GUI based inversion code for automatic quantification of strike limited listric fault sources and regional gravity background from observed Bouguer gravity anomalies

A method coupled with a GUI based code in JAVA is developed in the space domain to simultaneously estimate the structures of strike limited listric fault sources and regional gravity background from a set of observed Bouguer gravity anomalies. The density contrast within the hanging wall of the structure is assumed to be varying continuously with depth based on a parabolic equation. The limiting surface of the fault plane is described with an exponential function. This method is automatic in the sense that it initializes both parameters of a strike limited listric fault source and regional gravity background from a set of observed Bouguer gravity anomalies and improves them iteratively until the modeled gravity anomalies fit the observed anomalies within the specified convergence criteria. The advantage of the code is that besides generating output in both ASCII and graphical forms it displays the animated versions of (i) the changes in model geometry, (ii) variation of each model parameter and misfit with iteration number, (iii) improvements in modeled gravity anomalies, and (iv) variation of density contrast with depth. The applicability of the code is demonstrated on both synthetic and real field gravity anomalies. In case of synthetic example pseudorandom noise is added to the residual gravity anomalies of the structure prior to inversion. The noisy anomalies are then inverted for the unknown parameters presuming (i) an ideal listric fault structure bounded by an exponential limiting surface with perfect flat top and bottom surfaces, (ii) non-ideal structure with uneven top and bottom surfaces with imperfect exponential limiting surface. Further, the robustness of the algorithm is exemplified by adding both regional gravity background and pseudorandom noise to the anomalies of the structure before inversion. In all cases, the interpreted parameters of the structure closely mimic the assumed parameters. The interpretation of gravity anomalies across the master fault of the Chintalpudi sub-basin in India has yielded information that is consistent with both DSS results and drilling information. The highlight of the code is that it can be used to interpret the gravity anomalies of listric fault sources even when the profile along which the interpretation is intended fails to bisect the strike length of the structure.     

A method and a GUI based JAVA code for interactive gravity modeling of strike limited listric fault sources with arbitrary density-depth variations

A method coupled with a GUI based computer program, FRGMLSTRK, coded in JAVA, has been developed to interactively model the gravity anomalies of strike-limited listric fault sources where the detached hanging wall of the structure consists of several geologic formations that have different densities and thicknesses. The program is simple and user friendly in the sense that it allows interactive model construction and modification, the display of fault geometry, depth and the densities of various sub-surface formations, and real-time computation of the gravity anomalies arising from the model. The non-planar fault planes are analytically constructed by fitting a polynomial function of arbitrary but specific degree to a set of points selected on the fault plane by means of a few mouse clicks in the structure panel of the graphical layout. Further, input parameters pertaining to depths and densities of formations can be specified by means of mouse clicks in respective panels. Subsequent changes in these parameters can be realized by simple drag and drop mouse operations. The modeled gravity anomalies are automatically updated and displayed whenever changes are made to: (i) the geometry of the fault plane; (ii) depths of density interfaces; and (iii) densities of formations. These changes can be made either independently or in combination. In addition to displaying the results in graphical form, the code also generates the output in ASCII format. The applicability of the code is demonstrated with both a simple synthetic model and real-world gravity anomalies from the margin of the Chintalpudi sub-basin in India.     

Two-dimensional interpretation of gravity anomalies over sedimentary basins with an exponential decrease of density contrast with depth

The decrease of density contrast with depth in sedimentary basins is approximated by an exponential function. The anomaly equation, in frequency domain, of a prismatic model with an exponential density function is derived. The method has been extended to derive the Fourier transforms of the gravity anomalies of the sedimentary basin, wherein the basin is viewed as vertical prisms placed in juxtaposition. The gravity anomalies of the sedimentary basin are obtained by taking the inverse Fourier transforms. Filon’s method has been extended for calculating accurate inverse Fourier transforms. The accuracy of the method has been tested using a synthetic example. A combination of space and frequency domain methods have been developed for inversion of gravity anomalies over the sedimentary basin. The method has been applied to interpret one synthetic profile and one field profile over the Godavari basin. The method developed in this paper to calculate the inverse Fourier transforms yields continuous spectrum with accurate values. The maximum depth deduced from the gravity anomalies is of the same order as the depth encountered to the basement at the Aswaraopeta borewell.     

