基于自适应稀疏反演的地震数据重构

发布时间：2018-05-01 02:27

本文选题：地震数据重构 + 自适应稀疏反演方法　；参考：《哈尔滨工业大学》2017年博士论文

【摘要】：稀疏变换是一种将数据进行稀疏表示的工具,在地震数据去噪、重构、压缩等过程中起着重要作用,尤其对于高维大尺度数据,在变换域下可以大幅度减少存储量和计算量。一般情况下,我们用显式稀疏变换来表示地震数据,如傅立叶变换、小波变换、曲波变换等。但是对于结构复杂的地震数据,显式稀疏变换往往不能很好地进行稀疏表示,这时候我们需要使用自适应方法来得到对数据自适应的稀疏变换。本文分别研究了数据域和频率域的自适应稀疏变换方法及其在地震数据重构中的应用,具体内容涉及:首先,针对自适应方法在高维地震数据处理中的计算量问题,本文提出了基于高维数据驱动紧框架(DDTF)理论的地震数据重构方法。DDTF以最优稀疏表示形式从数据中训练得到字典,是一种快速的、能得到具有紧框架性质字典的字典学习方法。紧框架字典不仅具有完全恢复性质,还可以实现快速的字典更新。将DDTF方法应用于三维和五维地震数据重构,可以比传统字典学习方法提速近一百倍,并且能得到相似的效果,这使得字典学习方法有望应用于实际地震资料处理。但是对于大规模的高维数据,DDTF方法仍需花费较多计算时间,主要原因是训练样本集合规模庞大,造成字典训练效率低下。然后,为了进一步加速DDTF中的字典训练过程,在样本规模一定的情况下,本文针对样本选取方法进行了研究,并提出了基于蒙特卡罗算法的样本选取方法。每一个样本对字典训练的贡献是一样的,然而我们更关心数据中的精细结构,如果结构信息丰富的样本在样本集中占据主导地位,则训练得到的字典能够更优稀疏表示精细结构,因此结构信息丰富的数据块被选入训练集的概率应该更大。数值结果显示蒙特卡罗DDTF方法大大提高了字典学习效率,并能够比规则或随机选择训练集得到更好的效果。最后,针对地震数据频谱的带限特征,本文提出了基于一种频率域自适应的变分模态分解(VMD)理论的地震数据处理方法。基于VMD的地震数据去噪方法等价于在分解过程中对每个模态应用维纳滤波。数值结果证明VMD方法得到了比经验模态分解方法更好的结果。为了进一步利用不同频率切片之间的关系,本文接着提出了一种新的基于傅立叶谱上的线状带限假设的地震数据分解方法,称之为几何模态分解(GMD)。GMD方法通过考虑不同频率之间的关系,形成了一种自适应的斜率提取方法,相当于将固定基变换在频率域进行了自适应化。本文通过交替求解几何参数和傅立叶域对应的模态来求解GMD问题。数值算例部分将GMD应用于地震数据分解、噪声压制、插值和多次波去除,结果证明GMD方法是地震信号处理中的一种有效的自适应工具。
[Abstract]:Sparse transformation is a tool for sparse representation of data, which plays an important role in the process of seismic data denoising, reconstruction, compression and so on. Especially for high-dimensional and large-scale data, storage and computation can be greatly reduced in the transform domain. In general, we use explicit sparse transform to represent seismic data, such as Fourier transform, wavelet transform, Qu Bo transform and so on. However, for seismic data with complex structures, explicit sparse transformation is often not well represented. In this case, we need to use adaptive methods to obtain adaptive sparse transformation of data. In this paper, the adaptive sparse transform method in data domain and frequency domain and its application in seismic data reconstruction are studied respectively. The main contents are as follows: firstly, aiming at the computational complexity of adaptive method in high-dimensional seismic data processing, In this paper, a method of seismic data reconstruction based on the theory of high dimensional data driven compact frame (DDTF). DDTF is proposed to train the dictionary from the data in the form of optimal sparse representation. It is a fast dictionary learning method which can obtain the dictionary with compact frame properties. Compact-frame dictionaries not only have the property of full recovery, but also can be quickly updated. The application of DDTF method to 3D and 5-D seismic data reconstruction can increase the speed of dictionary learning by nearly 100 times compared with the traditional dictionary learning method, and obtain similar results, which makes it possible to apply the dictionary learning method to the actual seismic data processing. However, the large scale DDTF method of high-dimensional data still needs more computation time, which is mainly due to the large scale of training samples and the low efficiency of dictionary training. Then, in order to further accelerate the dictionary training process in DDTF, the sample selection method is studied in this paper, and a sample selection method based on Monte Carlo algorithm is proposed. The contribution of each sample to dictionary training is the same, however, we are more concerned with the fine structure of the data, if the sample with rich structural information dominates the sample set. The trained dictionary can represent the fine structure more sparsely, so the probability of the data block with rich structure information being selected into the training set should be higher. Numerical results show that the Monte-Carlo DDTF method greatly improves the dictionary learning efficiency and can achieve better results than the regular or random selection training set. Finally, a method of seismic data processing based on the frequency domain adaptive variational mode decomposition (VMD) theory is proposed. The de-noising method of seismic data based on VMD is equivalent to applying Wiener filter to each mode in the process of decomposition. Numerical results show that the VMD method is better than the empirical mode decomposition method. In order to further utilize the relationship between different frequency slices, a new method of seismic data decomposition based on the assumption of linear band limit on Fourier spectrum is proposed. By considering the relationship between different frequencies, an adaptive slope extraction method is developed, which is equivalent to the adaptation of the fixed basis transform in the frequency domain. In this paper, the GMD problem is solved by alternately solving the geometric parameters and the corresponding modes in the Fourier domain. Numerical examples show that the GMD method is an effective adaptive tool for seismic signal processing by applying GMD to seismic data decomposition, noise suppression, interpolation and multiple wave removal.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：P631.4

【相似文献】