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.     

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.     

THREE-DIMENSIONAL INTERPRETATION OF GRAVITY DATA FROM SEDIMENTARY BASINS USING AN EXPONENTIAL DENSITY-DEPTH FUNCTION*

In mapping the topography of the basement of deep sedimentary basins by gravity modelling, the accuracy can be improved by incorporating an exponential increase in density with depth. For calculating the gravity effect of a three-dimensional (3D) structure with such an exponential density-depth relation a frequency-domain forward algorithm based on series expansion is presented, the numerical evaluation of which can be performed efficiently by fast Fourier transform. The algorithm can be applied in a recursive procedure to give the inverse solution in terms of basement relief. The inversion procedure is satisfactorily tested on a 2D synthetic example and a 3D field example of gravity data from the western margin of the Pannonian Basin in eastern Austria, where up to 2.2 km of Tertiary sediments overlie an igneous or metamorphic basement. The results are confirmed by basement intersections in several wells.     

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.     

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.     

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.     

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.     

3D AND 2½ D MODELLING OF GRAVITY ANOMALIES WITH VARIABLE DENSITY CONTRAST1

The decrease of density contrast in sedimentary basins may be approximated by a quadratic function. A sedimentary basin may be viewed as a number of prisms placed in juxtaposition. Equations in closed form for the gravity anomalies of 3D and 2½ D prismatic models are derived. Approximate equations for these models are also derived for rapid calculations. Efficient methods are developed for anomaly calculation by an appropriate use of the exact and approximate equations, and hence, for 3D and 2½ D modelling. The depths to the basement are adjusted iteratively by comparing the calculated anomalies with the observed anomalies. These methods are applied for analysis of the residual anomaly map of the Los Angeles Basin, California.     

Gravity Anomalies of 2.5-D Multiple Prismatic Structures with Variable Density: A Marquardt Inversion

We present an inversion technique based on the Marquardt algorithm to estimate the depth of a 2.5-D sedimentary basin in addition to the regional gravity anomaly that is associated with the residual gravity anomaly, wherein the density contrast varies parabolically with depth. Forward modeling is carried out through a derived analytical gravity expression of a 2.5-D vertical prism. Inversion of a theoretical gravity anomaly with and without a regional gravity anomaly illustrates the procedure that it is found to be insensitive to the regional gravity effect. Furthermore, the algorithm is exemplified with the gravity anomalies of the derived density-depth model of the Godavari subbasin, India with a parabolic density profile resulting in a more consistent geological model rather than a constant density profile. The main advantage of this method is that it works well even when the profile of interpretation does not bisect the strike length of the sedimentary basin.     

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.     

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.     

ESTIMATION OF THE MINIMUM DENSITY CONTRAST OF A HOMOGENEOUS BODY AS AN AID TO THE INTERPRETATION OF GRAVITY ANOMALIES*

Goodacre A.K. 1980, Estimation of the Minimum Density Contrast of a Homogenous Body as an Aid to the Interpretation of Gravity Anomalies, Geophysical Prospecting 28, 408–414. The minimum density contrast value for which a homogeneous body will accurately reproduce an observed gravity low can often be used to determine whether the causative body is a low-density granite batholith or a sedimentary basin. If the minimum density contrast value is large, the anomaly source is probably a sedimentary basin; if it is small, the source may be either a sedimentary basin or a granite batholith. The minimum density contrast method is tested on the Cheshire Basin and the Weardale Granite.     