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.     

Listric normal fault profiles: calculation using bed-length balance and fault displacement

A bed-length balance technique is presented to calculate listric normal fault trajectories using roll-over geometry and fault displacements. The technique can also be applied to subsidiary listric normal fault fans above a major fault to calculate the major listric fault geometry.     

利用重、磁资料研究于都-赣县矿集区盘古山地区断裂构造及花岗岩体分布

盘古山地区是于都-赣县矿集区内一个重要的钨锡矿成矿区,研究区断裂构造和花岗岩体与成矿关系密切。利用重、磁资料研究盘古山地区断裂构造及花岗岩体分布,为深部找矿提供地球物理依据。利用重力异常归一化总水平导数垂向导数技术推断断裂构造平面位置;利用欧拉反褶积方法对重力异常垂向一阶导数进行反演计算,推断断裂构造平均深度;利用重磁异常垂向一阶导数技术推断花岗岩体平面位置;利用RGIS软件2.5D重磁剖面人机交互正反演技术推断花岗岩体断面位置,并用钻孔验证解释结果的正确性;利用RGIS软件3D重磁模型编辑模块展示花岗岩体空间位置。研究结果显示盘古山地区既有出露断裂,又有隐伏断裂,既有出露低密度、弱磁性花岗岩体,又有隐伏低密度、强磁性花岗岩体,花岗岩体分布受断裂构造控制,矿体分布受断裂构造和花岗岩体共同控制。     

Gravity anomaly modeling of sedimentary basins by means of multiple structures and exponential density contrast-depth variations: A space domain approach

An automatic modeling scheme is developed in the space domain to interpret the gravity anomalies of sedimentary basins, among which the density contrast decreases exponentially with depth. Forward modeling is realized in the space domain using a combination of both analytical and numerical approaches. A collage of vertical prisms having equal widths, whose depths are to be estimated, describes the geometry of a sedimentary basin. Initial depths of a sedimentary basin are predicted using the Bouguer slab formula and subsequently updated, iteratively, based on the differences between the observed and theoretical gravity anomalies until the modeled gravity anomalies mimic the observed ones. The validity and applicability of the method is demonstrated with a synthetic and two real field gravity anomalies, one each over the Chintalpudi sub-basin in India and the other over the San Jacinto graben, California. In case of synthetic example, the assumed structure resembles a typical intracratonic rift basin formed by normal block faulting and filled with thick section of sediments. The proposed modeling technique yielded information that is consistent with the assumed parameters in the case of synthetic structure and with the available/drilling depths in case of field examples.     

Gravity anomalies of a trapezoidal model with quadratic density function

The decrease of density contrast with depth in sedimentary strata is approximated by a quadratic function. The anomaly equation of a trapezoidal model with the quadratic density function is derived. Nonlinear optimization technique using the Marquardt algorithm has been developed and used to interpret a synthetic anomaly profile of the trapezoidal model. The exact values of the coefficients of the quadratic density function are assumed to be known. The convergence of the method is shown by plotting the values of the objective function λ and the various parameters with respect to iteration number. θ and half-width of the trapezoidal model are found to be correlated. The method is also applied to interpret the gravity anomalies over San Jacinto graben, California. Finally, the use of modelling with quadratic density function is discussed.     

