Interpretation of gravity anomalies of dykes by pseudo-magnetic transformation

Summary A simple transformation called pseudo-magnetic transformation is introduced in which the horizontal derivatives of the observed gravity anomalies of any body will be calculated. These horizontal derivatives, called the pseudo-magnetic anomalies, are proportional to the vertical magnetic anomalies of the same body assumed to be polarised horizontally. It is shown that the interpretation of gravity anomalies of dykes is not unique except by computing the pseudo-magnetic anomalies, which will be interpreted by the logarithmic curve fitting technique indicated earlier [5]²).     

重震反演中国东北地壳上地幔三维密度结构

本文利用重力和地震P波到时数据反演得到了中国东北地区地壳上地幔三维密度结构.与单一的重力或地震反演相比,重震反演一方面有效地克服了重力反演结果垂向分辨率低的问题,另一方面也提高了地震反演结果的可靠性.结果显示:中国东北地区的地壳及上地幔剩余密度异常分布与构造单元具有明显的相关性,造山带对应低密度异常,盆地对应高密度异常;区域内火山下方有明显的低密度体存在,可能是由于太平洋板块俯冲进入上地幔并部分滞留,在滞留板块深部脱水和软流圈热物质共同作用下产生了上涌岩浆,喷发后形成了火山.     

A new technique of interpreting gravity and vertical magnetic anomalies due to infinite horizontal cylindrical ore bodies

Summary A novel method of interpreting gravity and magnetic anomalies is presented here. Two diagrams of master curves, one for gravity and the other for vertical magnetic interpretation are presented. They are useful in calculating the depth of burial and the radius of infinite horizontal cylindrical bodies irrespective of density contrast or strength and direction of magnetisation. This method also enables us to infer the direction of magnetisation, resultant intensity of magnetisation and from them the susceptibility contrast; and density contrast. ThoughHenderson [8]²) reported the applicability of continuations and derivatives in the interpretation of magnetic anomalies for the first time, the authors have treated them in a more exhaustive manner in the present paper to obtain valuable relationships.     

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.     

Correction to the crustal thickness of the northwestern China using the data of seis-mic tomography

Introduction The gravity anomaly is an indicator of the density distribution of the underground material. Therefore the gravity anomalies have been important data used for studying the deep crustal struc-ture for a long time. Many people have made detailed researches on the regional crustal structure inverted by Bouguer anomalies. In particular some empirical formulae and practical algorithms about the crustal thickness were brought forward, and a series of results were obtained (MENG, 1996)…     

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.     

Global Crust-Mantle Density Contrast Estimated from EGM2008, DTM2008, CRUST2.0, and ICE-5G

We compute globally the consolidated crust-stripped gravity disturbances/anomalies. These refined gravity field quantities are obtained from the EGM2008 gravity data after applying the topographic and crust density contrasts stripping corrections computed using the global topography/bathymetry model DTM2006.0, the global continental ice-thickness data ICE-5G, and the global crustal model CRUST2.0. All crust components density contrasts are defined relative to the reference crustal density of 2,670 kg/m³. We demonstrate that the consolidated crust-stripped gravity data have the strongest correlation with the crustal thickness. Therefore, they are the most suitable gravity data type for the recovery of the Moho density interface by means of the gravimetric modelling or inversion. The consolidated crust-stripped gravity data and the CRUST2.0 crust-thickness data are used to estimate the global average value of the crust-mantle density contrast. This is done by minimising the correlation between these refined gravity and crust-thickness data by adding the crust-mantle density contrast to the original reference crustal density of 2,670?kg/m³. The estimated values of 485 kg/m³ (for the refined gravity disturbances) and 481?kg/m³ (for the refined gravity anomalies) very closely agree with the value of the crust-mantle density contrast of 480?kg/m³, which is adopted in the definition of the Preliminary Reference Earth Model (PREM). This agreement is more likely due to the fact that our results of the gravimetric forward modelling are significantly constrained by the CRUST2.0 model density structure and crust-thickness data derived purely based on methods of seismic refraction.     

Seismic velocity structure around the Hyuganada region, Southwest Japan, derived from seismic tomography using land and OBS data and its implications for interplate coupling and vertical crustal uplift