鄂尔多斯地块及邻区重力均衡研究

为更加精细地了解鄂尔多斯及其邻区的地壳均衡状态,本文在考虑地壳密度横向变化的基础上计算了该区域的重力均衡异常。首先,利用研究区内重力异常和真实莫霍面深度进行反演得到壳幔密度差分布,以艾里均衡理论为基础计算了莫霍面的理论深度;其次,通过莫霍深度理论值与真实值对比来获得研究区的重力均衡异常;最后,结合区内地震分布,讨论了重力均衡异常与地震活动的关系。结果表明:研究区内盆地以负均衡异常为主,山地则表现为正均衡异常,鄂尔多斯地块内部基本均衡;研究区内中强地震主要分布在重力均衡异常梯度带上。      

The concentrations of the heavy metals in the four new Antarctic meteorites Yamato (a), (b), (c) and (d) and in Orgueil, Murray, Allende, Abee, Allegan, Mocs and Johnstown

All active midocean ridges show a uniform relationship between depth and age of the oceanic crust. Recently, it has been shown by numerical methods that convective flow in a Newtonian fluid will have a positive gravity anomaly and an upward surface deformation associated with an ascending limb. If there is thermal convection in the upper mantle, these calculations predict that there may be a correlation between free air gravity anomalies and differences from the uniform relationship between oceanic depth and age. To investigate such a correlation, we considered the crestal elevation and free air gravity anomaly over the crest of the midocean ridges. It has been suggested that the differences from the depth versus age relationship are related to spreading rate. Thus, we also considered a correlation between crestal elevation and changes in rate along the ridge axis.We found a positive correlation between free air gravity and differences in crestal depth of the midocean ridge system. We found no correlation between spreading rate and gravity and no uniform relationship which holds in all the oceans between spreading rate and observed crestal depths.The long wavelength gravity anomalies which are correlated with the differences in crestal depth cannot be supported by an 80 km thick lithosphere. Thus, they are considered evidence of flow within the aesthenosphere. Further, the correlation between gravity anomaly and differences in crestal depth has the same sign and gradient as predicted by the investigations of convection in a Newtonian fluid.     

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.     

由地面、卫星重力资料研究岩石层密度

地球内部物质密度的分布决定了地球表面及外空的重力场,不过在特定的条件下,也可以根据地面或外空的重力场推求地球内部异常密度的分布。本文在单层位理论的基础上,利用上述资料确定了我国大陆下面地球深部的异常密度,试用分离重力场长、短波长的方法,求出了地球外层-岩石层内异常密度的侧向分布,对此,还初步作了地球物理的解释,其结果与地震测深的较为一致。     

Improved salt imaging in a basin context by high resolution potential field data: Nordkapp Basin,Barents Sea

The seismic imaging of salt diapirs in the Nordkapp Basin gave rise to considerable problems in defining their shape and volume. Independent information was added by integrating the interpretation with high resolution gravity and magnetic data. We developed a novel, iterative workflow, separated into sub‐categories: sediments, salt structures, basement and Moho. Distinctions between the sources of the anomalies from different depths was achieved by utilizing the different decay characteristics of gravity, gravity gradiometry and high resolution magnetic anomalies. The workflow was applied to the southern part of the Nordkapp Basin. It started with the sedimentary model derived from seismics, populated with measured densities and magnetic susceptibilities and a starting model for the base salt. The residual after the removal of this model was interpreted in terms of a crustal model, including flexural isostatic calculations for the Moho with the sedimentary load. The residual after the removal of crustal and early sedimentary model was used to tune the salt model. As these major and minor modelling steps depend on each other, an iterative process was applied to stepwise improve the density and magnetic susceptibility model. The first vertical gradient of gravity and the magnetic field were found to give most information about the cap rock of the diapirs. The improvement in salt imaging, integrated with results from controlled‐source electromagnetic and magneto‐telluric modelling is shown for the salt diapir Uranus, where a well, terminated in the salt, constrains the minimum of the depth to base salt.     

关于中国海陆莫霍面深度图编绘的思考

莫霍面是地壳和上地幔的分界面,是一个重要的密度界面.布格重力异常与莫霍面深度之间具有紧密的联系,利用重力异常反演莫霍面深度成是研究莫霍面深度和编制莫霍面深度图的主要手段之一.本文总结了前人编制莫霍图的方法和结果,并加以分析讨论.提出应用布格重力异常反演中国海陆莫霍面深度的方法与技术,并考虑到中国海、陆构造的一体性,进行海陆统一编图以展示莫霍面的海、陆演化与构造关系.