导　　师： 刘天佑

学科专业： 081802

授予学位： 博士

作　　者： ;

机构地区： 中国地质大学

摘　　要： 矿产资源是国民经济的基础,重磁勘探在金属、石油资源探测及区域地质构造研究中起着重要作用。重磁勘探包括三个环节：重磁数据采集、重磁数据处理和重磁资料解释,重磁数据处理是其中的重要环节,处理结果的好坏直接影响着重磁解释。随着勘探条件日益复杂,从野外采集的重磁数据信噪比越来越低,如何对这些数据进行有效处理,是我们急需解决的问题 在复杂勘探条件下采集的重磁数据,常常面临着三个问题：其一、采集数据中包含大量噪声/(随机噪声和背景噪声/),如何去除这些噪声,是获取有效数据的基础；其二、地质体埋深越来越大,产生的重磁信号比较微弱,可能被背景噪声和随机噪声掩盖,如何提取弱信号,是一个越来越现实的问题；其三、重磁数据是若干地质体信息的叠加,对叠加信息进行分离,有利于提高重磁解释的准确度和精度。 许多学者对上述问题进行研究,提出各种解决办法,他们将偏微分方程、计算数学、非线性科学、人工智能等最新研究成果渗透到重磁处理中。遗憾的是,从目前的资料来看,这些方法大多是基于功率谱或相关性的,需要一些先验条件,如假设信号为平稳过程、服从高斯分布等。实际重磁勘探时,这些先验条件往往不易满足/(或者代价太高/),故需要寻找新的信号处理方法,正因如此,本文尝试将盲源分离技术引入重磁数据处理。 盲源分离是目前信号处理领域最热门的技术之一,它的最大优点是：无需知道源信号特征和信道传输参数,仅仅根据观测信号即可完成对混合信号的分离。重磁勘探中,面临的问题与盲源分离非常吻合：既不知道地下有多少地质体,也不知道这些地质信号如何混合,仅仅知道观测信号,我们期待通过这些观测信号来判断地下情况。本文尝试用盲源分离方法处理重磁数据,主要工作和取得的成果有： 1.通过“鸡尾酒会”现象对盲源分离进行了描述,指出盲源分离的“盲”有两层含义：一是源信号不能直接观测得到；二是传输通道未知/(信号混合方式未知/)。给出盲源分离的定义,对广义盲源分离和线性瞬时混合盲源分离问题进行了界定。指出盲源分离的基本条件是：源信号尽量统计独立,且服从高斯分布的信号不超过1个。还用推理的方法说明盲源分离的两个不确定性：解的幅度不确定、解的顺序不确定。 2.阐述盲源分离的相关理论,包括概率与统计理论、信息理论、盲源分离的预处理。在概率与统计理论中,给出统计独立性、高阶累积量和峭度的概念；在信息论中,给出用来度量信号独立性的名词：熵/(Entropy/)、负熵/(Negentropy/)、Kullback-Leibler散度、互信息/(Mutual Information/);指出盲源分离前应进行预处理,包括对信号的零均值化/(中心化/)、白化。 3.依据信号独立性测度的不同,将盲源分离算法分为三类：基于信息论的盲源分离算法、基于高阶统计量的盲源分离算法/(HOS/)、基于二阶统计量的盲源分离算法/(SOS/)。 /(1/)基于信息论的算法,主要包括三类：信息量最大化算法/(Infomax/)、最大似然估计算法/(MLE/)和输出互信息最小化算法/(MMI/)。通过推导发现,Infomax算法与MMI算法事实上是等价的。当输出信号各分量的边缘概率密度函数与各源信号的概率密度函数相等时,MLE也与Infomax等价。可见,三种算法在本质上是一致的,可以用性能指标PI证明它们的一致性。 /(2/)基于高阶统计量的算法/(HOS/),既可实现对混合信号的盲分离,也可只提取某些特殊信号/(可用于提取弱信号/),这一点是二阶统计量算法/(SOS/)难以做到的。主要介绍三种HOS方法：H-J神经网络算法、JADE算法、FastICA算法。其中,H-J算法不够稳定,在低信噪比时会失效；JADE算法中引入向量的四阶累计矩阵,算法简单且稳健性好；EFICA是在FastICA基础上发展起来的一种算法,更适合于实际工程数据处理,但时间复杂度大约是FastICA的3倍。文中用JADE、EFICA算法对重磁数据进行了处理。 /(3/)基于二阶统计量的算法/(SOS/),主要介绍二阶盲辨识/(SOBI/),其核心思想是对白化后的协方差矩阵进行联合近似对角化。文中用SOBI方法对实际重力数据进行了处理。 4.选择Infomax、FastICA两种方法进行了仿真实验,验证算法的有效性。 5.对重磁信号的非高斯性进行判断。给出高斯信号的定义：概率密度服从正态分布的信号。同时给出两个衡量高斯性的指标：峭度K和偏斜度S,说明了高斯性判断准则：K、S同时为0时为高斯信号,否则为非高斯信号。选择球体、直立长方体的重力模型、磁力模型和斜磁化模型,分别计算不同埋深时的峭度K和偏斜度S,未发现二者同时为0的情况,故重磁信号一般是非高斯信号。 6.用盲源分离方法对垂直方向上两球体重力信号进行分离/(两个球心均在Z轴上/)。选择相邻两条测线/(相距50mm/),对两球体在第一条测线上的分离结果进行分析,发现： /(1/)盲源分离效果与测线位置有关,当两球体位置固定时,测线离球体中心在地面的投影位置较远时,分离效果较好。 /(2/)盲源分离效果与两球体间距有关,第一个球体固定时,两球体间距越大,分离效果越好； /(3/)盲源分离效果与两球体埋深有关,两球体间距不变时,埋深加大时,在一定范围内分离效果变好。 /(4/)当剩余密度固定,盲源分离效果与球体半径有关,两球心位置不变时,球体半径越小,分离效果越好。 7.用盲源分离方法对水平叠加与垂直叠加并存的两球体重力信号进行分离/(两球心在XOZ平面上,但既不在一条水平线上,又不在一条垂直线上/)。选择相邻两条测线/(相距50m/),对两个球体在第一条测线上的分离结果进行分析,发现： /(1/)盲源分离效果与测线位置有关,当两球体位置固定时,测线离球体中心在地面的投影位置越远,分离效果越好。 /(2/)与两球体的垂直距离有关,当水平距离不变时,垂直距离越大,分离效果越好。 /(3/)与两球体的水平距离有关,当垂直距离不变时,水平距离越大,分离效果越好。 /(4/)盲源分离效果与两球体埋深有关,两球体相对位置不变时,埋深增大加大时,在一定范围内分离效果变好。 /(5/)当剩余密度固定,盲源分离效果与球体半径有关,两球心位置不变时,球体半径越小,分离效果越好。 8.用盲源分离方法对重磁数据去噪和提取弱信号。本文采用EFICA算法,分四种情况讨论该问题：一是线性背景场条件下的弱信号提取/(线性背景场,不含随机噪声/)；二是线性背景场及随机噪声条件下的弱信号提取/(线性背景场,含随机噪声/)；三是非线性背景场条件下的弱信号提取/(非线性背景场,不含随机噪声/)；四是非线性背景场及随机噪声条件下的弱信号提取/(非线性背景场,含随机噪声/)。实验结果表明,EFICA方法在上述四种情况下均能较好提取弱信号。另外,还用EFICA方法与滑动平均法、匹配滤波法、趋势分析法、小波尺度分解等位场分离方法进行比较,结果表明：相对于传统位场处理方法,盲源分离在提取弱信号方面有一定的优势。 9.用盲源分离方法对实际重磁数据进行处理。选择南岭地区1：20万布格重力异常平面图、△T航磁异常平面图作为研究对象。在两幅图中,分别选择两条测线,用SOBI进行分离,结果与地质情况吻合。再说明从测线过渡到平面的步骤,给出关键程序。用该程序对布格重力异常平面图进行处理,得到区域场和局部场,实验结果表明：该方法得到的区域场,与向上延拓5公里的布格重力异常平面图比较相似；该方法所得的局域场重力低与隐伏花岗岩边界的对应关系较好。以上说明,盲源分离是一种有效的重磁数据处理方法,值得进一步研究。 Mineral resources are the basis of the national economy. Gravity and magnetic exploration occupies an important position in the metal, oil and regional geological studies. Gravity and magnetic exploration mainly includes three aspects:gravity and magnetic data acquisition, data processing and interpretation of gravity and magnetic data. Gravity and magnetic data processing is the most important part and is the basis of gravity and magnetic interpretation. With the increasing complexity of exploration conditions, the signal to noise ratio of collected gravity and magnetic signal becomes lower and lower, and how to denoise and separate these gravity and magnetic data so