The Hyuganada region, a forearc region of Southwest Japan, is characterized by several interesting geological and geophysical features, i.e., significant aseismic crustal uplift of 120 m during the past 120 thousand years at the Miyazaki Plain, negative free-air gravity anomalies with the maximum magnitude of −130 mgal, and relatively less cohesive interplate coupling compared with that for off the Shikoku and Kii Peninsula. In order to examine the causes of these observations, we determined a detailed three-dimensional seismic velocity structure based on the seismic data observed by ocean bottom seismometers (OBS) and land stations. P- and S-wave tomographic velocity structures clearly indicate the subducting slab and also the zones of high Poisson's ratio at 25–35 km depth along the coastline of the northeastern part of the Hyuganada. The region with high Poisson's ratio may correspond to the serpentinized mantle wedge as suggested for other mantle wedges, and appears to be coincident with the zone for observed aseismic slips such as the slow-slip and after-slip events. Also, the detection may be related to a relatively weak interplate coupling in the Hyuganada region. The tomographic structures also indicate low velocity zones with a horizontal scale comparable to the Kyushu-Palau Ridge in and around the subducting slab. If we assume that the low velocity zones correspond to the subducted Kyushu-Palau Ridge, then the predicted gravity anomaly due to the density contrast between the low velocity zones and the surrounding region can explain about 60% of the gravity anomaly in the Hyuganada region. The buoyancy is probably an important factor for the crustal uplift observed in the Miyazaki Plain, the steep bending of the subducting slab and the normal fault-type earthquakes around the Hyuganada region.     

The Alpha Ridge: Gravity, seismic and magnetic evidence for a homogenous, mafic crust

Gravity and bathymetric results from the 1983 Canadian Expedition to Study the Alpha Ridge (CESAR) have outlined positive free-air anomalies centred on the continental break off Ellesmere Island characteristic of normal Atlantic-type passive margins. These data confirm implications derived from depth-to-magnetic basement calculations that the ridge may not be structurally connected to the continent. Across the Alpha Ridge magnetic and gravity anomalies mimic the bathymetry. The magnetic anomalies apparently are not caused, to any great extent, by internal structures or magnetic reversals, but rather seem to result simply from variations in depths to a homogenous magnetic structure. The gravity anomalies across a 500 km wide section of the Alpha Ridge can be almost completely accounted for by topography, shallow sedimentary fill and a simple two-tier crustal model. This implies an extraordinary lateral density homogeneity unknown in continental structures of comparable size. Gravity models show the crustal thickness to increase gradually from 20 km at the Marvin Spur to 38 km at the ridge crest. A comparison of this model with a gravity model of the continental-type Lomonosov Ridge, which has a thickness of about 25 km, indicates that, at the same thickness of 25 km, the average crustal density of the Alpha Ridge is 0.08 Mg/m³ greater. These gravity constraints, the unusually homogenous seismic velocity structure revealed by the CESAR studies, the homogeneous magnetic structure, and the extraordinary high intensity satellite magnetic anomaly associated with the Alpha Ridge, indicate that the ridge may be composed of a large pile of mafic rock, possibly unique on this planet.     

蒙古及周边地区重力异常和地壳不均匀体分布

基于全球EGM2008自由空气重力异常模型,本文计算了蒙古及周边地区的布格重力异常和AiryHeiskanen均衡重力异常.在此基础上,本文采用Crust 1.0地壳模型为参考,通过重力正演方法,对蒙古及周边地区不同深度地壳密度结构模型的重力异常进行了计算,并对得到的正演布格重力异常与实际重力异常进行了对比和分析.研究结果表明:蒙古西部杭爱山地区与阿尔泰山地区的构造变形差异性明显,现今均衡重力异常中杭爱山周边没有明显的均衡异常高值区,而阿尔泰山地区西南方向存在均衡重力异常高值分布,分析与新构造运动密切相关;Crust 1.0模型给出的壳幔横向密度不均匀体分布对于计算Moho面起伏引起的重力异常作用明显;Crust 1.0给出的地壳内界面变形可以反映深大活动断裂的深部构造变形.研究结果对于认识蒙古东西部构造特征差异,以及现今西部活动断裂的地球物理场特征具有参考意义,也可以为进一步应用Crust 1.0模型为参考开展三维密度结构反演提供一定帮助.     

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.     

华北克拉通岩石圈三维密度结构

显生宙以来华北克拉通岩石圈遭到破坏,这一现象的科学问题已受到世界地学家广泛关注.本文首先将地震层析成像反演得到的P波速度扰动转化为密度扰动,以此作为初始密度模型,然后利用布格重力异常反演得到了华北克拉通岩石圈高分辨三维密度结构.为了避开大型稀疏矩阵求逆计算,提高计算效率,我们将代数重构技术用于密度反演解算.反演结果表明:华北克拉通岩石圈密度在横向和纵向上均存在明显的不均匀性,密度分布形态与地表构造格局有很好的相关性;研究区地壳整体表现为低密度异常,地壳以下岩石圈部分则以高密度异常为主;鄂尔多斯块体地壳范围内以低密度异常为主,80~120 km深度上为呈南北两端集中分布的高密度异常,并分别与秦岭造山带和阴山造山带的高密度异常分布相连,这暗示了鄂尔多斯块体可能受到了来自其南北两端造山带深部动力学过程的影响;80~120 km深度上,华北克拉通东部地区呈现出显著的南北向非均匀的高密度异常,这表明遭到破坏后该地区上地幔物质分布具有强烈的南北向非均匀性.     

