Outlier detection algorithms and their performance in GOCE gravity field processing

The satellite missions CHAMP, GRACE, and GOCE mark the beginning of a new era in gravity field determination and modeling. They provide unique models of the global stationary gravity field and its variation in time. Due to inevitable measurement errors, sophisticated pre-processing steps have to be applied before further use of the satellite measurements. In the framework of the GOCE mission, this includes outlier detection, absolute calibration and validation of the SGG (satellite gravity gradiometry) measurements, and removal of temporal effects. In general, outliers are defined as observations that appear to be inconsistent with the remainder of the data set. One goal is to evaluate the effect of additive, innovative and bulk outliers on the estimates of the spherical harmonic coefficients. It can be shown that even a small number of undetected outliers (<0.2 of all data points) can have an adverse effect on the coefficient estimates. Consequently, concepts for the identification and removal of outliers have to be developed. Novel outlier detection algorithms are derived and statistical methods are presented that may be used for this purpose. The methods aim at high outlier identification rates as well as small failure rates. A combined algorithm, based on wavelets and a statistical method, shows best performance with an identification rate of about 99%. To further reduce the influence of undetected outliers, an outlier detection algorithm is implemented inside the gravity field solver (the Quick-Look Gravity Field Analysis tool was used). This results in spherical harmonic coefficient estimates that are of similar quality to those obtained without outliers in the input data.     

Old inherited origin for the present near-bimodal topography of Africa

Africa’s landscape is dominated by a manifold of second-order epeirogenic structures superimposed on a first-order bimodal topography. Bivariate regression analysis of Africa’s surface topography shows that this is a complexly folded surface with regionally elevated areas in southern and eastern Africa, and a topographically low northern and western Africa. The apparent spatial relationships between these features are analysed using anomaly correlation between surface topography and free-air gravity anomalies. Occurrences of positively correlated features between gravity and topography in Africa are found to be limited to second-order epeirogenic features. Geophysical modelling and geologic evidence indicate that Africa’s bimodal topography is genetically distinct from these second-order features, and linked to sources as deep as the sublithospheric mantle. The age, measured and modelled elevation of the bimodal topography require that topographic uplift of south-central Africa be episodic. We infer from our findings together with relative sea-level changes, that the near-bimodality of Africa’s topography is an ancient feature inherited at least from upper Paleozoic times. Our reconstructed paleotopography suggests that Africa was largely a low-lying continent dominated by its cratons, and that basement distribution disregards the present-day uplift patterns of Africa.     

The 1.80–1.74-Ga gabbro–anorthosite–rapakivi Korosten Pluton in the Ukrainian Shield: a 3-D geophysical reconstruction of deep structure

The deep structure of the gabbro–anorthosite–rapakivi granite (“AMCG-type”) Korosten Pluton (KP) in the northwestern Ukrainian Shield was studied by 3-D modelling of the gravity and magnetic fields together with previous seismic data. The KP occupies an area of ca. 12,500 km² and comprises several layered gabbro-anorthositic intrusions enveloped by large volumes of rapakivi-type granitoids. Between 1.80 and 1.74 Ga, the emplacement of mafic and associated granitoid melts took place in several pulses. The 3-D geophysical reconstruction included: (a) modelling of the density distribution in the crust using the observed Bouguer anomaly field constrained by seismic data on Moho depth, and (b) modelling of the magnetic anomaly field in order to outline rock domains of various magnetisation, size and shape in the upper and lower crust. The density modelling was referred to three depth levels of 0 to 5, 5 to 18, and 18 km to Moho, respectively. The 3-D reconstruction demonstrates close links between the subsurface geology of the KP and the structure of the lower crust. The existence of a non-magnetic body with anomalously high seismic velocity and density is documented. Most plausibly, it represents a gabbroic stock (a parent magma chamber) with a vertical extent of ca. 20 km, penetrating the entire lower crust. This stock has a half-cylindrical shape and a diameter of ca. 90 km. It appears to be connected with a crust–mantle transitional lens previously discovered by EUROBRIDGE seismic profiling. The position of the stock relative to the subsurface outlines of the KP is somewhat asymmetric. This may be due to a connection between the magmatism and sets of opposite-dipping faults initially developed during late Palaeoproterozoic collisional deformation in the Sarmatian crustal segment. Continuing movements and disturbances of the upper mantle and the lower crust during post-collisional tectonic events between 1.80 and 1.74 Ga may account for the long-lived, recurrent AMCG magmatism.     