as to improve the quality of data processing is the key problem we are eager to solve. There are three problems in the gravity and magnetic signals collected under Complex exploration:First, the acquisition of gravity and magnetic data contains a lot of noise /(random noise and background noise/), removing noise is the base to obtain valid data; Second, with increasing depth geological, gravity and magnetic signals generated are relatively weak, it may be background noise and random noise mask. How to extract the weak signal is an increasingly real problem; Third, gravity and magnetic data collected is superimposed on several geological information. To separate the superimposed signal will help improve the accuracy and precision of gravity and magnetic interpretation. Many scholars have conducted research on these issues, propose various solutions. They apply partial differential equations, computational mathematics, nonlinear science, artificial intelligence, the latest research results into infiltrate gravity and magnetic treatment. Regrettably, the information from the current point of view, these methods are mostly based on power spectrum or correlation, requires some a priori conditions, such as assuming the signal is stationary process, Gaussian, etc. Actually, during gravity and magnetic exploration, these prior conditions are often difficult to meet /(or too expensive/), so the need to find new signal processing method, and as such, this paper attempts to blind source separation technology into the gravity and magnetic data processing. Blind source separation is the most popular field of signal processing technologies. And its biggest advantage is:we need not to know the source signal characteristics and channel transmission parameters, based solely on the observed signal to complete the separation of the mixed signal. The problems during gravity and magnetic exploration are very identical to blind source separation:we did not know how many underground geologic body, nor did we know how these geological signals are mixed, except just that the observed signal, we expect these signals to determine subsurface observations. This paper attempts to deal with blind source separation of gravity and magnetic data, the main work and the results include: 1. Through the "cocktail party" phenomenon, we has been described for blind source separation, noting blind source separation "blind" has two meanings:First, the source signal can not be observed directly; Second, transmission channels is unknown /(unknown signal mixed mode/). Blind source separation gives the definition of the generalized linear blind source separation and blind source separation problem instantaneous mixture. Pointed out that the basic conditions for blind source separation are:source signals as statistically independent and Gaussian signal is not more than one. The method is also described with reasoning the two uncertainties of blind source separation:the magnitude of uncertainty solution, the solution sequence uncertain. 2. Expounded the theory of blind source separation, including probability and statistical theory, information theory, blind source separation pretreatment. In the theory of probability and statistics, the concept of statistical independence, cumulant and kurtosis are given; In information theory, given the independence of the term used to measure the signal:Entropy /(Entropy/), negative entropy /(Negentropy/), Kullback-Leibler divergence, mutual information /(Mutual Information/); We pointed blind source separation should be conducted before preprocessing, including the signal of zero mean /(centered/), albino. 