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.     

用于区域重力场定量解释的多尺度刻痕分析方法

本文介绍一个把小波多尺度分析、表面刻痕分析以及位场频率域解释理论和反演方法结合起来的数据处理、反演解释和信息提取的方法系统.这一方法系统简称为区域重力场多尺度刻痕分析方法,应用于刻画地壳分层的三维密度结构、地壳变形带分布和构造单元分区.多尺度刻痕分析包含频率域重力场场源分层、重力场小波变换多尺度分解、场源分层深度及密度扰动反演、分层刻痕分析和构造边界定位四个子系统.文中扼要地介绍这四个子系统基本原理、方法技术及应用效果.从地球物理探测到大地构造学发现,是一个多学科综合研究的探索过程.要取得重大研究成果,必须研发和组合来自不同学科的多个新方法技术,使多学科综合研究有宽厚的理论支撑.本文介绍的四个子系统组合的理论支撑分别来自应用数学、地球物理学和信息科学.     

利用低阶卫星重力位系数研究下地幔横向密度异常分布

本文试图采用卫星重力资料和一种新的反演方法来研究地幔的横向密度异常分布.先将密度异常△（r,,（?））在一个三维正交函数系下进行展开,其展开系数待定.然后,根据密度异常与重力扰动位之间的关系建立观测方程组,其中未知向量由密度异常展开系数组成,重力扰动观测向量由 GEM10B 重力模型中的位系数计算而得,并通过适当选取重力位系数的阶数,对观测向量进行滤波.最后,就下地幔（670km——CM 界面）作了实际计算.计算中,重力扰动位阶数取为2——11阶,密度异常展开式的截断阶数取为 K=4和 L=6,求解观测方程组时采用阻尼最小二乘法.结果表明:密度扰动值在670km 不连续面及核幔界面处达到极大值,且在环太平洋地区存在一高密度带,太平洋中部对应于一低密度区,这些特征与 Dziewonski 得到的下地幔三维波速异常分布特征相一致.但是,在南极地区、大西洋及印度洋部分地区,所得的密度异常分布与三维波速异常分布呈负相关,文章就其原因作了初步分析.      

Geoid anomalies over Gorringe Ridge,North Atlantic Ocean

Gorringe Ridge is a strong uplifted block of oceanic crust and upper mantle lying at the eastern end of the Azores-Gibraltar plate boundary. The geoid over this structure derived from Seasat altimeter data exhibits a 9-m height anomaly with a north-south lateral extension smaller than 200 km. An attempt is made to interpret this geoid together with the gravity anomalies and with the seismicity, which has been compiled as a function of depth.It is first shown that the flexure of the oceanic lithosphere due to the ridge loading does not provide a good fit of the geoid anomalies and probably should be discarded, as it assumes a continuous unfractured elastic plate.Models involving local heterogeneities are then tested. The comparison of the observed geoid anomalies with the anomalies due to the uncompensated relief indicates that the topographic high has no shallow compensation.Uncompensated models, previously proposed to explain the gravity anomalies, are tested using the geoid. One model (Purdy and Bonnin, in Bonnin [11]), which involves an uplift of upper mantle material at depth, generates too strong geoid anomalies and must be discarded. Another model, which represents a nascent subduction zone (Le Pichon et al. [25]), fits both the gravity and geoid anomalies, but leads to difficulties in explaining the deep seismicity north of Gorringe Ridge.A model in isostatic equilibrium is also able to fit both gravity and geoid anomalies. This model involves a deep root of density 3.0 g cm^?3, as has been previously proposed for many oceanic ridges and plateaus. This model is compatible with the deep seismicity, but the origin of this low-density material at great depth is up to now an unresolved question.More likely, dynamical models taking into account the forces induced by the convection related to the slow plate convergence in this area will have to be considered.     

基于重力数据特征的东北地区深部动力机制解析

中国东北地区处于古亚洲构造域、蒙古—鄂霍茨克构造域和环太平洋构造域叠加作用最为显著的地区,是地学研究的热点区域.为了探析欧亚大陆下西太平洋板片的俯冲形态以及揭示该区域深部地球动力学机制,利用卫星重力数据通过预处理共轭梯度快速密度反演算法获得了包含东北地区、华北部分地区及日本海海域在内的研究区域上地幔三维密度结构,结合天然地震三维层析成像结果共同揭示太平洋板片的俯冲形态和深部动力机制.俯冲的太平洋板片在日本海沟处呈高密度异常,向西横向持续扩张,深度方向上有逐渐增加趋势.不连续的高密度体俯冲至地幔转换带(410～660km)后继续水平西向俯冲,部分滞留板片可能进入下地幔;在大兴安岭断裂带下面转换带中同样发现水平分布的高密度体,推断是大兴安岭断裂带下方地幔岩石圈拆沉的结果,横向不均匀分布的俯冲板片边缘已抵至大兴安岭造山带附近,这对于研究东北地区深部动力学机制具有重要的意义.     

