重力异常二维正演中的无网格方法

无网格法是一类新型数值算法,具有精度高、高阶形函数构造与物性加载便利等特点,在计算力学领域应用广泛。将无网格方法（PIM、RPIM及EFGM）用于重力异常场二维正演计算：首先从重力异常二维变分问题出发,利用Galerkin法结合高斯积分公式推导了对应的无网格离散系统矩阵表达式;其次通过数值试验得出了RPIM-MQ、RPIM-exp及EFGM-exp形状参数的建议值,最后比较分析了最优形状参数下不同无网格法的计算效果。结果表明：无网格法适用于介质物性分布变化较大的重力异常二维正演,exp函数形状参数α_c最优取值区间为[1.5,1.7],β建议值为0.6,MQ函数q取值区间为-4.1~1.9;EFGM较PIM及RPIM具有更高的计算精度。     

三度体球冠模型重力异常计算方法及其重力归一化总梯度场特征

提出利用铅垂柱体薄片作为面元的面元积分法,计算三度体球冠重力异常的计算公式,用三度体球冠模型模拟三度背斜体,计算了均匀密度球冠模型、非均匀密度储油球冠模型的重力异常。最后通过误差分析,验证了该方法的可行性。采用波数域重力归一化总梯度计算方法,计算了均匀密度球冠模型、非均匀密度储油气球冠模型G^H场,发现似三度背斜体与二度背斜体有相似的G^H场等值线特征,似三度贮油气藏背斜构造的G^H场亦表现出明显的“两高夹一低”的储油典型标志。所以,可以用非均匀密度三度体储油球冠模型模拟三度贮油气藏背斜构造。     

基于数据库的地球化学异常特征参数计算方法

介绍了在地球化学普查中,一种单元素异常特征参数的计算方法。在确定了单元素异常下限,建立了取样点位数据图层,完成了单元素异常图制作的基础上,将单元素异常区图层与点位数据图层做点对区的相交分析,把单元素异常区中异常编号、异常面积字段的空间信息相交分析到异常区内点位数据图层中,将该点图层属性转换成DBF文件,应用FORXPRO软件编写了程序,从而计算单元素异常特征参数。     

Lithospheric structure of the North China Craton: Integrated gravity,geoid and topography data

The lithospheric structure of ancient cratons provides important constraints on models relating to tectonic evolution and mantle dynamics. Here we present the 3D lithospheric structure of the North China Craton (NCC) from a joint inversion of gravity, geoid and topography data. The NCC records a prolonged history of Archean and Paleoproterozoic accretion of crustal blocks through subduction and collision building the cratonic architecture, which was subsequently differentially destroyed during Mesozoic through extensive magmatism. The thermal structure obtained in our study is considered to define the lithosphere-asthenosphere boundary (LAB) of the NCC, and reflects the density variations within the mantle lithosphere. Employing the Moho depths from deep seismic sounding profiles for the inversion, and based on repeated computations using different parameters, we estimate the Moho depth, LAB depth and average crustal density of the craton. The Moho depth varies from 28 to 50 km and the LAB depth varies from 105 to 205 km. The LAB and Moho show concordant thinning from West to East of the NCC. The average crustal density is 2870 kg m^− 3 in the western part of the NCC, higher than that in the eastern part (2750 kg m^− 3). The results of joint inversion in our study yielded LAB depth and lithospheric thinning features similar to those estimated from thermal and seismic studies, although our results show different depth and variations in the thickness. The lithosphere gently thins from 145 to 105 km in the eastern NCC, where as the thinning is much less pronounced in the western NCC with average depth of about 175 km. The joint inversion results in this study provide another perspective on the lithospheric structure from the density properties and corresponding geophysical responses in an ancient craton.     

A rapid method to map the crustal and lithospheric thickness using elevation, geoid anomaly and thermal analysis. Application to the Gibraltar Arc System, Atlas Mountains and adjacent zones

We present a method based on the combination of elevation and geoid anomaly data together with thermal field to map crustal and lithospheric thickness. The main assumptions are local isostasy and a four-layered model composed of crust, lithospheric mantle, sea water and the asthenosphere. We consider a linear density gradient for the crust and a temperature dependent density for the lithospheric mantle. We perform sensitivity tests to evaluate the effect of the variation of the model parameters and the influence of RMS error of elevation and geoid anomaly databases. The application of this method to the Gibraltar Arc System, Atlas Mountains and adjacent zones reveals the presence of a lithospheric thinning zone, SW–NE oriented. This zone affects the High and Middle Atlas and extends from the Canary Islands to the eastern Alboran Basin and is probably linked with a similarly trending zone of thick lithosphere constituting the western Betics, eastern Rif, Rharb Basin, and Gulf of Cadiz. A number of different, even mutually opposite, geodynamic models have been proposed to explain the origin and evolution of the study area. Our results suggest that a plausible slab-retreating model should incorporate tear and asymmetric roll-back of the subducting slab to fit the present-day observed lithosphere geometry. In this context, the lithospheric thinning would be caused by lateral asthenospheric flow. An alternative mechanism responsible for lithospheric thinning is the presence of a hot magmatic reservoir derived from a deep ancient plume centred in the Canary Island, and extending as far as Central Europe.     