Slab behaviour and its surface expression: new insights from gravity modelling in the SE-Carpathians

We use lithosphere-scale gravity models to calculate gravity anomalies resulting from oceanic subduction, continental collision, slab steepening, delamination, and break-off. Local isostasy was assumed for determining vertical movements caused by mass changes related to these tectonic processes. Our results show that subduction is accompanied by basin subsidence on the upper plate caused by the heavy lithospheric root of the subducting slab. The basin evolution goes parallel with the slab evolution and shows considerable modifications when the processes at depth change (slab steepening, delamination, break-off). Characteristic gravity anomaly curves were acquired for the different tectonic scenarios. These curves together with other data (e.g. basin evolution on the upper and the lower plate) were used for the reconstruction of the tectonic evolution of the SE-Carpathians which includes Tertiary subduction and collision followed by slab steepening and delamination.     

The gravity field and GGOS

The gravity field of the earth is a natural element of the Global Geodetic Observing System (GGOS). Gravity field quantities are like spatial geodetic observations of potential very high accuracy, with measurements, currently at part-per-billion (ppb) accuracy, but gravity field quantities are also unique as they can be globally represented by harmonic functions (long-wavelength geopotential model primarily from satellite gravity field missions), or based on point sampling (airborne and in situ absolute and superconducting gravimetry). From a GGOS global perspective, one of the main challenges is to ensure the consistency of the global and regional geopotential and geoid models, and the temporal changes of the gravity field at large spatial scales. The International Gravity Field Service, an umbrella “level-2” IAG service (incorporating the International Gravity Bureau, International Geoid Service, International Center for Earth Tides, International Center for Global Earth models, and other future new services for, e.g., digital terrain models), would be a natural key element contributing to GGOS. Major parts of the work of the services would, however, remain complementary to the GGOS contributions, which focus on the long-wavelength components of the geopotential and its temporal variations, the consistent procedures for regional data processing in a unified vertical datum and Terrestrial Reference Frame, and the ensuring validations of long-wavelength gravity field data products.     

Crustal structure of the Lofoten–Vesterålen continental margin, off Norway

By compiling wide-angle seismic velocity profiles along the 400-km-long Lofoten–Vesterålen continental margin off Norway, and integrating them with an extensive seismic reflection data set and crustal-scale two-dimensional gravity modelling, we outline the crustal margin structure. The structure is illustrated by across-margin regional transects and by contour maps of depth to Moho, thickness of the crystalline crust, and thickness of the 7+ km/s lower crustal body. The data reveal a normal thickness oceanic crust seaward of anomaly 23 and an increase in thickness towards the continent–ocean boundary associated with breakup magmatism. The southern boundary of the Lofoten–Vesterålen margin, the Bivrost Fracture Zone and its landward prolongation, appears as a major across-margin magmatic and structural crustal feature that governed the evolution of the margin. In particular, a steeply dipping and relatively narrow, 10–40-km-wide, Moho-gradient zone exists within a continent–ocean transition, which decreases in width northward along the Lofoten–Vesterålen margin. To the south, the zone continues along the Vøring margin, however it is offset 70–80 km to the northwest along the Bivrost Fracture Zone/Lineament. Here, the Moho-gradient zone corresponds to a distinct, 25-km-wide, zone of rapid landward increase in crustal thickness that defines the transition between the Lofoten platform and the Vøring Basin. The continental crust on the Lofoten–Vesterålen margin reaches a thickness of 26 km and appears to have experienced only moderate extension, contrasting with the greatly extended crust in the Vøring Basin farther south. There are also distinct differences between the Lofoten and Vesterålen margin segments as revealed by changes in structural style and crustal thickness as well as in the extent of elongate potential-field anomalies. These changes may be related to transfer zones. Gravity modelling shows that the prominent belt of shelf-edge gravity anomalies results from a shallow basement structural relief, while the elongate Lofoten Islands belt requires increased lower crustal densities along the entire area of crustal thinning beneath the islands. Furthermore, gravity modelling offers a robust diagnostic tool for the existence of the lower crustal body. From modelling results and previous studies on- and off-shore mid-Norway, we postulate that the development of a core complex in the middle to lower crust in the Lofoten Islands region, which has been exhumed along detachments during large-scale extension, brought high-grade, lower crustal rocks, possibly including accreted decompressional melts, to shallower levels.     