3. Depending on the signal independence measure difference, will blind source separation algorithm is divided into three categories:information theory-based blind source separation algorithm, based on higher order statistics for blind source separation algorithm /(HOS/), based on second-order statistics for blind source separation algorithm /(SOS/). /(1/)An algorithm based on information theory, including three categories:the amount of information maximization algorithm /(Infomax/), maximum likelihood estimation /(MLE/) and the output mutual information minimization algorithm /(MMI/). By derivation we found, Infomax algorithm and algorithm is actually equivalent to the MMI. When the output signal of the edge components of the probability density function of each source signal is equal to the probability density function, MLE Infomax also equivalent. It can be seen, three algorithms are identical in nature,the consistency can be proved by their performance index PI. /(2/)Algorithm based on higher order statistics /(HOS/), can realize the blind separation of mixed-signal can also extract only some special signal /(can be used to extract the weak signal/), this is where the second-order statistics /(SOS/) can not work. HOS describes three main ways:HJ neural network algorithm, JADE algorithm, FastICA algorithm, in which, HJ algorithm is not stable enough, will fail at low SNR; JADE algorithm introduced in the fourth-order cumulant matrix vector.The algorithm is simple,robust and good; EFICA is developed on the basis of an FastICA algorithm and is more suitable for actual project data processing, but the time complexity is about three times FastICA. Man using JADE, EFICA algorithm gravity and magnetic data were processed /(3/)An algorithm based on second-order statistics /(SOS/), introduces the second-order blind identification /(SOBI/), the core idea is dialogue after the covariance matrix of the joint approximate diagonalization. SOBI methods used in the text to process the actual gravity data. 4. We select Infomax, FastICA for simulation experiment and the results verify the effectiveness of the algorithm. 5.Gravity and magnetic signals for non-Gaussian judgement.The non-Gaussian of gravity and magnetic signal, is the prerequisites of use of blind source separation technology. Gaussian definition:normal distribution probability density signal. Gaussian measure defines two indicators:skewness kurtosis K and S, illustrating the Gaussian criterion:K, S for both the0is Gaussian, or non-Gaussian signal. Select the sphere, the gravity model upright rectangular, oblique magnetic force model and model were calculated at different depths of skewness kurtosis K and S, we didn't find both K and S at the same is0, so the weight of the magnetic signal is generally non-Gaussian signal. 6. Separate the gravity signals of the two spheres on the vertical dimension by blind source separation /(both of the cores are on the Z axis/). Choose two adjacent survey lines /(at a distance of50m/), after the analysis of the separable outcomes from the first survey line of the two spheres can found that: /(1/) The effect of the blind source separation is related to the position of the survey line. When the location of the two spheres is fixed, the longer distance between the survey line and the projection position on the ground of the center of the sphere, the better effect of the blind source separation. /(2/) The effect of the blind source separation is related to the distance of two spheres. When the location of the first sphere is fixed, the greater distance between the spheres, the better effect of the blind source separation. /(3/) The effect of the blind source separation is related to the depth of burial. When two sphere's distance is unchanged, the larger extent of the depth of burial, the better effect of the blind source separation under certain conditions. /(4/) When the residual density is fixed,the effect of the blind source separation is related to the radius of the two spheres. When the position of the sphere cores is fixed, the smaller length of the radius, the better effect of the blind source separation. 