天津市重力数据反演解释

重力数据反演是获取地下地质信息的有效手段。本文通过对天津市全区密度和电性参数的统计分析,了解天津市地层的物性分布规律。在对研究区布格重力异常数据采用归一化总水平导数垂向导数（NVDR-THDR）技术处理的基础上,对断裂构造进行了识别,对构造单元进行了划分。然后结合研究区地质资料,应用Geosoft软件中的密度界面反演模块对各构造单元内的密度界面起伏进行反演。并以GOCAD软件为平台,构建了天津市三维可视化地质模型,借助大地电磁（MT）测深点虚拟钻孔,实现了对主要地质界面和构造的标定。最后利用布格重力异常数据拟合同位置地质剖面,验证了模型的可靠性。应用上述反演成果,结合区内地质认识,推断宝坻断裂（F₁）、蓟运河断裂（F₂）、F₃、杨柳青断裂（F₄）、F₇在中生代后活动性较强,沧东断裂（F₆）和天津断裂（F₃₀）在古近纪后活动性较强。     

海原-六盘山断裂带现今地震危险性的数值模拟分析

基于正交各向异性理论表征断层的变形行为,将平行断层面的剪切模量和周围介质剪切模量的比值作为反演参数,以海原-六盘山断裂附近现今GPS观测地壳水平运动速度场作为约束,通过构建三维有限元模型,采用遗传算法,反演了海原-六盘山断裂平行断层面的剪切模量分布.结果显示:六盘山断裂中南段平行断层面剪切模量与周围介质接近,且沿断层面...     

Theoretical Study on Stochastic Modeling of Combined Gravity-Magnetic-Electric-Seismic Inversion and Its Application

As gravity field,magnetic field,electric field and seismic wave field are all physical fields,their object function,reverse function and compound function are certainly infinite contiuously differentiable func-tions which can be expanded into Taylor (Fourier) series within domain of definition and be further reduced in-to solving stochastic distribution function of series and statistic inference of optimal approximation,This is the basis of combined gravity-magnetic-electric-seismic inversion built on the basis of separation of field and source gravity-magnetic difference-value(D-value)trend surface,taking distribution-independent fault sys-tem as its unit,depths of seismic and electric interfaces of interests as its corresponding bivariate compound re-verse function of gravity-magnetic anomalies and using high order polynomial(high order trigonometric func-tion)approximating to its series distribution,The difference from current dominant inversion techniques is that,first,it does not respectively create gravity-seismic,magnetic-seismic deterministic inversion model from theoretical model,but combines gravity-magnetic-electric-seismic stochastic inversion model from stochastic model;second,after the concept of equivalent geological body being introduced,using feature of independent variable of gravity-magnetic field functions,taking density and susceptibility related to gravity-magnetic func-tion as default parameters of model,the deterministic model is established owing to better solution to the con-tradictioc of difficulty in identifying strata and less test analytical data for density and susceptibility in newly explored area;third,under assumption of independent parent distribution,a real modeling by strata,the prob-lem of difficult plane closure arising in profile modeling is avoided,This technology has richer and more detailed fault and strata information than sparse pattern seismic data in newly explored area,successfully inverses and plots structural map of Indosinian discontinuty in Hefei basin with combined gravity-magnetic-electric-seismic inversion,With development of high precision gravity-magnetic and overall geophysical technology,it is certain for introducing new methods of stochastic modeling and computational intelligence and promoting the develop-ment of combined gravity-magnetic-electric-seismic inversion to open a new substantial and promoting the develop-ment of combined gravity-magnetic-electric-seismic inversion to open a new substantial path.     

Hanging-wall deformation and gas-migration associated to a major salt detaching fault in the Norwegian Danish Basin

The central and southern regions of the North Sea Basin are characterized by mobile Zechstein Salt and represent an excellent area to study listric normal fault development related to halokinesis. The North Sea Basin–in spite of being a mature explored hydrocarbon producing basin-contains a generally not fully understood hydrocarbon plumbing system. Faults and associated fluid migration routes represent critical elements of the plumbing system. Here we present a combined 3D seismic mapping of a listric fault and detailed seismic attribute analysis of shallow gas anomalies near the fault implying a close and complex relationship between a major detaching fault, hangingwall deformation and fluid migration and entrapment. The fault and associated antithetic and secondary synthetic faults is controlled by the growth of the underlying salt structure. Three separate segments of the fault are recognized showing distinct and varying characteristics of structural maturity and fluid migration. The studied fault and shallow gas anomalies thus represent an example of a complex faulted shallow fluid migration system developing in relation to an underlying salt structure which could be relevant for understanding similar salt, fault and fluid migration systems around the world.     

