Isostatic status in North China (1) Method and local compensation

Following Airy and Pratt principles, five kinds of local-compensation models are analysed and a rapid 3-D gravity formula is utilized to calculate isostatic anomalies for 66 models with different parameters. It is noted that isostatic gravity maps appear nearly identical in their main patterns and features. The optimum compensation model in North China is one of modified Airy models in which the different density distribution in the surface, upper crust and lower crust is taken into account and the standard crustal thickness is about 50km. The position of the complete compensation interface is located in the upper mantle. The North China platform as a whole is under sub-isostatic equilibrium status with an isostatic anomaly of about 18·10⁻⁵ m/s² on an average. The distribution of isostatic gravity anomaly shows an obvious blockwise pattern. Most positive anomaly areas occur over the eastern part, the Jiao-Liao Block, Mt. Yan block and northern margin of the Hebei-Shandong block, whereas a negative area occurs in the Shanxi graben. The comparison of models indicates that the Moho discontinuity is not suitable to be taken as a compensation interface, and the compensation effects in Airy model are better than that in Pratt model, which is consistent with the feature of dominant layered structure and less lateral inhomogeneity in crust. Some results about composite compensation, the basic characteristics of isostatic anomaly and deep stucture will be published later in the second part of this paper. Wang Bowen took part in some work in this paper.     

论华北地区的均衡状态(一)——方法和局部补偿

根据经典均衡的原理,本文重点分析了五种局部均衡补偿模式.在计算方法上利用频域三维重力场的理论公式,快速求得均衡校正值,据此计算了66个模型的均衡重力异常场,注意到对这许多不同参量的模型而言,它们的均衡异常场在形态与分布特征上基本一致,其中计入了地表和上下地壳密度差异分布的 Airy 模型具有最佳的补偿效果,它的均衡面在莫霍界面以下的上地幔中,标准深度50km.从整体上看,华北地台处于亚均衡状态,均衡异常的均值为1810-5m/s2.均衡重力异常的分布表现出明显的块体特征,正均衡异常区主要分布在东部胶辽地块和冀中平原北缘,在汾渭裂谷区存在负异常.模型对比表明,以莫霍界面作为均衡补偿面的模型是不可取的;Airy 模型比 Pratt 模型的补偿效果略好,这同地壳构造以层状为主而侧向变化有限的特征相符.有关复合补偿、均衡重力异常的基本特征和深部构造的关系等结果,将在文章的第二部分发表.      

Expressions for the Global Gravimetric Moho Modeling in Spectral Domain

We apply a newly developed numerical method to improve the Moho geometry by the implementation of gravity data. This method utilizes expressions for the gravimetric forward and inverse modeling derived in a frequency domain. Methods for a spectral analysis and synthesis of the gravity field and crust density structures are applied in the gravimetric forward modeling of the consolidated crust-stripped gravity disturbances, which have a maximum correlation with the (a priori) Moho model. These gravity disturbances are obtained from the Earth’s gravity disturbances after applying the topographic and stripping gravity corrections of major known anomalous crust density structures; in the absence of a global mantle model, mantle density heterogeneities are disregarded. The isostatic scheme applied is based on a complete compensation of the crust relative to the upper mantle density. The functional relation is established between the (unknown) Moho depths and the complete crust-stripped isostatic gravity disturbances, which according to the adopted isostatic scheme have (theoretically) a minimum correlation with the Moho geometry. The system of observation equations, which describes the relation between spherical functions of the isostatic gravity field and the Moho geometry, is defined by means of a linearized Fredholm integral equation of the first kind. The Moho depths are determined based on solving the gravimetric inverse problem. The regularization is applied to stabilize the ill-posed solution. This numerical procedure is utilized to determine the Moho depths globally. The gravimetric result is presented and compared with the seismic Moho model. Our gravimetric result has a relatively good agreement with the CRUST2.0 Moho model by means of the RMS of differences (of 3.5 km). However, the gravimetric solution has a systematic bias. We explain this bias between the gravimetric and seismic Moho models by the unmodelled mantle heterogeneities and uncertainties in the CRUST2.0 global crustal model.     

