in the time and wavelet domains and thus approximate the actual data. Specifically,the reconstruction of irregular seismic data is transformed into the wavelet coefficient prediction of components of different directions in each scale under the framework of a CNN to reconstruct regularized seismic data. A joint loss function in the time and wavelet domains is constructed,and by the overall distribution and local details of seismic data,the network model is constrained. The attention of CNN learning can be adjusted by the modification of the weight of the joint loss function to raise the signal-to-noise ratio (SNR) of the reconstructed seismic data. The experiments demonstrate that the proposed method can better preserve details compared with other methods,and it is insensitive to the missing location of seismic data and has good robustness.
霍志周,熊登,张剑锋. 地震数据重建方法综述[J]. 地球物理学进展,2013,28(4):1749-1756.HUO Zhizhou,XIONG Deng,ZHANG Jianfeng. The overview of seismic data reconstruction methods[J]. Progress in Geophysics,2013,28(4):1749-1756.
[2]
HATTON L,LARNER K,GIBSON B S. Migration of seismic data from inhomogeneous media[J]. Geophysics,1981,46(5):751-767.
[3]
俞寿朋,蔡希玲,苏永昌. 用地震信号多项式拟合提高叠加剖面信噪比[J]. 石油地球物理勘探,1988,23(2):131-139.YU Shoupeng,CAI Xiling,SU Yongchang. Improvement of signal-to-noise ratio of stack section using polynomial fitting of seismic signals[J]. Oil Geophysical Prospecting,1988,23(2):131-139.
[4]
PIEPRZAK A W,MCCLEAN J W. Trace interpolation of severely aliased events[J]. SEG Technical Program Expanded Abstracts,1988,7:658-660.
[5]
THORSON J R,CLAERBOUT J F. Velocity-stack and slant-stack stochastic inversion[J]. Geophysics,1985,50(12):2727-2741.
[6]
ZWARTJES P M,SACCHI M D. Fourier reconstruction of nonuniformly sampled,aliased seismic data[J]. Geophysics,2004,72(1):V21-V32.
[7]
DO M N,VETTERLI M. The contourlet transform:an efficient directional multiresolution image representation[J]. IEEE Transactions on Image Proces-sing,2005,14(12):2091-2106.
[8]
ZHANG H L,SONG S,LIU T Y. The ridgelet transform with non-linear threshold for seismic noise attenuation in marine carbonates[J]. Applied Geophysics,2007,4(4):271-275.
[9]
彭才,常智,朱仕军. 基于曲波变换的地震数据去噪方法[J]. 石油物探,2008,47(5):461-464.PENG Cai,CHANG Zhi,ZHU Shijun. Noise elimination method based on curvelet transform[J]. Geophysical Prospecting for Petroleum,2008,47(5):461-464.
CANDES E J,ROMBERG J,TAO T. Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory,2006,52(2):489-509.
[18]
DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[19]
ABMA R,KABIR N. 3D interpolation of irregular data with a POCS algorithm[J]. Geophysics,2006,71(6):E91-E97.
[20]
HERRMANN F J,HENNENFENT G. Non-parametric seismic data recovery with curvelet frames[J]. Geophysical Journal International,2008,173(1):233-248.
[21]
陈杰,牛聪,李勇,等. 基于数据驱动紧框架理论的三维地震数据去噪与重建[J]. 石油地球物理勘探,2020,55(4):725-732.CHEN Jie,NIU Cong,LI Yong,et al. Denoising and reconstruction of 3D seismic data on a data-driven tight frame[J]. Oil Geophysical Prospecting,2020,55(4):725-732.
[22]
WANG B F,ZHANG N,LU W K,et al. Deep-lear-ning-based seismic data interpolation:a preliminary result[J]. Geophysics,2019,84(1):V11-V20.
[23]
WANG F,CHEN S C. Residual learning of deep convolutional neural network for seismic random noise attenuation[J]. IEEE Geoscience and Remote Sensing Letters,2019,16(8):1314-1318.
[24]
高静怀,毛剑,满蔚仕,等. 叠前地震资料噪声衰减的小波域方法研究[J]. 地球物理学报,2006,49(4):1155-1163.GAO Jinghuai,MAO Jian,MAN Weishi,et al. On the denoising method of prestack seismic data in wavelet domain[J]. Chinese Journal of Geophysics,2006,49(4):1155-1163.
[25]
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.
[26]
CHANG D K,YANG W Y,YONG X S,et al. Seismic data interpolation using dual-domain conditional generative adversarial networks[J]. IEEE Geoscience and Remote Sensing Letters,2021,18(10):1856-1860.
[27]
OLIVEIRA D A B,FERREIRA R S,SILVA R,et al. Interpolating seismic data with conditional generative adversarial networks[J]. IEEE Geoscience and Remote Sensing Letters,2018,15(12):1952-1956.
[28]
郑浩,张兵. 基于卷积神经网络的智能化地震数据插值技术[J]. 地球物理学进展,2020,35(2):721-727.ZHENG Hao,ZHANG Bing. Intelligent seismic data interpolation via convolutional neural network[J]. Progress in Geophysics,2020,35(2):721-727.
[29]
JIA Y N,MA J W. What can machine learning do for seismic data processing? An interpolation application[J]. Geophysics,2017,82(3):V163-V177.
[30]
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.
[31]
ZHU W Q,MOUSAVI S M,BEROZA G C. Seismic signal denoising and decomposition using deep neural networks[J]. IEEE Transactions on Geoscience and Remote Sensing,2019,57(11):9476-9488.
[32]
ANBARJAFARI G,DEMIREL H. Image super resolution based on interpolation of wavelet domain high frequency subbands and the spatial domain input image[J]. ETRI Journal,2010,32(3):390-394.
[33]
GAO X,XIONG H K. A hybrid wavelet convolution network with sparse-coding for image super-resolution[C]. 2016 IEEE International Conference on Image Processing (ICIP),Phoenix,AZ,USA,2016,1439-1443.
[34]
张岩,李新月,王斌,等. 基于联合深度学习的地震数据随机噪声压制[J]. 石油地球物理勘探,2021,56(1):9-25,56.ZHANG Yan,LI Xinyue,WANG Bin,et al. Random noise suppression of seismic data based on joint deep learning[J]. Oil Geophysical Prospecting,2021,56(1):9-25,56.
[35]
WANG Y Q,GE Q,LU W K,et al. Well-Logging constrained seismic inversion based on closed-loop convolutional neural network[J]. IEEE Transactions on Geoscience and Remote Sensing,2020,58(8):5564-5574.
[36]
MALLAT S. Wavelets for a vision[J]. Proceedings of the IEEE,1996,84(4):604-614.
[37]
MALLAT S G. A theory for multiresolution signal decomposition:the wavelet representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(7):674-693.
[38]
DABOV K,FOI A,KATKOVNIK V,et al. Image denoising by sparse 3-D transform-domain collaborative filtering[J]. IEEE Transactions on Image Processing,2007,16(8):2080-2095.
[39]
ELAD M,AHARON M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Transactions on Image Processing,2006,15(12):3736-3745.
[40]
KIM J,LEE J K,LEE K M. Accurate image super-resolution using very deep convolutional networks[C].2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR),Las Vegas,NV,USA,2016,1646-1654.
[41]
LIM B,SON S,KIM H,et al. Enhanced deep residual networks for single image super-resolution[C].2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW),Honolulu,HI,USA,2017,1132-1140.
