本文選題：張量空間　切入點(diǎn)：張量數(shù)值方法　出處：《成都理工大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：由于在復(fù)雜表層地質(zhì)條件下所得到的地震數(shù)據(jù)質(zhì)量普遍不高,所以復(fù)雜表層地質(zhì)條件下的地震勘探一直是一個(gè)難點(diǎn)。在地震勘探中,三維地震數(shù)據(jù)明顯優(yōu)于二維地震數(shù)據(jù)對(duì)復(fù)雜表層的適應(yīng)性,由于三維地震數(shù)據(jù)更加充分地利用了地震數(shù)據(jù)高維的有效信息,所以能更好地應(yīng)對(duì)復(fù)雜表層地質(zhì)的情況。因此,研究地震信號(hào)高維特性,充分利用地震勘探數(shù)據(jù)中的高維信息,是提高復(fù)雜表層地質(zhì)條件下地震勘探效果的有效方法。本文根據(jù)地震數(shù)據(jù)中的一些有效信號(hào)(如反射波、折射波等)在共炮集和共道集上的規(guī)律研究基礎(chǔ)上,提出了高維(高于三維)地震數(shù)據(jù)和廣義時(shí)距方程的概念。并通過(guò)對(duì)廣義時(shí)距方程中每個(gè)自變量的分析,驗(yàn)證了地震數(shù)據(jù)的高維空間數(shù)據(jù)結(jié)構(gòu),并證明了二維及三維地震數(shù)據(jù)在高維空間數(shù)據(jù)結(jié)構(gòu)下各維度方向具有的數(shù)據(jù)關(guān)聯(lián)性。為了分析研究高維地震數(shù)據(jù)處理方法,本文引入了張量及張量空間的概念,并提出地震數(shù)據(jù)空間的概念。根據(jù)數(shù)值張量的定義及其一系列的性質(zhì)將高維數(shù)據(jù)結(jié)構(gòu)下的地震數(shù)據(jù)視作一個(gè)數(shù)值張量,把對(duì)地震數(shù)據(jù)的處理視作是對(duì)數(shù)值張量的處理。同時(shí),根據(jù)張量空間理論,將高維數(shù)據(jù)結(jié)構(gòu)下特定的地震數(shù)據(jù)抽象為特定地震數(shù)據(jù)空間中的一個(gè)元素,將高維數(shù)據(jù)結(jié)構(gòu)下的地震數(shù)據(jù)處理過(guò)程抽象為地震數(shù)據(jù)空間中的映射。由此為張量空間下的高維地震數(shù)據(jù)處理提供理論依據(jù)。同時(shí),論文研究了張量的多種數(shù)值方法。本文利用張量的高階奇異值分解與重構(gòu)方法實(shí)現(xiàn)對(duì)張量的插值與逼近;利用基于薄板模型的散點(diǎn)曲面擬合方法實(shí)現(xiàn)了對(duì)二階張量的平滑擬合;利用Robust局部權(quán)回歸方法實(shí)現(xiàn)對(duì)高階張量的平滑擬合。通過(guò)以上幾種數(shù)學(xué)工具,論文提出了張量空間下的地震數(shù)據(jù)恢復(fù)和隨機(jī)干擾壓制方法。該方法利用高階奇異值分解法將張量空間下的高維地震數(shù)據(jù)進(jìn)行分解,并將分解后的地震數(shù)據(jù)進(jìn)行低秩重構(gòu)。通過(guò)重構(gòu)恢復(fù)地震數(shù)據(jù)中缺失或異常的數(shù)據(jù),將數(shù)據(jù)規(guī)則化,同時(shí)壓制隨機(jī)干擾。另外,論文提出了張量空間下的初至波剩余靜校正方法。該方法在現(xiàn)有的基于初至波剩余靜校正方法基礎(chǔ)上,將常規(guī)分別在共炮域和共接收點(diǎn)域處理的初至波時(shí)間放在更高維度的高維地震數(shù)據(jù)結(jié)構(gòu)下進(jìn)行張量的平滑擬合處理。該方法相較于常規(guī)分炮域和接收點(diǎn)域的剩余靜校正方法具有更好的效果,同時(shí)能克服數(shù)據(jù)異常對(duì)靜校正結(jié)果的影響。綜上所述,本文基于張量、張量空間理論以及張量的數(shù)值方法提出了在張量空間下進(jìn)行高維地震數(shù)據(jù)處理的思想。給出了地震數(shù)據(jù)的數(shù)據(jù)恢復(fù)及隨機(jī)干擾壓制、剩余靜校正等方面進(jìn)行高維度處理的應(yīng)用實(shí)例,取得了優(yōu)異的成果,對(duì)復(fù)雜地表層質(zhì)條件下的地震數(shù)據(jù)處理具有重要的實(shí)用價(jià)值。同時(shí),為其它地震數(shù)據(jù)處理方法提供了在張量空間下進(jìn)行處理的新思路。
[Abstract]:Since the quality of seismic data obtained under complex surface geological conditions is generally not high, seismic exploration under complex surface geological conditions is always a difficult point. Three-dimensional seismic data is obviously superior to two-dimensional seismic data in adaptability to complex surface layer. Because 3D seismic data make full use of the high-dimensional effective information of seismic data, it can better deal with the complex surface geological conditions. To study the high dimensional characteristics of seismic signals and make full use of the high-dimensional information in seismic exploration data is an effective method to improve the seismic exploration results under complex surface geological conditions. In this paper, some effective signals (such as reflected waves) in seismic data are studied. Based on the study of the laws of the common shot set and the common trace set, the concepts of high dimensional (higher than 3D) seismic data and generalized time-distance equation are proposed, and each independent variable in the generalized time-distance equation is analyzed. The high-dimensional spatial data