地形-均衡补偿重力、大地水准面异常频谱分析

将地形高、地球内部质量异常以及重力、大地水准面展开成球谐级数,依据岩石圈弹性挠曲均衡补偿理论建立地形—均衡补偿重力、大地水准面异常的球谐级数表达式.由此我们可以研究地形—均衡补偿重力、大地水准面异常与球谐级数阶次的关系,以及不同波长地形荷载与岩石圈挠曲补偿的关系,探讨地形—均衡补偿重力、大地水准面的频谱特性.从观测大地水准面异常和自由空气重力异常扣除地形—均衡补偿大地水准面、重力异常,可以得到均衡大地水准面异常和均衡重力异常.均衡大地水准面异常已经消除了浅层物质不均匀的影响,反映的是地球深部物质密度不均匀分布.均衡重力异常显示出中短波长特性,反映的是地壳上地幔物质分布的失衡和物质调整的动力学特征.     

论华北地区的均衡状态(二)——复合补偿与深部构造

由试验均衡的理论出发,得到了该区的均衡响应函数并建立了复合补偿模式。地形高度对重力场的影响很复杂,波长小于300km的地形起伏具有偏高的均衡响应值。 局部补偿是华北地区的主要补偿机制,所占比例达90%。区域补偿的等效弹性板厚度偏小,仅18km, 表明了华北地壳破裂程度严重和下地壳流变性突出。 均衡重力异常具有块体分布和均衡调整方向同新生代构造运动方向不完全符合等特点,其中一些成分是由于表浅层地质体的非均匀载荷所造成,不能简单地归因于欠补偿或过补偿。均衡异常的垂直导数分布清晰地揭示了华北地区几条重要的断块分界线。从深部构造上看,均衡补偿过程发生在下地壳特别是上地幔中。本文从均衡的角度探讨了地震危险性。      

TOPOGRAPHIC AND ISOSTATIC CORRECTIONS TO GRAVITY SURVEYS IN MOUNTAINOUS AREAS*

In mountainous areas it is an inadequate procedure to reduce gravity observations by merely subtracting the effect of an infinite flat slab of material between the station and sea-level, and adding a terrain correction. A programme is described which directly computes the effect of masses above sea-level, and mass-deficiencies below it; as well as the effect of compensating masses under the Pratt and Airy isostatic systems. As an example, the method has been applied to a regional gravity survey of Papua and New Guinea where it is seen to remove the usually high correlation of the Bouguer anomaly with local topography.     

The gravity and isostatic Moho in North China Craton and their implications to seismicity

The Bouguer gravity is the combination of field sources in different depths. Based on the multi-scale analysis of the Bouguer gravity, we can get the gravity anomaly caused by the Moho undulation. This study presents the various orders of approximation of gravity anomaly in North China Craton (NCC), the possible source depths with radial logarithmic power spectrum, and the relationship between the deep structure and gravity anomaly. Furthermore, we discuss the isostatic compensation about the Moho depth from gravity and deep seismic sounding profiles (DSS). The results show that: (1) the fourth approximation could have resulted from the Moho undulation, (2) in contrast to the isostatic Moho, the inverted gravity Moho and the DSS Moho show that most of NCC has been isostatically compensated, and (3) the isostatic compensation rate has some close relation to the seismicity.     

南北地震带北段深部构造特征

本文利用重力资料,采用单层地壳模式反演南北地震带北段的地壳厚度.根据艾利均衡假设,进行均衡补偿归算.编制莫氏界面图和11均衡异常图.根据地壳构造特征,划分六个地壳构造区.对天水-文县间立交构造格架进行初步的探讨.结合历史地震资料,讨论了地壳构造、均衡异常与地震的关系.      

甘肃西部地区深部构造

本文利用重力资料,采用单层地壳模式反演了甘肃西部地区的地壳厚度。根据艾利的均衡假设,进行了均衡补偿的归算,编制了莫霍界面图和均衡异常图。作者对甘肃西部地区的地壳变异带形成的力源进行了简要的探讨,结合历史地震资料,讨论了地壳构造、均衡异常与地震的关系。     