7. Separate the gravity signals of the two spheres on both horizontal stacking and vertical stacking by blind source separation. Choose two adjacent survey lines /(at a distance of50m/), after the analysis of the separable outcome from the first survey line of the two spheres can found that: /(1/) The effect of the blind source separation is related to the position of the survey line. When the location of the two spheres is fixed, the longer distance between the survey line and the projection position on the ground of the center of the sphere, the better effect of the blind source separation. /(2/) The effect of the blind source separation is related to the vertical distance of the two spheres. When two sphere's horizontal distance is unchanged, the greater length of the vertical distance, the better effect of the blind source separation.. /(3/) The effect of the blind source separation is related to the horizontal distance of the two spheres. When two sphere's vertical distance is unchanged, the greater length of the horizontal distance, the better effect of the blind source separation. /(4/) The effect of the blind source separation is related to the depth of burial. When two sphere's relative position is unchanged, the larger extent of the depth of burial, the better effect of the blind source separation under certain conditions. /(5/) When the residual density is fixed,the effect of the blind source separation is related to the radius of the two spheres. When the position of the sphere cores is fixed, the smaller length of the radius, the better effect of the blind source separation. 8. Blind source separation method are used of gravity and magnetic data de-noising and extraction of weak signals. In this paper, EFICA algorithm are used and sub-four cases discussed in this issue:First, the linear background field conditions, weak signal extraction /(linear background field, excluding random noise/); Second,linear background field and under the conditions of weak random noise signal extraction /(linear background field, including random noise/); Thrid,non-linear background field under weak signal extraction /(nonlinear background field, excluding random noise/); Fourth,non-linear and random noise background field under weak signal extraction /(nonlinear background field, including random noise/). Experimental results show that, EFICA procedure of the above four cases can detect a weak signal well. In addition,EFICA method,moving average method, matched filtering, trend analysis, wavelet decomposition potential field-scale separation methods were compared, the results showed that: Compared with the traditional potential field approach, blind source separation in weak signal extraction has certain advantages. 9. We process the actual gravity and magnetic data with a blind source separation method. We select Nanling region1:200,000Bouguer gravity anomalies plan,△T aeromagnetic anomalies plan for the study. In the two figures, two survey lines were selected with SOBI separation, results consistent with the geological conditions. Then explain the step of the transition from the survey line to the plane, gived the key procedures. The Program is used for Bouguer gravity anomalies process and got regional courts and local courts. Experimental results show that:the regional courts got from the method, compared with5km upward continuation plan Bouguer gravity anomaly are quite similar; Obtained by this method, Bureau domain field of gravity low and concealed granite boundary correspondence is good. Described above, blind source separation is an effective method for gravity and magnetic data processing, it is worth further study.

关 键 词： 盲源分离 独立分量分析 重磁数据处理 去噪 弱信号提取

分 类 号： [P631.1 P631.2]

领　　域： [天文地球] [天文地球] [天文地球] [天文地球]