Bernstein preprocessing for nonlinear least squares inversion of gravity and magnetic data

Nonlinear, nonlocal and adaptive optimization algorithms, now readily available, as applied to parameter estimation problems, require that the data to be inverted should not be very noisy. If they are so, the algorithm tends to fit them, rather than smoothening the noise component out. Here, use of Bernstein polynomials is proposed to prefilter noise out, before inversion with the help of a sophisticated optimization algorithm. Their properties are described. Inversion of gravity and magnetic data for basement depth estimation, singly and jointly, and without and after Bernstein-preprocessing is conducted to illustrate that the inversion of Bernstein-preprocessed gravity data alone may be slightly superior to the joint inversion of gravity and magnetic data.     

基于重力全张量数据的Parker-Oldenburg算法研究

相比重力数据,重力张量数据通常包含更多的异常信息。本文根据重力数据与重力张量数据的关系,利用位场转化技术,将重力张量数据应用于传统的Parker-Oldenburg密度界面反演算法中。通过模型试验,证明了在网格间距较大或者数据存在一定噪音时,使用本文算法进行反演能得到更好的效果。实验结果说明利用重力张量数据可以有效地提高密度界面反演的分辨率。     

重力资料的三维密度反演

分别论述了在空间域与频率域中由重力资料反演三维密度分布的理论及其实现的方法,并提出了一种简便、实用的频率域三维密度反演算法。     

Lemniscate representation for inversion of gravity and magnetic data through nonlocal optimization

A method of representing surfaces and volumes by a set of geometric points and a small set of auxiliary parameters, based on generalization of Bernoulli’s notion of lemniscates is introduced. It provides for easy generation and modification of surfaces and volumes, which could be connected, disjoint or even with very irregular boundaries. This allows solving geophysical inversion problems, without constraining the anomalous volumes to some ideal or simple forms. This is illustrated by the example of joint inversion of gravity and magnetic data sets attributable to two-dimensional anomalous bodies. A nonlocal optimization algorithm calledsegmented Hamming scan is used for inversion. Comparison with nonlinear least-squares algorithm shows the advantages of the chosen approach. The concepts ofdesideratal andprocedural detours are illustrated.     

重磁2.5D/3D互相约束反演技术在三维地质填图中的应用研究

三维地质填图为我国启动的新一轮地质调查项目,为提高重磁资料在三维地质填图中的应用效果,笔者提出重磁资料2.5D/3D相互约束重磁反演技术方案:利用重磁资料2.5D剖面反演结果、3D物性反演结果作为彼此反演约束条件,并通过了理论模型试验。试验结果表明,该技术方案使反演结果中物性参数、空间位置更接近理论模型体。通过对本溪—临江地区思山岭铁矿磁异常及酸性岩体重力异常进行反演实践——估算磁异常铁矿资源量、研究酸性侵入岩深部展布形态的效果良好,可为大面积三维填图提供有效途径。     

High resolution local Moho determination using gravity inversion: A case study in Sri Lanka

The seismic data incorporated in global Moho models are sparse and therefore the interpolation of global Moho depths on a local area may give unrealistic results, especially in regions without adequate seismic information. Gravity inversion is a useful tool that can be used to determine Moho depths in the mentioned regions. This paper describes an interactive way of local Moho depth determination using the gravity inversion method constrained with available seismic data. Before applying inversion algorithms, the Bouguer gravity data is filtered in various stages that reduce the potential bias usually expected in Moho depth determination using gravity methods with constant density contrast assumption. A test area with reliable seismic data is used to validate the results of Moho computation, and subsequently the same computation procedure is applied to the Sri Lankan region. The results of the test area are in better agreement with seismically determined Moho depths than those obtained by global Moho models. In the Sri Lankan region, Moho determination reveals a fairly uniform thin crust of average thickness around 20 km. The overall result suggests that our gravity inversion method is robust and may be suitable for local Moho determination in virgin regions, especially those without sufficient seismic data.     