EGMlab, a scientific software for determining the gravity and gradient components from global geopotential models

Nowadays, Global Geopotential Models (GGMs) are used as a routine stage in the procedures to compute a gravimetric geoid. The GGMs based geoidal height also can be used for GPS/levelling and navigation purposes in developing countries which do not have accurate gravimetric geoid models. Also, the GGM based gravity anomaly including the digital elevation model can be used in evaluation and outlier detections schemes of the ground gravity anomaly data. Further, the deflection of vertical and gravity gradients components from the GGMs can be used for different geodetic and geophysical interpretation purposes. However, still a complete and user-friendly software package is not available for universities and geosciences communities. In this article, first we review the procedure for determination of the basic gravity field and gradient components from the GGMs, then general MATLAB based software is presented and applied as a sample case study for determination of gravity components based on the most recent EIGEN-GL04C GRACE model in Sweden. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

天然软土地基路堤临界高度一种计算方法研究

考虑地表硬壳层应力扩散作用、硬壳层的抗剪强度、中间主应力 对地基承载力的影响,从实际情况下土的静止侧压力系数出发,依据极坐标表示的弗拉曼公式和统一强度理论,推导出天然软土地基临塑与临界荷载公式,提出天然软土地基上路堤临界高度的一种计算方法。结合算例,探讨了软土层和硬壳层静止侧压力系数 、中间主剪应力系数 取不同值对路堤临界高度 的影响。结果表明： 与 的改变对路堤临界高度 影响很大,新的理论公式更能反应软土地基承载力的实质,对覆有硬壳层的软土地基上路堤的修筑具有一定的指导意义。     

一种重力异常向上延拓高度最优化确定方法

向上延拓方法是重力异常分离中的重要方法之一,但在应用时如何定量地选取合适的延拓高度是一直以来存在的问题。本文针对该问题展开研究,提出一种基于二乘误差的曲率分析方法来定量地给出相对合理的延拓高度。该方法对观测数据进行相邻不同高度的向上延拓,并用二乘法估算相邻高度延拓值的二乘误差,在各相邻高度延拓值二乘曲线中存在一个曲率最大值,在这个点最大程度地使局部异常衰减并尽可能地保留区域异常,可近似视为最佳延拓高度。利用理论模型数据对所提出的方法进行了测试,表明该方法能够定性给出较合适的延拓高度,从而为实际应用中延拓高度的选取提供参考。     

单桩荷载-沉降关系的数值模拟方法

以桩的荷载传递函数为基础,考虑桩-土（岩）共同作用,从理论上推导了桩身荷载与沉降关系的数值模拟的迭代模型。通过数值模拟分析得到桩顶的P-S曲线,可做为确定桩的承载力的依据。经过对工程实例的计算与实测对比分析,证明该理论可靠、方法简单,且具有较好的实用性。计算得到的P-S曲线与实测的曲线非常吻合。     

The geological significance of a negative gravity anomaly in the South Wales Coalfield

Three gravity traverses across the eastern half of the South Wales Coalfield indicate a local, elongate, negative Bouguer anomaly of a few milligals amplitude bordering the southern rim. The anomaly has a maximum amplitude of 4 mgal near Maesteg and attenuates eastward, dying out in the vicinity of the East Crop. Two possible geological causes of the anomaly are examined, namely a local thick sequence of normal Upper Carboniferous strata and a discrete, low-density body of Carboniferous age with no apparent surface expression. The former, uncontroversial explanation requires rock densities at variance with measured values. In the case of the hypothetical low density body which can explain the anomaly, a variety of possible ages and configurations are discussed.     

