Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods

Based on the line integral (LI) and maximum difference reduction (MDR) methods, an automated iterative forward modelling scheme (LI‐MDR algorithm) is developed for the inversion of 2D bedrock topography from a gravity anomaly profile for heterogeneous sedimentary basins. The unknown basin topography can be smooth as for intracratonic basins or discontinuous as for rift and strike‐slip basins. In case studies using synthetic data, the new algorithm can invert the sedimentary basins bedrock depth within a mean accuracy better than 5% when the gravity anomaly data have an accuracy of better than 0.5 mGal. The main characteristics of the inversion algorithm include: (1) the density contrast of sedimentary basins can be constant or vary horizontally and/or vertically in a very broad but a priori known manner; (2) three inputs are required: the measured gravity anomaly, accuracy level and the density contrast function, (3) the simplification that each gravity station has only one bedrock depth leads to an approach to perform rapid inversions using the forward modelling calculated by LI. The inversion process stops when the residual anomalies (the observed minus the calculated) falls within an ‘error envelope’ whose amplitude is the input accuracy level. The inversion algorithm offers in many cases the possibility of performing an agile 2D gravity inversion on basins with heterogeneous sediments. Both smooth and discontinuous bedrock topography with steep spatial gradients can be well recovered. Limitations include: (1) for each station position, there is only one corresponding point vertically down at the basement; and (2) the largest error in inverting bedrock topography occurs at the deepest points.     

Gravity interpretation of nonoutcropping sedimentary basins in which the density contrast decreases parabolically with depth

The decrease in density contrast of sedimentary rocks with depth in many sedimentary basins can be approximated by a parabolic density function. Analytical gravity expression of an outcropping two-dimensional vertical step along which the density contrast decreases parabolically with depth is derived in the space domain. A modification ofBott's (1960) method of gravity interpretation is proposed by considering two outcropping vertical steps on either side of the first and last observation points in addition toN outcropping vertical prisms in order to interpret the gravity anomalies of nonoutcropping basins. The thicknesses of the two outcropping vertical steps are made equal to the thicknesses of the two outcropping vertical prisms placed below the first and last observation points. The initial depth estimates of the sedimentary basin are calculated by the infinite slab formula ofVisweswara Rao et al. (1993). The gravity effects of theN outcropping prisms and the two outcropping vertical steps are calculated at each anomaly point and the depth to the floor of the basin are adjusted based on the differences between the observed and calculated anomalies. A gravity anomaly profile of Los Angeles basin, California is interpreted.     

TWO-DIMENSIONAL MASS DISTRIBUTIONS FROM GRAVITY ANOMALIES: A COMPUTER METHOD*

A gravity anomaly profile, considered to be associated with a two-dimensional mass distribution of constant density contrast, may be interpreted with the help of a digital computer. Using the infinite slab formula and anomaly values at selected points of the profile, an initial model of the anomalous mass is built. The gravity effect of the model is computed with a simplified version of the formula derived by Talwani, Worzel and Landisman (1959) for line-integration. After the effect is computed at a point, the model is adjusted depending upon the residual anomaly. The effect of the adjusted model is computed at the following point. Within one cycle of computation the model is adjusted as many times as the number of the selected points. Five such cycles are sufficient to minimize residuals in most cases. A final cycle is computed without adjustment. Local anomaly profiles have been interpreted to obtain the shape of a sedimentary basin and of a faulted block. A regional anomaly profile has been interpreted to obtain crustal structure.     

Parabolic density function in sedimentary basin modelling

For modelling sedimentary basins of large thickness from their gravity anomalies, the concept of parabolic density function which explains the variation of true density contrast of the sediments with depth in such basins is introduced inBott's (1960) procedure. The analytical expression the gravity anomaly of a two-dimensional vertical prism with parabolic density contrast needed to estimate the gravity effect of the basin in modelling procedure is derived in a closed form. Two profiles of gravity anomalies, one across San Jacinto Graben, California and the other across Tucson basin, Arizona where the density of sediments is found to vary with depth are interpreted.     