基于重力模型的中国城市体系空间联系与层域划分

新中国成立以来,中国大陆城市体系空间格局发生了深刻的变化。传统的城市体系空间联系主要从人流、物流、技术流、信息流、金融流进行数据的收集和分析,也有运用图论原理进行Rd链分析。近来,随着社会主义市场经济的迅速发展,城市之间的联系变得异常复杂、数据不易得到。本文试图运用重力模型方法对中国城市间的空间联系强度进行定量计算,据此刻画中国城市体系的空间联系状态和结节区结构。从研究结果看,所得结论与实际情况基本吻合。     

基于球面重力反演苏拉威西地区莫霍面结构

基于球坐标系的地球物理反演能有效避免地球曲率的影响, 适用于大尺度构造研究.本文基于重力异常数据在球坐标系下反演莫霍面深度, 结合数据误差及光滑正则化项建立反演目标函数并求解, 同时将该方法应用于苏拉威西地区.苏拉威西地区具有复杂的断裂系统、年轻的俯冲带, 是研究俯冲起始机制等前沿科学问题的理想场所.目前研究区的地球物理观测尚不充分, 缺乏对莫霍面形成有效约束的地震数据, 对研究区莫霍面的整体认识较少.本文基于卫星重力观测数据, 通过匹配滤波方法提取与研究区莫霍面结构相关的重力异常, 并结合频谱分析确定该地区的莫霍面深度参考值.在反演中, 通过两次随机子抽样交叉验证选择最优的超参数, 包括正则化因子、莫霍面密度差以及参考莫霍面深度, 迭代反演获得莫霍面深度.反演结果表明: 研究区莫霍面平均深度为20.0 km, 深度变化范围为9.2~33.3 km.总体上, 海区莫霍面浅, 约10.0~20.0 km, 陆区莫霍面深, 约25.0~33.0 km, 该结果与Crust1.0全球模型、前人重力反演结果以及地震数据基本相符, 总体上反映了苏拉威西地区的莫霍面变化特征.

     

基于重力地质法的南中国海海底地形反演

根据重力地质法（GGM）,利用南中国海海域内63179个船测控制点水深将测高自由空间重力异常划分为长波参考场和短波残差场,并反演出了该海域112°E—119°E,12°N—20°N范围的1’×1’海底地形模型,该过程中使用的海水和海底洋壳密度差异常数1.32 g·cm-3通过实测水深估计得到.利用反演得到的GGM模型对剩余的10529个检核点船测水深插值计算后与实测水深进行比较,其较差结果的均值为-1.64 m,标准差为76.95 m,相对精度为4.06%.此外,根据船测点数量、分布和海底地形的不同,选择了三个海域进行统计,结果表明：在船测控制点分布均匀的海域,GGM模型精度优于ETOPO1模型,在控制点过于分散的海域其精度会有所下降,但好于船测水深的直接格网化结果.为进一步探究检核点的较差结果中出现较大数值的成因,本文对精度较差的点位进行了单独分析,选择了两条船测航迹剖面进行了研究,并分析了检核点的水深较差、相对精度与水深和重力异常的关系,结果表明：GGM模型精度受水深和重力异常的相关性影响较小,受海底地形复杂程度影响较大,地形坡度变化平缓海域的预测精度明显高于海山地区.最后,综合GGM模型和ETOPO1模型优势,利用所有船测水深作为控制,生成了综合的海底地形模型.     

一种改进的重力梯度全张量数据的边界识别方法

边界识别是重力资料解释中的一项重要任务.随着重力梯度测量技术的迅速发展,重力梯度张量数据在边界识别中的应用越来越广泛.本文重点研究了随着深度的增加,边界识别能力下降,正负异常中出现假边缘的问题.另外,有些边缘检测方法对走向不同的地质体识别能力有所差异.本文对基于重力梯度张量的水平方向Theta法进行改进,通过选择合适的...