Sea-level changes, geoid and gravity anomalies due to Pleistocene deglaciation by means of multilayered, analytical Earth models

A new class of analytical, multilayered, viscoelastic Earth models based on PREM, with an incompressible, linear, viscoelastic Maxwell rheology, is applied to the modeling of global sea-level changes due to Pleistocene deglaciation. Until now, analytical schemes based on normal mode theory, have dealt with at most five layers, an elastic lithosphere, a three layered mantle including a transition zone, and a core (Spada et al., 1992. Geophys. J. Int. 109, 683–700). The novelty of our approach, used for the first time in sea-level studies, stands on an analytical scheme that can reproduce continuous elastic and rheological stratification when a sufficient number of layers is taken into account. We specifically assess the importance of our results for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission. GOCE will resolve the gravity field with a spatial resolution (half-wavelength) of 75 km and amplitude of 1.5 mgal, with a uniform coverage over the Earth, including presently unsurveyed, remote areas. Our models lead to post-glacial rebound induced free air gravity anomalies of a few mgals peak-to-peak in the harmonic degree range l=80–200, which will be discernible by GOCE. This finding demonstrates that post-glacial rebound has a high frequency component in the gravity field that can in principle be resolved by high resolution gravity satellite missions. We show that post-glacial rebound can contribute a substantial fraction to present-day sea-level variations and point out that for the Mediterranean Sea they are of the same order of magnitude as those induced by tectonic processes.     

The structure of Jebel El Mourra,Tunisia: a diapiric structure causing a positive gravity anomaly

Detailed gravity data integrated with geological data and mining well data are analysed to constrain the shape of the Triassic evaporitic body at Jebel El Mourra (northern Tunisian Atlas) and the mechanism of its emplacement at the surface. The gravity data analysis included the construction of a gravity anomaly maps, and synthetic and forward 2.5D gravity models. The complete Bouguer and residual gravity anomaly maps indicate a positive amplitude gravity anomaly over the Triassic evaporitic outcrops and prominent NE–SW‐trending features associated with the boundary of the Triassic rocks and surrounded layers. A NW–SE‐trending gravity model that crosses the Triassic evaporitic outcrop at Jebel El Mourra shows that the positive gravity anomaly can be explained by a deep‐rooted salt diapir. Conventional models of salt dome formation suggest that they produce negative gravity anomalies; however, this study shows that this model is not universal. The studied area is an example of a diapir expressed by positive gravity anomaly and this result is supported by synthetic gravity models at different stages of salt piercing.     

复杂条件二维重力场及重力张量场空间波数域正演方法

随着传感器技术的发展,重力场与重力张量场测量技术发展迅速,为实现地下密度分布精细反演提供了数据保障。正演是反演的基础,解决任意密度分布复杂地质体重力场与重力张量正演高效、高精度计算问题,是实现重力高效、精细反演、人机交互反演解释的关键。针对起伏地形和任意密度分布这种复杂条件下二维重力场及重力张量场高效高精度正演问题,这里提出了一种空间波数混合域正演算法,其关键环节包括:①结合新的矩形二度体组合模型波数域表达式和一维Gauss-FFT算法,提出了一种任意密度分布和起伏地形下重力场及重力张量高效、高精度正演算法;②采用新的二维正演算法,计算观测最高点和最低点之间多个不同高度水平网格重力场及重力张量,结合三次样条插值方法,实现了起伏地形上重力场及重力张量场高效、高精度正演。模型算例结果表明,新方法具有高效、高精度的显著特点。     

对称非各向同性体大地电磁法二维异常特征

大量观测资料表明,地下介质的物性普遍存在非各向同性现象,只有建立非各向同性模型才能真实地反应地下介质情况.在分析前人研究成果的基础上,从实际地质情况出发,以层状介质的电学性质为基础引入非各向同性系数到对称非各向同性体的研究当中,推导出对称非各向同性体二维大地电磁场的变分方程,实现了模拟对称非各向同性体的有限单元法.将计算结果与Pek的有限差分法的计算结果进行对比验证了程序的正确性.通过固定非各向同性系数在不同倾角下的模型,说明倾角对非各向同性效应的影响;通过固定倾角在不同非各向同性系数下的模型,说明非各向同性系数对非各向同性效应的影响;通过不同倾角和不同非各向同性系数模型的正演拟断面图,更加形象地展示两者与非各向同性效应之间的关系.     

“区域异常集中度”的概念、计算方法及其与成矿的关系

为了解释普遍存在的成矿规模与区域化探异常面积大小不成比例的问题,提出了“区域异常集中度”的概念,给出了概念的定义、相关要素和计算方法.探讨了区域异常集中度的主要特点,数值大小、计算尺度与成矿规模的关系,适用条件等.认为区域异常集中度反映了成矿物质的集中程度,应用它找大矿是在区域成矿要素范围内众多异常中“同中求异”的过程...     