裂陷盆地基底双界面模式二维重力反演

裂陷盆地基底的起伏表现为非光滑的几何形态,传统的重力反演结果并不能很好地反映这种特点.此外,大多数情况下,重力观测面并不位于盆地上界面,应为单独的起伏观测面,盆地应为上界面和基底组成的双界面模式.基于此,本文研究了起伏观测面上裂陷盆地基底双界面模式二维重力反演方法.研究中假设沉积盆地的沉积层与基底的密度差随深度按双曲线规律变化.将沉积盆地的沉积层剖分成相邻的垂直柱体,其水平尺寸是已知的,顶面与沉积层上界面重合,底面深度代表基底的深度,即为要反演的参数.反演中引入全变差函数作为盆地模型的约束,使得反演结果呈现非光滑形态,符合裂陷盆地基底特征.为减小反演多解性,引入已知深度点作为约束.建立由重力数据拟合、已知深度约束及全变差函数组成的目标函数,采用非线性共轭梯度算法使目标函数最小化.模型试算结果表明该方法可反演裂陷盆地基底起伏,并通过调整正则化参数的值可反演坳陷盆地基底起伏.将该反演方法用于珠江口盆地惠州凹陷和运城-临汾裂陷盆地实际资料处理,其结果较好地反映了裂陷盆地基底起伏特征,为研究盆地构造、油气勘探等提供重要参考.     

Three-dimensional analysis of gravity anomalies of sedimentary basins by polygonal prismatic model with a quadratic density function

The decrease of density contrast in sedimentary strata may be approximated by a quadratic function. A sedimentary basin may be considered as a number of horizontal polygonal prisms of finite thickness placed one over the other. Equations for the gravity anomaly of ann-sided polygon prism have been derived using a quadratic density function. A method has been developed for inversion of the gravity anomalies using a polygonal prismatic model. An analytical method has been employed for evaluating the necessary derivatives as the computing time by this method is much slower than by a numerical method. Approximate equations have been derived for rapid calculation of the anomalies and derivatives. Efficient computer programs have been developed for calculation of the anomalies and derivatives by an appropriate use of the exact and approximate equations. The depths to the polygon prisms constituting the basin are iteratively adjusted by minimizing the sum of the squares of the differences between the observed and calculated anomalies. These methods have been applied to analyze the Bouguer anomaly map of the Los Angeles basin, California.     

Three-dimensional structure of the Laguna Salada Basin and its thermal regime

A comprehensive reinterpretation of the available gravity, magnetic, geothermal, geological and borehole information has been made of the Laguna Salada Basin to establish a 3D model of the basement and sedimentary infill. According to statistical spectral analysis, the residual gravity anomaly is due to sources with a mean regional depth of 2.8 km. The topography of the basement was obtained from a three‐dimensional inversion carried out in the wavenumber domain using an iterative scheme. The maximum density contrast of ?300 kg/m³ estimated from previous studies and the mean depth of 2.5 km finally constrained this inversion. The resulting model indicated that the sedimentary infill is up to 4.2 km thick at its deepest point. According to the gravity‐derived basement topography, the basin presents an asymmetry (i.e. it is of the half‐graben type). It is deeper to the east, where it is delimited from the Sierra Cucapah by a step fault. By contrast, the limit with the Sierra de Juarez is a gently sloping fault (i.e. a listric fault). The basement is not even, but it comprises a series of structural highs and lows. N–S to NW–SE and E–W to NE–SW faults delimit these structural units. The magnetic modelling was constrained by (i) the gravity‐derived basement topography; (ii) a Curie isotherm assumed to be between 7 km and 10 km; (iii) assuming induced magnetization only; (iv) the available geological and borehole information. The magnetic anomalies were interpreted successfully using the gravity‐derived basement/sedimentary interface as the top of the magnetic bodies (i.e. the magnetic modelling supports the gravity basement topography). An elongated N–S to NW–SE trending highly magnetized body running from south to north along the basin is observed to the west of the basin. This magnetic anomaly has no gravity signature. Such a feature can be interpreted as an intrusive body emplaced along a fault running through the Laguna Salada Basin. Treatment of the gravity and magnetic information (and of their horizontal gradients) with satellite image processing techniques highlighted lineaments on the basement gravity topography correlating with mapped faults. Based on all this information, we derived detailed geological models along four selected profiles to simulate numerically the heat and fluid flow in the basin. We used a finite‐difference scheme to solve the coupled Darcy and Fourier differential equations. According to our results, we have fluid flow in the sedimentary layers and a redistribution of heat flow from the basin axis toward its rims (Sierra de Juárez and Sierra Cucapah). Our model temperatures agree within an error of 4% with the observed temperature profiles measured at boreholes. Our heat‐flow determinations agree within an error of ±15% with extrapolated observations. The numerical and chemical analyses support the hypothesis of fluid circulation between the clay–lutite layer and the fractured granitic basement. Thermal modelling shows low heat‐flow values along the Laguna Salada Basin. Deep fluid circulation patterns were observed that redistribute such flow at depth. Two patterns were distinguished. One displays the heat flow increasing from the basin axis towards its borders (temperature increase of 20°C). The second pattern shows an increasing heat flow from south to north of the basin. Such behaviour is confirmed by the temperature measurements in the thermometric boreholes.     