改进的重力模拟退火反演研究

通过对模拟退火方法中常用的VFSA算法的分析，针对其在模型扰动及退火计划上存在的缺陷，针对性地作了更合理的改进VFSA算法，提高了VFSA算法的计算速度与稳健性，并结合重力反演过程中对模型的修正，克服了常规重力反演方法所存在的等值效应。研究中还把重力正演计算的单元体改为垂直侧边梯形单元，并合单同一层位的垂直侧边梯形单元成为一大单元再作计算，加快了正反演计算速度并提高了正反演精度。通过模型试验及实际资料的处理，验证了作者所提出的改进的模拟退火重力反演方法的有效性。     

基于并行预处理算法的三维重力快速反演

随着地球物理设备和探测技术的不断发展,快速处理大规模地球物理数据的需求也随之增长。为了解决三维重力数据密度反演的耗时问题,提出一种并行的预处理共轭梯度算法来提高计算效率。本文分别采用两种不同的预处理算子通过组合模型数据反演进行测试比较,并利用迭代残差和计算用时共同评价其加速效果。结果表明：对称逐次超松弛预处理方法比对角预处理方法反演计算速度快,密度结果更贴近实际模型;与传统串行的共轭梯度算法相比,本文并行预处理快速算法可以获得近19倍的加速比。将该算法应用于美国Vinton盐丘的实测重力数据中,反演结果能够很好地圈定出岩体的位置,验证了本文并行预处理共轭梯度法在三维重力数据快速反演中的高效性和可行性。     

重力异常AlexNet深度神经网络反演

针对传统反演方法存在的初始模型依赖、计算时间较长等问题,提出了一种新的基于AlexNet深度神经网络的重力异常反演方法。该方法首先借鉴经典的深度神经网络AlexNet设计了一种用于重力异常反演的Alex反演网络(AlexInvNet),接着设计大量密度异常体模型并通过正演计算得到带标签的数据集,然后用该数据集训练AlexInvNet网络,最后将重力异常数据输入训练好的AlexInvNet网络直接得到反演结果。理论模型反演结果表明,该方法相较于全连接网络深度学习反演方法,能够更好地反演出异常体的位置和密度,具有较好的泛化能力和抗噪声能力。实测数据反演结果表明,该方法能有效解决重力异常反演问题。     

拟神经网络反演在煤田中应用

Parker快速富氏变换反演单一密度界面存在两方面问题：一是求解目标界面重力异常难度较大;二是受正演速度及反演参量维数的限制,不能对界面进行精细划分.拟神经网络BP算法的引入,首先解决了快速三维正演问题,又突破了反演参量维数的限制,实现快速收敛,有效解决两个或多个密度界面的反演问题.在实际应用中,先用密度“补偿法”正演求取剩余生力异常,然后利用拟神经网络BP算法同时反演两个二维密度界面,拟合求得两个界面的深度异常,在此基础上预测煤田.     

复杂条件二维重力场及重力张量场空间波数域正演方法

随着传感器技术的发展,重力场与重力张量场测量技术发展迅速,为实现地下密度分布精细反演提供了数据保障。正演是反演的基础,解决任意密度分布复杂地质体重力场与重力张量正演高效、高精度计算问题,是实现重力高效、精细反演、人机交互反演解释的关键。针对起伏地形和任意密度分布这种复杂条件下二维重力场及重力张量场高效高精度正演问题,这里提出了一种空间波数混合域正演算法,其关键环节包括:①结合新的矩形二度体组合模型波数域表达式和一维Gauss-FFT算法,提出了一种任意密度分布和起伏地形下重力场及重力张量高效、高精度正演算法;②采用新的二维正演算法,计算观测最高点和最低点之间多个不同高度水平网格重力场及重力张量,结合三次样条插值方法,实现了起伏地形上重力场及重力张量场高效、高精度正演。模型算例结果表明,新方法具有高效、高精度的显著特点。     