Global detailed geoid computation and model analysis

This paper presents a survey of recent work on the gravimetric geoid. The gravity models considered are those published in the past few years by the Goddard Space Flight Center (GSFC), the Smithsonian Astrophysical Observatory (SAO) and the Ohio State University (OSU). Comparisons and analyses have been carried out through the ose of detailed gravimetric geoids which we have computed by combining the above-mentioned models with a set of 26 000, 1^ox1^o mean free air gravity anomalies. The accuracy of the detailed gravimetric geoid computed using the most recent Goddard Earth Model (GEM-6) in conjunction with the set 1^ox1^o mean free air gravity anomalies is assessed at 2 m on the continents of North America, Europe And Australia, 2 to 5 m in the North-East Pacific and North Atlantic areas and 5 to 10 m in other areas where surface gravity data are sparse. Rms differences between this detailed geoid and the detailed geoids computed using the other satellite gravity fields in conjunction with same set of surface data range from 3 to 7 m. The maximum differences in all cases occurred in the Southern Hemisphere where surface data and satellite observations are sparse. These differences exhibited wavelengths of approximately 30^o to 50^o in longitude. Detailed geoidal heights were also computed with models truncated to 12th degree and order as well as 8th degree and order. This truncation resulted in a reduction of the rms differences to a maximum of 5 m. Comparisons have been made with the astrogeodetic data of Rice (United States), Bomford (Europe), and Mather (Australia) and also with geoidal heights from satellite solutions for geocentric station coordinates in North America and the Caribbean.     

Preliminary study on isostatic anomaly and recent tectonic stress field——Taking East China Sea and its eastern marginal seas as an example

On the basis of the reality of recent tectonic movement and discarding such a viewpoint that the isostatic adjust-ment only results from excessive or insufficient compensation,we have discussed the tectonic stress causing ine-auality and regarded the isostatic anomaly as a load on the earth‘s interior,thus the earth‘s inner stress can be cal-culated.The research results show that in the East China Sea and its eastern marginal seas the change of the verti-cal stress derived from the isostatic gravity anomaly is more marked than that of the horizontal stress.Along the Ryukyu trench there is an enhancement of vertical stress by 5MPa,which evidently reflects the effect of plate subduction.On contrary,along the island are to the northwest of the trench the vertical stress weakens by about5MPa.The horizontal stresses in eastern and western parts are obviously different,the east westward stress on the oceanic crust σx is negative(while the pressure is positive)but on the continental crust in positive.These facts indicate the effect of compression between plates.     

Investigations of local Bouguer gravity anomalies of the Apennines and Taurus Mountains of the Moon

Local line-of-sight (LOS) Bouguer gravity anomalies of the Apennines and Taurus Mountains of the Moon have been calculated form low-altitude LOS free-air Doppler gravity profiles. The topography of the mountain areas is reflected by free-air gravity highs indicating no complete isostatic compensation. The resultant Bouguer gravity shows no anomalies for the Apennines, indicating lack of isostatic compensation. For the older Taurus Mountains significant local Bouguer minima of about ? 15 mgal indicate at least partial compensation.If a viscoelastic compensation mechanism (bending of a viscoelastic plate overlying a fluid half-space) is assumed, models for the crustal viscosity as a function of time give limits of the range of possible models from 10²⁴ to 5 × 10²⁵ P at 4.4 × 10⁹ y BP, 10²⁶ – 10²⁷ P at 3.9 × 10⁹ y, and 5 × 10²⁶ – 10²⁸ P at 3.0 × 10⁹ y. For earlier times only a lower bound of 10²⁷ P can be given.Two profiles of the Taurus area have been investigated; they show no significant Bouguer anomalies across the mare basalt patches of Lacus Bonitatis and Sinus Amoris and thus can be used to estimate an upper limit for the basalt thicknesses. For Lacus Bonitatis this limit is 1.3 km; the limit is reached for Sinus Amoris at an average thickness of 0.3 km, with 1.5 km in the centre. Earlier results from DeHon and Waskom are consistent with the gravity data.     

