本文選題：地震信號恢復(fù) + 張量奇異值分解　； 參考：《電子科技大學(xué)》2017年碩士論文

【摘要】：隨著煤層氣、頁巖氣等非常規(guī)能源勘探開發(fā)的不斷深入,地震勘探對數(shù)據(jù)的規(guī)則性和完整性提出了更高要求。然而由于障礙物、禁采區(qū)、采集成本等因素的影響,導(dǎo)致地震數(shù)據(jù)不完整、不規(guī)則;常規(guī)的處理方法往往過于粗糙,難以滿足實際生產(chǎn)需要。根據(jù)地震數(shù)據(jù)的固有特性(如稀疏性、低秩性),采取更加有效的算法進行地震數(shù)據(jù)重建,已經(jīng)成為當(dāng)前研究的熱點。多維地震信號恢復(fù)就是根據(jù)地震數(shù)據(jù)的特點加入正則化約束,從而實現(xiàn)地震數(shù)據(jù)的重構(gòu)。目前地震信號處理中加入的約束主要有核范數(shù)正則化和字典學(xué)習(xí)正則化稀疏表示,其中大多數(shù)求解都是針對于二維地震數(shù)據(jù),并未有效利用多維地震信號間的信息,結(jié)果恢復(fù)的精度不高,重構(gòu)不出大量缺失的數(shù)據(jù);同樣常用的張量分解方法沒有很好利用多維地震數(shù)據(jù)間的冗余性。本文針對地震數(shù)據(jù)恢復(fù)中存在的問題進行研究,采用新的張量分解方法進行處理,具體工作概括如下:1.針對矩陣奇異值分解中恢復(fù)不出規(guī)則缺失、壓制噪聲不理想的情況,本文提出了一種Hankel張量核范數(shù)正則化的地震信號恢復(fù)方法。該方法通過一種新的張量分解方法將Hankel矩陣和張量核范數(shù)有效的結(jié)合起來,構(gòu)建新的目標(biāo)函數(shù);通過交替方向乘子法求解各個變量,同時引入隨機張量奇異值分解方法緩解了Hankel矩陣帶來的時間復(fù)雜度過高的問題,采用阻尼截斷的方法來降低了秩選取所引起的誤差。該方法能夠有效重構(gòu)缺失地震數(shù)據(jù)并壓制隨機噪聲。2.針對矩陣字典學(xué)習(xí)中不容易恢復(fù)整道地震數(shù)據(jù)缺失的情況,本文提出一種張量字典學(xué)習(xí)正則化稀疏表示處理方法。該方法將一種新的張量乘積方法應(yīng)用于張量字典學(xué)習(xí)過程中,構(gòu)建新的目標(biāo)函數(shù);通過交替迭代算法求解稀疏系數(shù),分別在時域和頻域求解各自的變量;通過拉格朗日對偶的方法訓(xùn)練張量字典,提高了計算速度;最后迭代更新張量字典和張量稀疏系數(shù),實現(xiàn)缺失地震信號的重構(gòu)。
[Abstract]:With the further exploration and development of unconventional energy sources such as coalbed methane, shale gas, seismic exploration has put forward higher requirements for the regularity and integrity of data.However, due to the influence of obstacles, no mining areas, acquisition cost and other factors, seismic data are incomplete and irregular, and the conventional processing methods are often too rough to meet the actual production needs.According to the inherent characteristics of seismic data, such as sparsity and low rank, a more effective algorithm for seismic data reconstruction has become the focus of current research.Multi-dimensional seismic signal restoration is to add regularization constraints according to the characteristics of seismic data, so as to achieve seismic data reconstruction.At present, the constraints in seismic signal processing are mainly kernel norm regularization and dictionary learning regularization sparse representation. Most of the solutions are aimed at two-dimensional seismic data, and the information between multidimensional seismic signals is not used effectively.The result is that the precision of restoration is not high, and the missing data can not be reconstructed, and Zhang Liang's decomposition method, which is also commonly used, does not make good use of the redundancy between multidimensional seismic data.In this paper, the problems existing in seismic data recovery are studied, and the new Zhang Liang decomposition method is used to deal with them. The concrete work is summarized as follows: 1.In this paper, a method of seismic signal recovery based on the regularization of Hankel Zhang Liang kernel norm is proposed to solve the problem that the rule of restoration is not missing and the suppression noise is not ideal in the singular value decomposition of matrix.In this method, a new objective function is constructed by combining the Hankel matrix with Zhang Liang kernel norm effectively by a new Zhang Liang decomposition method, and each variable is solved by alternating direction multiplier method.At the same time, the stochastic Zhang Liang singular value decomposition method is introduced to alleviate the high time complexity caused by the Hankel matrix, and the damping truncation method is used to reduce the error caused by rank selection.This method can effectively reconstruct missing seismic data and suppress random noise.In view of the fact that it is not easy to recover the missing seismic data in matrix dictionary learning, this paper presents a new method of learning regular sparse representation by Zhang Liang dictionary.In this method, a new Zhang Liang product method is applied to the learning process of Zhang Liang dictionary, a new objective function is constructed, the sparse coefficients are solved by alternating iteration algorithm, and their variables are solved in time domain and frequency domain, respectively.Zhang Liang dictionary is trained by Lagrangian duality method, and the calculation speed is improved. At last, we iteratively update Zhang Liang dictionary and Zhang Liang sparse coefficient to realize the reconstruction of missing seismic signal.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P631.4

【參考文獻】

相關(guān)博士學(xué)位論文 前1條

1 趙科科;低秩矩陣分解的正則化方法與應(yīng)用[D];浙江大學(xué);2012年

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本文編號：1756362