Artificial neural network inversion of magnetic anomalies caused by 2D fault structures

A new approach is proposed to interpret magnetic anomalies caused by 2D fault structures. This approach is based on the artificial neural network inversion, utilizing particularly modular neural network algorithm. The inversion process is implemented to estimate the parameters of 2D fault structures where it has been verified first on synthetic models. The results of the inversion show that the parameters derived from the inversion agree well with the true ones. The analysis of noise has been studied in order to investigate the stability of the approach where it has been tested for contaminated anomalies with 5 and 10 % of white Gaussian noise. The results of the inversion provide satisfactory results even with contaminated signals.The validity of the approach has been demonstrated through real data taken from New South Wales, Australia. A comparable and satisfactory agreement is shown between the inversion results of the neural network and those from techniques published in literatures.     

多边断层研究现状

多边断层在世界50多个沉积盆地中均有发现,它是指平面上走向多方位且相互交叉组合成多边形形态、具有层控特征的伸展断裂系统,主要发育在被动大陆边缘盆地和内克拉通盆地内的细粒沉积物中。这类断层为非构造成因断层,目前占主流地位的成因机制有密度反转、脱水收缩和重力载荷机制;与构造正断层相比,多边断层明显具有层控性、多边性和体积应变等方性等特点。共同的几何学特征有:延伸长度短,多为平直或铲式断层,倾角变化范围为30°～70°(平均为45°),走向随机,断层平面交叉组合呈多边形形态。多边断层对储层砂体形态以及流体、天然气水合物的运移和聚集具有重要的意义。文中综合了自多边断层提出以来的国内外研究资料,概括了多边断层发育的几何学特征和成因机制以及多边断层对流体运移的影响,希望能对中国以后的多边断层研究提供参考。     

南海重力异常特征及其显著的构造意义

在南海地区地震测深数据有限的情况下,利用重力异常可以研究南海大范围的深部地壳结构及地质构造展布特征。基于空间重力异常,结合最新的地形、沉积物厚度及地震测深等数据,分别从地震约束的莫霍面反演和无约束的三维相关成像两个视角研究南海的地壳结构,利用壳幔界面起伏、地壳厚度及三维等效密度分布来探讨地壳结构的纵横向变化。同时,联合采用延拓、水平梯度及线性构造增强滤波方法聚焦重力异常中的区域线性特征,突出显示了反映地壳横向变化的深断裂、洋陆转换边界、海盆扩张轴等线性构造的展布。重力解释与贯穿南海南北的广州-巴拉望地学断面对比表明,重力异常反演及异常的区域线性特征,较好地揭示了南海海域大范围的地壳结构与区域构造展布。     

重力异常三维反演——视密度成像方法技术的应用

将起伏地形上测量的重力异常,延拓至平均水平面;对平面上的重力场进行不同深度层源的切割分离;再将各层的重力场向下延拓至相应的深度,并反演出该深度层的密度结构.以此得到的密度,反映该深度层密度的近似分布,故称为视密度成像.在重力场的曲面向下延拓过程中,采用了新的延拓方法--迭代法,延拓深度大,延拓过程稳定;且不需解线性代数方程组,避开了制约三维反演实用化的计算时间的瓶颈问题.在主频1.73 GHz的微机上,完成71×81数据点反演的计算时间为10 s.以新疆一个地区的实例说明这种方法的反演效果.     

How normal faulting and sedimentation interact to produce listric fault profiles and stratigraphic wedges

In a series of scale-experiments, we generated listric normal faults by extending models composed of colored sand layers deposited at regular time intervals throughout deformation during syntectonic sedimentation. Progressive bulk extension along a single set of faults caused domino-type tilting of fault blocks. Underlying tilted faults propagated upwards, with constant dips into newly sedimented layers. Hence fault profiles become progressively more listric. Tilting of the free surface resulted in asymmetrical depressions and in fan-shaped deposits.Stepwise or continuous geometric models of domino-tilting and synchronous sedimentation yield the same structural and stratigraphic features as observed in the sand models. The continuous geometric model shows that a critical parameter governing fault curvature is the ratio R between rates of bulk strain and sedimentation.Both types of models reveal that synchronous sedimentation and bulk extension are capable by themselves of generating listric normal faults.     