A REGIONAL GRAVITY STUDY OF THE NORTHERN NORTH SEA (56–62° N)*

A Bouguer gravity anomaly map is presented of the North Sea and adjacent land areas in Norway and Denmark, covering an area situated between 56° and 62°N, 1°W and 10°E. The gravity data from the UK sector of the North Sea, the land and offshore areas of Denmark, and the land areas of Norway have been published before. However, the gravity data from the Norwegian sector of the North Sea are new. A large number (about 60) of individual gravity features can be defined in the mapped area. Most of those situated in the UK sector of the North Sea and on land in Norway have been discussed earlier; however, most of the anomalies found elsewhere which are qualitatively interpreted here have not been discussed before. An interpreted Bouguer anomaly map is presented which identifies all these features. The majority of the gravity anomalies encountered in the mapped area can be shown to be associated with one of the following geological features: (i) basement highs, (ii) large bodies of heavy basic or ultrabasic rock in the crystalline basement, (iii) large igneous intrusions within the sedimentary column and thick accumulations of volcanic rocks or their associated eruption centers, (iv) major basement faults. Large-scale geological structures such as the Central, Viking and Sogn Grabens and the East Shetland, Stord, Forth Approaches and Norwegian-Danish Basins are essentially in isostatic equilibrium and are only locally marked by relatively weak gravity minima. A residual gravity anomaly map has been produced by subtracting from the observed Bouguer anomalies the estimated gravity effect of an assumed thinned crust. This residual gravity anomaly map shows a number of features of the Bouguer anomaly field with greater clarity.     

Gravity anomaly and crustal density structure in Jilantai rift zone and its adjacent region

This paper deals with the interpretation of Bouguer gravity anomalies measured along a 250 km long Suhaitu-Etuokeqi gravity profile located at the transitional zone of the Alxa and Ordos blocks where geophysical characteristics are very complex. The analysis is carried out in terms of the ratio of elevation and Bouguer gravity anomaly, the normalized full gradient of a section of the Bouguer gravity anomaly (G ^h ) and the crustal density structure reveal that (1) the ratio of highs and lows of elevation and Bouguer gravity anomaly is large between Zhengyiguan fault (F4) and Helandonglu fault (F6), which can be explained due to crustal inhomogeneities related to the uplift of the Qinghai-Tibet block in the northeast; (2) the main active faults correspond to the G ^h contour strip or cut the local region, and generally show strong deformation characteristics, for example the Bayanwulashan mountain front fault (F1) or the southeast boundary of Alxa block is in accord with the western change belt of G ^h , a belt about 10 km wide that extends to about 30 km; (3) Yinchuan-Pingluo fault (F8) is the seismogenic structure of the Pingluo M earthquake, and its focal depth is about 15 km; (4) the Moho depth trend and Bouguer gravity anomaly variation indicates that the regional gravity field is strongly correlated with the Moho discontinuity.     

The gravity field and crustal thickness of Venus

The gravity and topography of Venus obtained from observations of the Magellan mission, as well as the gravity and topography from our numerical mantle convection model, are discussed in this paper. We used the hypothesis that the geoid of degrees 2–40 is produced by sublithospheric mantle density anomalies that are associated with dynamical process within the mantle. We obtained the model dynamical admittance(the geoid topography ratio based on a convection model) by a numerical simulation of the Venusian mantle convection, and used it to correct the dynamical effect in the calculation of crustal thickness. After deducting the dynamical effect, the thickness of the Venusian crust is presented. The results show that the gravity and topography are strongly correlated with the Venusian mantle convection and the Venusian crust has a significant influence on the topography. The Venusian crustal thickness varies from 28 to 70 km. Ishtar Terra, and Ovda Regio and Thetis Regio in western Aphrodite Terra have the highest crustal thickness(larger than 50 km). The high topography of these areas is thought to be supported by crustal compensation and our results are consistent with the hypothesis that these areas are remnants of ancient continents. The crustal thickness in the Beta, Themis, Dione, Eistla, Bell, and Lada regiones is thin and shows less correlation with the topography, especially in the Atla and Imdr regiones in the eastern part of Aphrodite Terra. This is consistent with the hypothesis that these highlands are mainly supported by mantle plumes. Compared with the crustal thickness calculated with the dynamical effect, our results are more consistent with the crust evolution and internal dynamical process of Venus.     

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.     

