基于张量理论的高维地震资料处理方法研究及应用

发布时间：2018-03-06 15:11

本文选题：张量空间　切入点：张量数值方法　出处：《成都理工大学》2016年博士论文　论文类型：学位论文

【摘要】：由于在复杂表层地质条件下所得到的地震数据质量普遍不高,所以复杂表层地质条件下的地震勘探一直是一个难点。在地震勘探中,三维地震数据明显优于二维地震数据对复杂表层的适应性,由于三维地震数据更加充分地利用了地震数据高维的有效信息,所以能更好地应对复杂表层地质的情况。因此,研究地震信号高维特性,充分利用地震勘探数据中的高维信息,是提高复杂表层地质条件下地震勘探效果的有效方法。本文根据地震数据中的一些有效信号(如反射波、折射波等)在共炮集和共道集上的规律研究基础上,提出了高维(高于三维)地震数据和广义时距方程的概念。并通过对广义时距方程中每个自变量的分析,验证了地震数据的高维空间数据结构,并证明了二维及三维地震数据在高维空间数据结构下各维度方向具有的数据关联性。为了分析研究高维地震数据处理方法,本文引入了张量及张量空间的概念,并提出地震数据空间的概念。根据数值张量的定义及其一系列的性质将高维数据结构下的地震数据视作一个数值张量,把对地震数据的处理视作是对数值张量的处理。同时,根据张量空间理论,将高维数据结构下特定的地震数据抽象为特定地震数据空间中的一个元素,将高维数据结构下的地震数据处理过程抽象为地震数据空间中的映射。由此为张量空间下的高维地震数据处理提供理论依据。同时,论文研究了张量的多种数值方法。本文利用张量的高阶奇异值分解与重构方法实现对张量的插值与逼近;利用基于薄板模型的散点曲面拟合方法实现了对二阶张量的平滑拟合;利用Robust局部权回归方法实现对高阶张量的平滑拟合。通过以上几种数学工具,论文提出了张量空间下的地震数据恢复和随机干扰压制方法。该方法利用高阶奇异值分解法将张量空间下的高维地震数据进行分解,并将分解后的地震数据进行低秩重构。通过重构恢复地震数据中缺失或异常的数据,将数据规则化,同时压制随机干扰。另外,论文提出了张量空间下的初至波剩余静校正方法。该方法在现有的基于初至波剩余静校正方法基础上,将常规分别在共炮域和共接收点域处理的初至波时间放在更高维度的高维地震数据结构下进行张量的平滑拟合处理。该方法相较于常规分炮域和接收点域的剩余静校正方法具有更好的效果,同时能克服数据异常对静校正结果的影响。综上所述,本文基于张量、张量空间理论以及张量的数值方法提出了在张量空间下进行高维地震数据处理的思想。给出了地震数据的数据恢复及随机干扰压制、剩余静校正等方面进行高维度处理的应用实例,取得了优异的成果,对复杂地表层质条件下的地震数据处理具有重要的实用价值。同时,为其它地震数据处理方法提供了在张量空间下进行处理的新思路。
[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.
【学位授予单位】：成都理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P631.44

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