重磁软件架构设计及实现方案研究

近年来重磁方法软件的发展正追随地质解释的需求不断与时俱进,逐步向三维可视化定量综合解释发展,目前国内重磁方法软件的研发亟待进一步提高.笔者针对国内重磁方法软件研发在数据管理、三维可视化、定量表达和软件开发技术等方面存在的问题,采用面向对象的思想设计了基于分层体系的组件+插件的系统架构,并对重磁方法软件的数据组织管理、三维可视化、定量表达、综合解释等功能的技术难点进行研究,设计系统各功能体系的实现方案,开发了重磁数据处理及反演软件.软件能够实现插件功能动态加载,并将重磁数据处理及反演结果与多学科信息结合,实现了地球物理多元数据三维集成分析及综合解释.同时,系统有多种标准化的组件接口、规范的插件模块,具备跨语言混合编程能力,兼具稳定性、灵活性、可重用性和可扩展性,在架构设计和实现方面为重磁方法软件的开发研究提供了思路及方案.     

基于数值流形法的重力坝水力劈裂研究

运用数值流形法在非连续介质领域的独特优势,并结合断裂力学的基本原理,分析了重力坝的水力劈裂破坏问题,实现了重力坝起裂、扩展和渐进破坏的全过程。充分发挥应力强度因子判别法和带抗拉强度的摩尔-库仑破坏准则各自的优势,根据不同情况选取其中某种方法确定断裂和扩展方向,且不需要预制初始裂纹。选取一个算例两种工况分析了重力坝在不考虑裂纹面内水压力和考虑裂纹面内水压力的水力劈裂破坏情况。计算结果表明,在重力坝的水力劈裂中,当不考虑裂纹面内水压力时,坝踵处裂纹向下游和深部扩展,上游折坡点处裂纹属于压剪型破坏;当考虑裂纹面内水压力时,坝踵处裂纹偏向深度方向扩展,折坡点处的裂纹逐渐由压剪破坏变成了拉剪破坏,并且考虑裂纹面内水压力后坝体破坏所需要的时步减少,故而考虑裂纹面内水后降低了重力坝的安全系数。该方法加深了对重力坝水力劈裂破坏的认识,具有较大的实际应用价值。     

Late Pleistocene crustal uplift and gravity anomaly in the eastern part of Kyushu, Japan, and its geophysical implications

The Miyazaki Plain, eastern part of Kyushu, Japan, is characterized by both significant negative gravity anomalies and aseismic crustal uplifting (1 mm/year) in the Late Pleistocene and Holocene. We examine the relationship between these two phenomena, which may provide important constraints on the interaction between the collision and/or subduction of the Kyushu-Palau Ridge and the forearc. We estimate the mass deficiency below 11-km depth by using the gravity anomalies and P-wave velocity structure of the upper crust. The onset of the load accumulation, 0.5–0.4 Ma, is inferred from the movement of the fluvial terraces considering the tephrochronology. The loading history is assumed to be a linear function of time. We evaluate the crustal rebound by assuming a viscoelastic plate deformation with an underplating load existing at 20- or 30-km depth. The predicted crustal movement for models with a lithospheric (crustal) viscosity of 10²³–10²⁴ Pa s can explain the observed altitudes of the shoreline of the marine terraces formed at the Last Interglacial of about 125 kyr BP and the middle Holocene of 5–6 kyr BP. Although we cannot restrict the origin of the buoyant body, the subduction of the Kyushu-Palau Ridge, remnant arc associated with back-arc opening of the Shikoku Basin, may be related to the buoyancy for the uplifting region examined here. On the other hand, the buoyant body off the Miyazaki Plain probably plays an important role in the interaction between the subducting oceanic slab and the overriding forearc crust. Thus, the observed lateral variation of the interplate coupling on the convergent boundary along the Nankai Trough may be attributed to the existence of the buoyant body.     

The Northern and Southern Scandes — structural differences revealed by an analysis of gravity anomalies, the geoid and regional isostasy

We investigate the Scandes mountain range by analysing the gravity field, the geoid heights and the degree of isostatic compensation of the lithosphere. Topographically, the Scandes mountain range can be divided in the Northern and Southern Scandes. Comparisons between the present topographic expression and the gravity field and the geoid show that the axis of highest elevation in the Northern Scandes is shifted eastwards compared to the minimum of the Bouguer anomaly, while the two coincide perfectly in the Southern Scandes. Geoid heights reduced by the effect of topographic masses show a large-scale minimum in the Northern Scandes, but no anomaly in the Southern Scandes.Regional, flexural isostatic calculations yield a flexural rigidity of D = 10²³ Nm for the lithosphere of the Southern Scandes and the isostatic gravity and geoid residuals point to additional isostatic support by low-density rocks below the Moho. On the other side, for the lithosphere in the Northern Scandes no significant flexural rigidity can be resolved. Here, the Bouguer anomaly is best modelled with a small flexural rigidity, indicating nearly Airy isostatic behaviour. Local subsurface loading and horizontal tectonic forces overprint the isostatic compensations and increase the tectonic complexity of the Northern Scandes. These distinctive features of the Scandes cannot be explained by currently existing models of the present and Neogene uplift and the isostatic mechanism of the Scandes.