structure of seismic data is verified, and the data correlation of two-dimensional and three-dimensional seismic data in each dimensional direction under high-dimensional spatial data structure is proved. In order to analyze and study high-dimensional seismic data processing methods, In this paper, the concepts of Zhang Liang and Zhang Liang space are introduced, and the concept of seismic data space is put forward. The processing of seismic data is regarded as the processing of the numerical value Zhang Liang. At the same time, according to Zhang Liang space theory, the specific seismic data under the high-dimensional data structure is abstracted as an element in the specific seismic data space. The process of seismic data processing under high-dimensional data structure is abstracted as the mapping in seismic data space, which provides a theoretical basis for high-dimensional seismic data processing in Zhang Liang space. In this paper, various numerical methods of Zhang Liang are studied. In this paper, the interpolation and approximation of Zhang Liang are realized by the method of higher-order singular value decomposition and reconstruction, and the smooth fitting of the second-order Zhang Liang is realized by using the scattered point surface fitting method based on thin plate model. The Robust local weight regression method is used to realize the smooth fitting of high order Zhang Liang. In this paper, a method of seismic data restoration and random interference suppression in Zhang Liang space is proposed, which decomposes the high-dimensional seismic data in Zhang Liang space by using higher-order singular value decomposition method. The decomposed seismic data is reconstructed with low rank. The missing or abnormal data in seismic data is reconstructed and regularized, and the random interference is suppressed at the same time. In this paper, a method of residual statics of first arrival wave in Zhang Liang space is proposed, which is based on the existing methods of residual statics of first arrival wave. Zhang Liang's smooth fitting of the initial arrival time in the common shot domain and the common receiving point domain is carried out under the high-dimensional seismic data structure of higher dimensions. The method is compared with the rest of the conventional sub-shot domain and the receiving point domain. Static correction method has better effect. At the same time, it can overcome the influence of data anomalies on static correction results. In summary, based on Zhang Liang, Zhang Liang's space theory and Zhang Liang's numerical method put forward the idea of high-dimensional seismic data processing in Zhang Liang space, and gave the data recovery and random interference suppression of seismic data. The application examples of residual static correction in high-dimensional processing have achieved excellent results and have important practical value for seismic data processing under complex ground surface conditions. It provides a new idea for other seismic data processing methods in Zhang Liang space.
【學(xué)位授予單位】：成都理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：P631.44

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本文編號(hào)：1575351