一种类RNN的改进ISTA稀疏脉冲反褶积
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摘要
稀疏脉冲反褶积方法对提高地震资料分辨率有着重要作用,迭代阈值收缩算法(ISTA)是其核心算法,首先利用地震数据提取子波,再利用ISTA求解反射系数。当地震子波提取不准确时,反褶积效果不理想。为此,在ISTA基础上,结合循环神经网络(RNN)中反向传播(BPTT)的思想,研究形成了一种类RNN的改进ISTA稀疏脉冲反褶积方法。该算法首先使用常规手段从实际地震数据中提取地震子波,构建反褶积的子波字典;然后将构建的地震子波字典作为已知的初始条件,结合ISTA求取的反射系数;再根据BPTT算法思想,将求取的反射系数与子波褶积并与实际数据进行比较,反向修改地震子波;最终,经过多次迭代修改获得合理的地震子波字典,并利用该地震子波字典求解实际地震数据的反射系数序列。为验证算法的有效性,采用不同信噪比的理论地震记录,给定存在较大误差的初始子波,进行了反褶积计算。采用传统的ISTA和类RNN的改进ISTA进行对比处理,结果表明,改进ISTA具有较好的抗噪能力和子波自适应能力,可使实测地震资料的有效频带拓展约1.5倍,能够较好地适应实际地震资料的反褶积处理。
The sparse spike deconvolution plays an important role in improving the resolution of seismic data.A successful deconvolution requires accurate wavelet data for the calculation of the reflection coefficient,which is performed using the core algorithm of the Iterative Shrinkage Thresholding Algorithm(ISTA).An inaccurate extraction of wavelet data can affect the result of the deconvolution.In this study,an RNN-like ISTA algorithm is proposed,which combines the concept of Back-Propagation Through Time(BPTT) in Recurrent Neural Network(RNN) with the traditional ISTA algorithm.First,seismic wavelets are extracted from the actual seismic data to construct a wavelet dictionary,which is taken as the initial condition,and the reflection coefficient is calculated using ISTA algorithm.Subsequently,the reflection coefficient is convoluted with the wavelets to construct seismic data by means of the BPTT algorithm,and a seismic wavelet correction is performed by comparing the obtained seismic data with the actual data.Finally,a reasonable seismic wavelet dictionary is obtained after several iterations,which can be used to calculate the actual reflection coefficient series.Tests on theoretical seismic records with different signal-to-noise ratio showed that the improved algorithm has a better anti-noise and wavelet adaptive abilities than the conventional ISTA algorithm.Moreover,the frequency band of the actual seismic data can be expanded by about 1.5 times.These results demonstrate that the proposed method can be successfully applied to the deconvolution of actual seismic data.
The sparse spike deconvolution plays an important role in improving the resolution of seismic data.A successful deconvolution requires accurate wavelet data for the calculation of the reflection coefficient,which is performed using the core algorithm of the Iterative Shrinkage Thresholding Algorithm(ISTA).An inaccurate extraction of wavelet data can affect the result of the deconvolution.In this study,an RNN-like ISTA algorithm is proposed,which combines the concept of Back-Propagation Through Time(BPTT) in Recurrent Neural Network(RNN) with the traditional ISTA algorithm.First,seismic wavelets are extracted from the actual seismic data to construct a wavelet dictionary,which is taken as the initial condition,and the reflection coefficient is calculated using ISTA algorithm.Subsequently,the reflection coefficient is convoluted with the wavelets to construct seismic data by means of the BPTT algorithm,and a seismic wavelet correction is performed by comparing the obtained seismic data with the actual data.Finally,a reasonable seismic wavelet dictionary is obtained after several iterations,which can be used to calculate the actual reflection coefficient series.Tests on theoretical seismic records with different signal-to-noise ratio showed that the improved algorithm has a better anti-noise and wavelet adaptive abilities than the conventional ISTA algorithm.Moreover,the frequency band of the actual seismic data can be expanded by about 1.5 times.These results demonstrate that the proposed method can be successfully applied to the deconvolution of actual seismic data.
引文
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[3] MALLAT S G,ZHANG Z.Matching pursuits with time-frequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415
[4] CAI T T,WANG L.Orthogonal matching pursuit for sparse signal recovery with noise[J].IEEE Transactions on Information Theory,2011,57(7):4680-4688
[5] 李海山,杨午阳,田军,等.匹配追踪煤层强反射分离方法[J].石油地球物理勘探,2014,49(5):866-870 LI H S,YANG W Y,TIAN J,et al.Coal seam strong reflection separation with matching pursuit[J].Oil Geophysical Prospecting,2014,49(5):866-870
[6] CHEN S,DONOHO D L,SAUNDERS M A.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1998,20(1):33-61
[7] 张繁昌,彭德木,张营革,等.基于对偶对数障碍规划算法的基追踪反演[J].石油物探,2017,56(2):273-279ZHANG F C,PENG D M,ZHANG Y G,et al.A basis pursuit inversion method based on the primal-dual log-barrier programming algorithm[J].Geophysical Prospecting for Petroleum,2017,56(2):273-279
[8] 曹静杰.基于广义高斯分布和非凸Lp范数正则化的地震稀疏盲反褶积[J].石油地球物理勘探,2016,51(3):428-433CAO J J.Seismic sparse blind deconvolution based on generalized Gaussian distribution and non-convex Lp norm regularization[J].Oil Geophysical Prospecting,2016,51(3):428-433
[9] DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306
[10] 孔德辉,彭真明.利用改进的在线字典学习估计时变子波[J].石油地球物理勘探,2016,51(5):901-908KONG D H,PENG Z M.Time-varying wavelet estimation based on improved online dictionary learning[J].Oil Geophysical Prospecting,2016,51(5):901-908
[11] 练秋生,王小娜,石保顺,等.基于多重解析字典学习和观测矩阵优化的压缩感知[J].计算机学报,2015,38(6):1162-1171LIAN Q S,WANG X N,SHI B S,et al.Compressed sensing based on multiple analytical dictionary learning and observation matrix optimization[J].Journal of Computer Science,2015,38(6):1162-1171
[12] MAIRAL J,BACH F,PONCE J,et al.“Online dictionary learning for sparse coding.” International Conference on Machine Learning[C]//Proceedings of the 26th Annual International Conference on Machine Learning.Montreal:ICML,2009:689-696
[13] BECK A,TEBOULLE M.A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J].SIAM Journal on Imaging Sciences,2009,2(1):183-202
[14] LECUN Y,BENGIO Y,HINTON G.Deep learning[J].Nature,2015,521(7553):436-444
[15] SCHMIDHUBER J.Deep Learning in neural networks:An overview[J].Neural Networks,2015,61(1):85-117
[16] GRAVES A,MOHAMED A R,HINTON G.Speech recognition with deep recurrent neural networks[C]//2013 IEEE International Conference on Acoustics,Speech and Signal Processing.Vancouver:IEEE,2013:6645-6649
[17] GRAVES A.Long short-term memory[M].Supervised sequence labelling with recurrent neural networks.Berlin Heidelberg:Springer,2012:1735-1780
[18] PINEDA F J.Generalization of back-propagation to rcurrent neural networks[J].Physical Review Letters,1987,59(19):2229-2232
[19] WERBOS P J.Backpropagation through time:what it does and how to do it[J].Proceedings of the IEEE,1990,78(10):1550-1560
[20] KASAC J,DEUR J,NOVAKOVIC B,et al.A conjugate gradient-based BPTT-like optimal control algorithm[J].2009 IEEE Multi-conference on Systems and Control,2009:861-866