The Rapid Inversion of 3-D Potential Field and Program Design

The application of three-dimensional inversion of gravity and magnetic fields is very important not only in geophysical researches, but also in the study of geological structures. A formula of potential field in frequency-domain, developed by Parker in 1973, can be used as a rapid and effective algorithm in gravity and magnetic inversion. The technique has been improved then by Oldenburg, Sprenke, Feng and others.In addition to a brief introduction of Parker's algorithm and its applications, this paper includes the following five parts: basic computational techniques, inversion of single layer, convergence and constraints, simultaneous inversion for density and topography as well as inversion of multilayers. The authors present relevant practical iterative formulas and its varieties when density distribution varies with depth in linear or exponential relation. In order to maintain computation stability and speed up iteration convergence, some approaches are taken in the program design, for instance shifting lower interface of the studied layer, inverting corrections of topography, reducing grid boundary effects and utilizing low-pass filter. With the consideration of the nonuniqueness of the inversion, a method of using seismic data to constrain the range ofpossible models is discussed. It is pointed out that the density variation generates less effects than those of topography on the spectrum of gravity anomaly in second order. Therefore density contrast and topography can be inverted simultaneously by an alternative weighting iteration. By analogy, the inversion of multilayer model can be done in the above procedure. An approach of model decomposition is useful in the computation of multilayer model. The techniques discussed in the present paper for gravitational field are also valid for magnetic field.     

改进的蚁群算法及其在南岭地区花岗岩侵入体探测中的应用

蚁群算法（ACO）主要应用于组合优化问题（COPs）,很少应用于地球物理重磁资料物性反演。首先,对蚁群系统中目标函数值与信息素的映射机制进行改进。理论模拟表明,改进后的Gauss模型在收敛速度和反演精度方面比传统的ant-cycle模型要好,适用于重磁资料物性反演。然后,将蚁群算法应用于南岭地区千里山岩体和九嶷山岩体重力资料反演与解释。结果表明:蚁群算法圈定的花岗岩岩体与地面地质填图结果及大地电磁测深反演结果吻合,较好地控制了千里山岩体和九嶷山岩体的深度和形状。该结果可为研究南岭地区花岗岩侵入模式和多金属成矿规律提供参考。     

重磁反演的群体优生遗传算法

重磁反演常具有众多变量,通常的遗传算法编码方式和搜索模式不能适用。采用０—１ 编码群体优生遗传算法,实现了把遗传算法运用于众多变量的重磁反演,使用进化变异能使运算后期顺利收敛,同时更加接近全局极值,取得了良好的实用效果     

基于重磁反演的三维岩性填图试验——以安徽庐枞矿集区为例

开展大型矿集区深部精细结构探测研究,通过岩性识别与填图实现矿集区5km以内"透明化",发现深部矿产、揭示成矿规律是实现资源可持续发展的主要途径。鉴于重力和磁力数据覆盖面积广、采样密度高,重磁三维反演算法比较成熟,采用重磁反演进行岩性填图是现阶段实现三维岩性填图最有可能的途径。本文以安徽庐枞矿集区为例,提出了基于重力、磁力三维反演的岩性填图流程并开展了填图试验。在分析岩性和密度、磁化率关系的基础上,采用高精度的重力和航磁数据,进行先验信息约束的重磁三维反演,对反演所得的密度体和磁化率体进行逻辑拓扑运算,获得了庐枞矿集区地下5km以内五类主要岩性的三维分布。岩性填图结果显示的浅部特征与地表地质填图结果基本吻合,更重要的是反映了深部岩性的变化,弥补了地表地质填图的不足。庐枞矿集区岩性填图试验结果表明,开展基于重磁三维反演的岩性填图,是了解矿集区深部岩性特征,发现深部矿产的有效方法。     

S-wave velocity profiling from refraction microtremor Rayleigh wave dispersion curves via PSO inversion algorithm

The refraction microtremor method has been increasingly used as an appealing tool for investigating near surface S-wave structure. However, inversion, as a main stage in processing refraction microtremor data, is challenging for most local search methods due to its high nonlinearity. With the development of data optimization approaches, fast and easier techniques can be employed for processing geophysical data. Recently, particle swarm optimization algorithm has been used in many fields of studies. Use of particle swarm optimization in geophysical inverse problems is a relatively recent development which offers many advantages in dealing with the nonlinearity inherent in such applications. In this study, the reliability and efficiency of particle swarm optimization algorithm in the inversion of refraction microtremor data were investigated. A new framework was also proposed for the inversion of refraction microtremor Rayleigh wave dispersion curves. First, particle swarm optimization code in MATLAB was developed; then, in order to evaluate the efficiency and stability of proposed algorithm, two noise-free and two noise-corrupted synthetic datasets were inverted. Finally, particle swarm optimization inversion algorithm in refraction microtremor data was applied for geotechnical assessment in a case study in the area in city of Tabriz in northwest of Iran. The S-wave structure in the study area successfully delineated. Then, for evaluation, the estimated Vs profile was compared with downhole data available around of the considered area. It could be concluded that particle swarm optimization inversion algorithm is a suitable technique for inverting microtremor waves.     