An integrated geodynamic model of the Nankai subduction zone and neighboring regions from geophysical inversion and modeling

I investigate large-scale deep crustal structures of the Nankai subduction zone and neighboring region using regional magnetic and gravity anomalies, heat flow measurements, and earthquake hypocenters. It is found that ages, dip angles, and geothermal states of the subducting slab have direct influences on mantle wedge serpentinization. The weakest serpentinization observed in the Nankai forearc region is associated with the youngest downgoing plate of the Shikoku Basin. Conspicuous gravity anomalies identified in the forearc region are coincidental spatially with magnetic anomalies after the reduction to the pole, a mathematical procedure that helps relocate magnetic sources and boundaries, and allows us to more easily interpret magnetic data. It is argued that these patches of magnetic and gravity anomalies are caused by the same sources of anomalous density and magnetization, and are linked directly to preexisting structures such as magnetic anomalies and their boundaries in the subducting oceanic crust. Since the gravity and magnetic anomaly patches are found to be closely related to interplate seismogenic behaviors in the Nankai subduction zone, I suggest that major magnetic boundaries in the Shikoku Basin are likely weak places for slab tears that trigger seismic segmentations along the subduction zone.     

St. John's Island (Red Sea): a new geophysical model and its implications for the emplacement of ultramafic rocks in fracture zones and at continental margins

New gravity and magnetic data from the northern Red Sea reveal the extent of the large gravity anomaly (164 mgal) and the presence of significant magnetic anomalies over St. John's Island. Spectral transformation and three-dimensional potential-field modelling delineate the surface configuration and vertical extent of the causative body and the enormous density contrast required (1.2 g/cm³) suggests that it is composed of unserpentinised peridotite (density 3.4 g/cm³) to a depth of at least 8 km.St. John's Island is uniquely located, not only at a passive continental margin but also within a fracture zone at the transition from plate separation by seafloor spreading to extension by lithospheric attenuation. This precludes several suggested mechanisms for the emplacement of ultramafic bodies in fracture zones.Thermal contraction, serpentinite diapirism and changes in the poles of rotation do not seem possible mechanisms in this tectonic environment and the emplacement is most probably related to the spreading readjustment necessary to create a continent-to-continent fracture zone. A post-Mesozoic age of emplacement, associated with the onset of continental rifting and the rejuvenation of a pre-existing continental fracture, seems most probable.     

Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts

During the last 15 years, more attention has been paid to derive analytic formulae for the gravitational potential and field of polyhedral mass bodies with complicated polynomial density contrasts, because such formulae can be more suitable to approximate the true mass density variations of the earth (e.g., sedimentary basins and bedrock topography) than methods that use finer volume discretization and constant density contrasts. In this study, we derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space. The anomalous mass density is allowed to vary in both horizontal and vertical directions in a polynomial form of \(\lambda =ax^m+by^n+cz^t\), where m, n, t are nonnegative integers and a, b, c are coefficients of mass density. First, the singular volume integrals of the gravity anomalies are transformed to regular or weakly singular surface integrals over each polygon of the polyhedral body. Then, in terms of the derived singularity-free analytic formulae of these surface integrals, singularity-free analytic formulae for gravity anomalies of arbitrary polyhedral bodies with horizontal and vertical polynomial density contrasts are obtained. For an arbitrary polyhedron, we successfully derived analytic formulae of the gravity potential and the gravity field in the case of \(m\le 1\), \(n\le 1\), \(t\le 1\), and an analytic formula of the gravity potential in the case of \(m=n=t=2\). For a rectangular prism, we derive an analytic formula of the gravity potential for \(m\le 3\), \(n\le 3\) and \(t\le 3\) and closed forms of the gravity field are presented for \(m\le 1\), \(n\le 1\) and \(t\le 4\). Besides generalizing previously published closed-form solutions for cases of constant and linear mass density contrasts to higher polynomial order, to our best knowledge, this is the first time that closed-form solutions are presented for the gravitational potential of a general polyhedral body with quadratic density contrast in all spatial directions and for the vertical gravitational field of a prismatic body with quartic density contrast along the vertical direction. To verify our new analytic formulae, a prismatic model with depth-dependent polynomial density contrast and a polyhedral body in the form of a triangular prism with constant contrast are tested. Excellent agreements between results of published analytic formulae and our results are achieved. Our new analytic formulae are useful tools to compute gravity anomalies of complicated mass density contrasts in the earth, when the observation sites are close to the surface or within mass bodies.