南海重力异常的沉积层密度改正及其对区域构造特征分析的意义

南海位于太平洋板块、印澳板块和欧亚板块交汇处,自晚中生代以来历经张裂作用、海底扩张以及印藏碰撞、菲律宾海板块西向运动等构造事件的叠加改造,不仅形成了复杂多样的构造格局,而且堆积了厚薄不均的沉积层.为了考察沉积层密度改正对利用重力资料分析南海不同尺度构造特征的影响,本文利用南海各区域不同深度沉积层的地震波速度及钻孔密度等数据,建立了沉积层与沉积基底密度差随深度变化的二次函数关系式,并基于该关系式,计算了南海沉积层相对基底密度低而产生的重力异常值.结果显示,南海沉积层的重力异常值在海盆区介于-40~-60 mGal,而在堆积巨厚沉积物的莺歌海盆地可达到-135 mGal;相对于空间重力异常、布格重力异常,经沉积层重力异常改正后的地壳布格重力异常更能突出深部不同尺度的密度结构和莫霍面的起伏特征,其总水平导数模更突显了南海西北部红河断裂带的海上延伸;利用谱分析技术估算岩石圈强度时,经沉积层重力异常改正的地壳布格重力异常数据获得的岩石圈有效弹性厚度值更为符合地质实际,特别是在长条形的巨厚沉积区如莺歌海盆地和马来盆地.分析表明,重力异常的沉积层密度改正对揭示南海构造特征具有重要的意义.     

Marquardt optimization of gravity anomalies of anticlinal and synclinal structures with prescribed depth-dependent density

An inversion technique using the Marquardt optimization is developed to interpret the gravity anomalies due to anticlinal and synclinal structures with density contrast varying continuously with depth. The algorithm simultaneously estimates the parameters of the respective models, in addition to the regional gravity background that is invariably associated with the residual gravity anomaly. Forward modelling is realized through analytically derived gravity expressions for the respective models in the space domain. The efficacy of the inversion is demonstrated with the gravity anomaly due to a theoretical model, in each case with and without the regional background. In addition, the applicability is illustrated using the gravity anomalies of the Pays De Bray anticline, situated north‐west of Paris, France. The interpreted depth of the Pays De Bray anticline using the present inversion compares well with the drilling depth.     

Gravity interpretation of sedimentary basins with hyperbolic density contrast1

The variation in the density of sediments with depth in a sedimentary basin can be represented by a hyperbolic function. Gravity anomaly expressions for a 2D vertical prism and an asymmetric trapezium with a hyperbolic density distribution are derived in a closed form. These are used in inverting the gravity anomaly of a sedimentary basin with variable density. Firstly, the basin is viewed as a series of prisms juxtaposed with each other. The initial thickness of each prism is obtained from the gravity anomaly at its centre, based on the gravity anomaly of an infinite slab with a hyperbolic density contrast. These thicknesses are improved, based on the differences between the observed and the calculated anomalies. For an improved rate of convergence of the solution, these thicknesses may alternatively be refined using the well-known ridge regression technique. Secondly, the basin is approximated by an asymmetric trapezium and its anomalies are inverted for the parameters of the trapezium using the ridge regression. Since this approximation serves to oversimplify the floor of the basin, it must be used only when the sediment-basement interface has minor undulations. The results of a hypothetical case and two field cases (the San Jacinto Graben, California and the Godavari Graben, southern India) are presented. In both field cases, the interpreted depths are comparable with the real ones, proving the validity of the assumption of a hyperbolic density distribution of the sediments in the two basins considered.     

Gravity profiling as a technique for determining the thickness of glacier ice

Summary Detailed gravity measurements recently carried out on the Gorner glacier, Switzerland, are used to determine the variation of thickness across the glacier ice. The Gorner glacier was chosen as a test site because seismic control was available. The glacier ice at a profile near the Monte Rosa massif is associated with a relative gravity low of about –23 mgal. Model oalculations yield a corresponding ice thickness of about 400 m at the central part of the profile. A comparison of the derived residual gravity anomaly with the calculated effect of the 3-D ice model based on seismic information is made. It is shown that the regional field determined for the Gorner glacier is appropriate and gives the correct residual anomaly associated with the glacier ice. Therefore, the proposed gravity technique for determining variations of the thickness of glacier ice appears to be a valuable and rather inexpensive method for surveying glaciers.Institut für Geophysik, ETH-Zürich, Contribution No 145.     