应用改进的遗传算法反演多层密度界面

利用具有全局优化功能的遗传算法直接反演多层密度界面.首先根据重力反演的特点对遗传算法进行改进, 使遗传算法基因交换过程中交换位置的确定同重力异常的拟合情况相结合, 给出适合于重力反演特点的遗传算法.然后利用改进后的遗传算法直接反演多层密度界面.理论模型和实际剖面的计算表明改进是有效的.      

三维重力梯度局部光滑约束反演

针对重力勘探中光滑反演存在的分辨率较低的问题,本文提出一种基于地质体埋深、地层倾向等一定先验信息的局部光滑约束三维反演算法,并提出了一种光滑反演中粗糙度矩阵的存储方式,该存储方式可以将M×N维粗糙度矩阵存储为M×2维,减少了计算机计算内存,且详细介绍了该存储方式下粗糙度矩阵与其他矩阵相乘时,粗糙度矩阵所存储的位置信息的读取方式以及与其他矩阵逐列逐步相乘最终得到计算结果的过程。最后,利用文中提出的算法对理论模型和实测数据进行反演试算,结果表明局部光滑反演算法相比于全局光滑反演结果更加准确,且该算法在一定噪声水平下依然稳定,在实际生产中有效可行。     

Gravity anomaly interpretation of 2D fault morphologies by means of nonplanar fault planes and exponential density contrast model: a space domain technique

Boundary faults associated with thick sedimentary basins are more often curved in cross section rather than planar. We develop a space domain-based automatic gravity inversion technique to quantify such listric fault sources from a set of observed gravity anomalies. The density contrast within the hanging wall of fault morphology is presumed to be known according to a prescribed exponential law. Furthermore, the fault plane is described by a polynomial function of arbitrary but specific degree, whose coefficients become the unknown parameters to be estimated from a set of observed gravity anomalies in addition to the thickness of the fault structure. Using a set of characteristic anomalies, the present inversion identifies approximate parameters pertaining to the origin of fault plane and depth to decollement horizon. Based on the errors between the observed and model gravity anomalies of the structure, the algorithm constructs and solves a system of normal equations to estimate the improvements in depth and coefficients of the polynomial in an iterative approach until one of the specified convergence criteria is fulfilled. The efficacy of the algorithm is shown with the analysis of gravity anomalies attributable to a synthetic model of a listric fault source in the presence of pseudorandom noise. Application of the proposed inversion technique on the observed gravity anomalies of the Ahri-Cherla master fault of the Godavari subbasin in India using the derived exponential density contrast model has yielded an interpretation that is consistent with the available/reported information.     

Inversion Reconstruction of Gravity Potential Based on Gravity Gradients

A new method was developed for the inversion reconstruction of gravity potential. This method offers the possibility to determine the potential function and all of its important derivatives using the common inversion of gravity gradients and the first derivatives of potential. Gravity gradients can be originated from Torsion balance measurements, while the first derivatives of potential can be derived from the deflections of the vertical data. Different fields having great importance can be originated from this reconstructed potential function at any points of the investigated area. The advantage of this method is that the solution can be performed by a significantly over-determined inverse problem. Test computations were performed for the inversion reconstruction of gravity potential. There were 248 torsion balance measurements and 13 points where the deflections of the vertical are known in our test area. This inversion algorithm is rather stable. Gravity potential, the first and the second derivatives of the potential were determined for the test area by this suggested method. This method gives a good possibility for a useful geodetic application; deflections of the vertical based on torsion balance measurements can be determined for the whole area for each torsion balance stations.