地形/均衡重力场模型构制及其拟稳分析

重力空白区数据填补的一个主要方法是基于地壳均衡理论进行的,该方法亦用于EGM系列模型的构建中.本文研究了地形数据在构制地形/均衡重力场模型中的应用,分析了补偿深度对Airy位模型和面凝聚位模型的影响,给出二者的最佳补偿深度分别为50 km和40 km.以纯卫星重力模型为参考,后者在前120阶的精度要高于前者,但在121~250阶的精度较低,组合模型精度高于单一模型精度.对地形/均衡地球重力场模型进行了EGM2008拟稳分析,研究了不同分辨率基准的拟稳效果,分析表明：30'分辨率的拟稳基准所得拟稳模型对应的阶方差与参考阶方差曲线直到360阶都有较好的一致性,以EGM2008为基准,其相对累计大地水准面高误差在140阶时为6.83cm,相对累计重力异常误差在220阶时为1.10 mGal.     

Gravity compensation in the mantle beneath the neovolcanic zone of Iceland

An enormous component of isostatic compensation(～?430±40mgal) is provided by subcrustal material beneath the neovolcanic zone of Iceland. Previously published values for the component of gravity contributed by anomalous mantle material beneath this region range from ?250 to ?140 mgal. These values are only a partial indication of the magnitude of the compensation mechanism. If one takes into account constraints on crustal thickness from seismic refraction studies and compares Iceland to less active tectonic regions near by, one obtains a mantle gravity effect of approximately?430±40mgal, which for a simple slab model leads to a vertically integrated mass deficit per unit surface area of 10⁶ g/cm². The effects of thermal expansion, solid-solid phase transitions and partial fusion can provide significant contributions to the total mass deficiency; however, none of these mechanisms alone seems sufficient to account for the entire anomaly.The relation of this mass anomaly to the evolution of the Iceland-Faeroe ridge is considered by examining two extreme end-members of a suite of possible evolutionary models for this region. The first of these is the case where, in time, the 10⁶ g/cm² mass deficit will be resorbed into the mantle with the effects of chemical segregation playing a minor role. The second case, which is preferred, involves a significant redistribution of material from the mantle such that basaltic melt segregated from high levels in the mantle accumulates and crystallizes in a zone at the base of the crust. In this latter model, if the Iceland-Faeroe ridge is considered to have evolved under a steady rate of magma production over the last 30–40 × 10⁶ years, then underplating of the crust may account for its increasing thickness as it matures from 8–10 km in the neovolcanic zone to a value of approximately 32 km for the Iceland-Faeroe ridge. If we assume a 10% increase in density upon crystallization, thickening of the crust by 22 km through underplating by magma accumulation leads to an increase in mass per unit surface area of 0.6 × 10⁶ g/cm², and accounts for approximately 60% of the total mass difference in the mantle between Iceland and the Iceland-Faeroe ridge.     

四川中西部地区地壳结构与重力均衡

汶川M_S8.0地震的“孕育”、发生和发展是深部物质分异、调整和运移的产物.为此,在四川中西部地区（松潘—甘孜,龙门山断裂系和四川盆地）应用重力布格异常场资料并通过两条典型剖面的地壳厚度(Moho界面深度）分布与依据Airy均衡理论给出的理论均衡地壳厚度做对比分析,探讨四川盆地、龙门山造山带、邛崃山等川西地域的地壳均衡状态,得到龙门山及其以西地带的深部地壳结构.龙门山造山带恰处于很不均衡的状态,即与其西北和东南部相比差异明显,故地壳处于不稳定状态.为探讨该区重力场均衡与强烈地震活动之间的关系,还必须进行新一轮的高精度观测,以对该区深部精细结构、重力场效应和均衡补偿深入研究.此外,本文研究结果有益于震后确定城镇布局和为不同类型建筑物重建选址提供深部要素.     

基于地形精化的金星重力场模型VGM2013

高精度金星重力场的获取,是金星探测的重要内容.本文利用最新的金星地形和重力模型,通过高通滤波后的残差地形（RTM）并在考虑均衡改正的情况下改进了重力的短波成分,最终提出了一个新的金星重力模型VGM2013,该模型赤道分辨率达10 km量级,大大高于现有的金星重力场模型,最终结果是金星表面重力加速度和重力扰动.研究中同时发现金星在Airy-Heiskanen均衡模型下的全球最优补偿深度为30 km,金星地壳的密度可能小于当前认为的2700~2900 kg·m^-3.VGM2013模型的结果可为将来的金星探测器定轨和着陆导航提供参考,作为重力计算的先验模型.但由于该模型没有包含短波重力观测信息,不建议直接用于更小尺度的地质和地球物理解释.