天山及邻区Vening Meinesz均衡重力异常特征及其动力学意义

本文基于Vening Meinesz区域均衡模型,通过试验不同参数计算Vening Meinesz均衡补偿深度,将其与CRUST1.0模型给出的莫霍面深度进行拟合,得到适应于天山及邻区的平均补偿深度、"地区性指标"以及区域补偿半径.结合地球重力场模型EIGEN-6C4与地形数据,利用球冠体积分方法进行地形效应、沉积层效应计算和均衡校正,得到了研究区的Vening Meinesz均衡重力异常.结果显示天山及邻区的均衡重力异常幅值在-110~120 mGal之间,表明了天山及周边盆地岩石圈所处于的均衡状态,同时揭示了研究区的壳幔密度分布特征.天山、塔里木盆地、准噶尔盆地等块体的地壳垂向形变可能部分地由均衡调整引起,且均衡调整趋势与地面形变测量结果相契合.通过对均衡重力异常成因的解释,从地壳均衡角度分析了该地区复杂的构造背景及其新生代以来的演化历程.     

布格重力异常建模反演在二连盆地油气勘探中的应用

二连盆地由众多小凹陷组成,伊和凹陷是其中之一.重力资料在盆地"探边摸底"、"定凹选带"等方面发挥着重要作用.本文基于布格重力异常资料,利用2.5D建模反演技术对其中横跨主洼槽的两条测线进行可视化建模及正演拟合.其中,初始模型的几何参数取自二维地震解释结果;物性参数中的纵向密度取自测井声波波速与密度的相关公式.正演拟合为建模反演技术的关键环节,密度横向变化,是在拟合过程中通过人机交互试错调整实现.通过正演拟合,揭示了主洼槽沉积层横向和纵向均存在较大的密度不均匀性,主洼槽有利于油气生成.与地震解释结果对比,二者在赛汉组-第四纪、腾格尔组深度相差不大,但凹陷底部拟合结果与地震解释结果有明显差异.通过钻井结果验证,正演拟合各沉积层深度与钻井揭示的各层深度结果一致,二维地震解释结果偏浅,其可能原因是时深转换选取的速度值偏小造成.     

Optimal Design of a Gravity Survey Network and its Application to Delineate the Jabera-Damoh Structure in the Vindhyan Basin,Central India

Fractal dimension analysis was carried out for optimal designing of 2-D gravity survey network and to determine an optimum range of gridding interval to generate least aliased Bouguer anomaly maps. As a test case, this method has been successfully applied to the Jabera-Damoh region of the Vindhyan Basin, which is considered as a potential hydrocarbon bearing area. In particular, we aim to delineate accurately the lateral extent of a possible hydrocarbon bearing structure. To achieve this aim, fractal dimension of survey network was computed using 2-D distributions of observation points in the planning phase of the survey so that the optimum station spacing for gravity survey can be obtained. A range of optimum gridding interval for the gravity data set was suggested using the box-counting method of fractal dimension determination. Bouguer anomaly maps of the region are prepared utilizing the optimum gridding interval. For the first time, these anomaly maps clearly outline the gravity evidence of an anomalous rifted structure, which is bounded by parallel faults on either side. This structure is interpreted as a favorable basin for the occurrence of hydrocarbons. Another finding of this study has been the delineation of an apparently small ridge-like structure running east-west, dividing this basin in two parts. A subsurface geological model along a profile across the Jabera structure has also been presented.     

Determination of Sedimentary Basin Basement Depth: A Space Domain Based Gravity Inversion using Exponential Density Function

An automatic inversion using ridge regression algorithm is developed in the space domain to analyze the gravity anomalies of sedimentary basins, among which the density contrast decreases with depth following a prescribed exponential function. A stack of vertical prisms having equal widths, whose depths become the unknown parameters to be estimated, describes the geometry of a sedimentary basin above the basement complex. Because no closed form analytical equation can be derivable in the space domain using the exponential density-depth function, a combination of analytical and numerical approaches is used to realize forward gravity modeling. The depth estimates of sediment-basement interface are initiated and subsequently improved iteratively by minimizing the objective function between the observed and modeled gravity anomalies within the specified convergence criteria. Two gravity anomaly profiles, one synthetic and a real, are interpreted using the proposed technique to demonstrate its applicability.     