3D gravity modeling of Büyük Menderes basin in Western Anatolia using parabolic density function

A method to model 3D sedimentary basins with parabolic density contrast is applied to Büyük Menderes basin in Western Anatolia. The measured gravity fields, reduced to a horizontal plane, are assumed to be available at grid nodes of a rectangular/square mesh. Juxtaposed 3D vertical prisms with their geometrical epicenters on top coincide with grid nodes of a mesh to approximate a sedimentary basin. The algorithm based on Newton’s forward difference formula automatically calculates the initial depth estimates of a sedimentary basin assuming that 2D infinite horizontal slabs can generate the measured gravity fields and among these slabs the density contrast varies with depth. The lower boundary of a sedimentary basin is formulated by estimating the depth values of the 3D prisms with in predetermined limits. Measured gravity fields pertaining to the Büyük Menderes basin, Turkey, where the density contrast varies with depth, are interpreted to show the applicability of the method.     

Listric versus planar normal fault geometry: an example from the Eisenstadt-Sopron Basin (E Austria)

In a gravel pit at the eastern margin of the Eisenstadt-Sopron Basin, a satellite of Vienna Basin (Austria), Neogene sediments are exposed in the hanging wall of a major normal fault. The anticlinal structure and associated conjugated secondary normal faults were previously interpreted as a rollover anticline above a listric normal fault. The spatial orientation and distribution of sedimentary horizons and crosscutting faults were mapped in detail on a laser scan of the outcrop wall. Subsequently, in order to assess the 3D distribution and geometry of this fault system, a series of parallel ground penetrating radar (GPR) profiles were recorded behind the outcrop wall. Both outcrop and GPR data were compiled in a 3D structural model, providing the basis for a kinematic reconstruction of the fault plane using balanced cross-section techniques. However, the kinematic reconstruction results in a geologically meaningless normal fault cutting down- and up-section. Additionally, no evidence for a weak layer serving as ductile detachment horizon (i.e. salt or clay horizon) can be identified in stratigraphic profiles. Instead, the observed deflection of stratigraphic horizons may be caused by a displacement gradient along a planar master fault, with a maximum displacement in the fault centre, decreasing towards the fault tips. Accordingly, the observed deflection of markers in the hanging wall—and in a nearby location in the footwall of the normal fault—is interpreted as large-scale fault drag along a planar fault that records a displacement gradient, instead of a rollover anticline related to a listric fault.     

南岭成矿带多尺度重力场及深部构造特征

利用小波多尺度分解方法分离不同深源尺度花岗岩侵入体的重力异常信息, 结合视密度填图方法划分了5 km、15 km及25 km深花岗岩体分布特征, 并综合地震成像和大地电磁测深资料, 对南岭花岗岩侵入体的赋存侵位、诱发热源以及成因模式等问题进行初步探讨.研究结果表明, 以茶陵-郴州断裂为界, 区内重力场和岩体构造呈明显分区, 东南区岩体局部重力异常幅值较小, 地表出露岩体较薄, 岩浆沿着小通道上涌形成岩盖; 西北区岩体局部重力异常幅值较大, 侵位深度较深; 区内大多数岩体侵位深度不超过25 km; 深部地球物理资料还揭示诸广山和猫儿岭地区15~25 km附近存在大规模低密度、低速特征的陆壳重熔区; 诸广山地区上地幔顶部存在低速、低阻熔体特征的软流圈上涌通道, 推测来自软流圈的玄武岩浆底侵造成该区中下地壳岩石部分熔融, 并为其周围大规模成岩成矿提供热源和物质来源.