北天山中段近期重力场变化特征研究

利用北天山中段最新的流动重力观测数据,通过整理计算平差,绘制该地区半年和一年尺度的重力场变化图像;选取横跨北天山中段乌鲁木齐、独山子两条测线,并分别绘制其重力剖面变化图;结合北天山中段地区动力构造环境,剖析该地区重力变化特征及其与地震孕育之间的关系。分析表明:北天山中段地区重力异常变化值不大,重力变化等值线图和剖面变化图均能较好地反映重力场随时空变化特征;北天山中段动态重力变化特征基本反映了该地区动力构造运动的外部环境;研究区域内的重力场空间格局分布特征较清晰,其重力变化具有明显的分区特征,山体和盆地之间的重力变化具有显著差异,山体与盆地边缘正负重力变化交替出现,且变化相对较平稳。     

基于抛物线密度模型的频率域三维界面反演及其在川滇地区的应用

密度界面反演作为了解地球内部结构的一种重要方法,长期以来都是重力学研究的主要内容.本文结合抛物线密度模型及频率域算法的优点,将抛物线密度函数应用于Parker-Oldenburg算法,经过理论推导得到了抛物线密度模型的频率域公式,从而建立了基于抛物线密度模型的三维密度界面重力异常正反演的算法和流程.理论模型数据试验表明本方法快速、有效,适用于大多数浅部比深部增加更快的实际地壳密度.研究中还利用该方法对川滇地区重力异常进行了反演,获得了该区的莫霍面深度分布,并与接收函数研究结果进行对比分析,进一步验证了本文方法的正确性和有效性.     

重力剖面和激电测深联合勘测在涡河断裂研究中的应用

为查明涡河断裂的位置、性质等参数,选择重力剖面和激电测深联合勘测方法,对指定区域进行物探勘测工作。结果表明:由密度差异引起的重力异常位置和岩石电阻率、极化率异常位置基本吻合,说明以重力剖面和激电测深为手段的联合勘测是查找断裂的有效方法。     

太行山重力梯级带的密度结构及其地质解释

斜贯中国东部地区的大兴安岭 -太行山 -武陵山重力梯级带是一条地壳深部构造变异带。选择与其中段———太行山重力梯级带相垂直的阜平 -定州剖面 ,利用人工地震测深与布格重力异常资料 ,进行了地壳 -上地幔密度反演分析。结果表明 ,该剖面的地壳 -上地幔密度分布具有明显的不均匀性。总体特征是剖面西部密度较低 ,东部密度较高 ,地壳厚度的横向变化基本上决定了布格重力异常梯级带的形成。结合华北地区的中新生代构造演化 ,认为太行山重力梯级带是燕山期以后形成的 ,它与板块之间的相互作用及上地幔热物质的运动相关     

Velocity Structure of the West-Bengal Sedimentary Basin, India along the Palashi-Kandi Profile Using a Travel-time Inversion of Wide-angle Seismic data and Gravity Modeling – An Update

The 2-D shallow velocity structure along the north-south Palashi-Kandi profile in the West Bengal sedimentary basin has been updated by travel-time inversion of seismic refraction, wide-angle reflection and gravity data. A six-layer shallow model up to a depth of about 7 km has been derived. The first layer, which has an average velocity of 2.0 kms^?1, represents the alluvium deposit, which rests over the shale formation with average velocity of 3.0 kms^?1. The thin (200 m) Sylhet limestone, observed at a nearby Palashi well, remains hidden in the present data set. Hence a 200-m thin layer with a velocity of 3.7 kms^?1, corresponding to the Sylhet limestone, has been assumed to be present throughout the profile. The fourth layer with a velocity of 4.5–4.7 kms^?1 at a depth of 1.7–2.4 km represents the Rajmahal traps. The ‘skip’ phenomenon and rapid amplitude decay of first arrivals indicate a low-velocity zone (LVZ) in the study area. Using the ‘skip’ phenomena and wide-angle reflection data, identified on seismograms, the LVZ with a velocity of 4.0 kms^?1, indicating the Gondwana sediments, has been delineated below the Rajmahal traps. The next layer with a velocity 5.4–5.6 kms^?1 overlying the crystalline basement (5.8–6.25 kms^?1) may be associated with the Singhbhum group of meta volcanic rock that has been exposed in the western part of the basin. The basement lies at a variable depth of 4.9 to 6.8 km. The overall uncertainties of various velocity and boundary nodes are ± 0.15 kms^?1 and ± 0.5 km, respectively. The elevated basement feature in the north might have acted as a structural barrier for the deposition of Sylhet limestone during the Eocene epoch. The seismically derived shallow structure correctly explains the observed Bouguer gravity anomaly along the profile. The addition of reflections in the present analysis provides a stronger control on the depths and velocities of basement and overlying sedimentary formations, compared to the earlier model derived mainly by the first arrival seismic data.