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。     

Structural characteristics of the KPR-CBR triple-junction inferred from gravity and magnetic interpretations,Philippine Sea Plate

The intersection of the Kyushu-Palau Ridge (KPR) and the Central Basin Rift (CBR) of the West Philippine Basin (WPB) is a relic of a trench-trench-rift (TTR) type triple-junction, which preserves some pivotal information on the cessation of the seafloor spreading of the WPB, the emplacement and disintegration of the proto-Izu-Bonin-Mariana (IBM) Arc, and the transition from initial rifting to steady-state spreading of the Parece Vela Basin (PVB). However, the structural characteristics of this triple-junction have not been thoroughly understood. In this paper, using the newly acquired multi-beam bathymetric, gravity, and magnetic data obtained by the Qingdao Institute of Marine Geology, China Geological Survey, the authors depict the topographic, gravity, and magnetic characteristics of the triple-junction and adjacent region. Calculations including the upward continuations and total horizontal derivatives of gravity anomaly are also performed to highlight the major structural features and discontinuities. Based on these works, the morphological and structural features and their formation mechanisms are analyzed. The results show that the last episode amagmatic extension along the CBR led to the formation of a deep rift valley, which extends eastward and incised the KPR. The morphological and structural fabrics of the KPR near and to the south of the triple-junction are consistent with those of the western PVB, manifesting as a series of NNE-SSW- and N-S-trending ridges and troughs, which were produced by the extensional faults associated with the initial rifting of the PVB. The superposition of the above two reasons induced the prominent discontinuity of the KPR in deep and shallow crustal structures between 15°N–15°30′N and 13°30′N–14°N. Combined with previous authors’ results, we propose that the stress produced by the early spreading of the PVB transmitted westward and promoted the final stage amagmatic extension of the CBR. The eastward propagation of the CBR destroyed the KPR, of which the magmatism had decayed or ceased at that time. The destruction mechanism of the KPR associated with the rifting of the PVB varies along strike the KPR. Adjacent to the triple-junction, the KPR was destroyed mainly due to the oblique intersection of the PVB rifting center. Whereas south of the triple-junction, the KPR was destroyed by the E-W-directional extensional faulting on its whole width.©2021 China Geology Editorial Office.     

Momentum and gravity effects during the constant velocity water entry of wedge-shaped sections

Computational fluid dynamics analysis was used to investigate the added mass momentum, flow momentum and gravity effects during the constant velocity water entry of wedge-shaped sections with deadrise angles from 5° to 45°. It is shown that the added mass continues to increase for a time after chine immersion and that added mass can be estimated in terms of a constant added mass coefficient and an effective wetted width. A momentum theory is presented in which the water entry force is explained as the sum of the rate of change of added mass momentum, which becomes zero at immersion to chine depth ratios greater than about three, and the rate of change of flow momentum, which continues at deep immersions. The effect of gravity on the water entry force is given as the hydrostatic force together with the force necessary to create the potential energy in the water pile up. Hydrodynamic forces are not significantly changed by the effect of gravity on the flow fields.     

区域重力地改“测点高程平移法”精度探讨

在讨论测点高程平移法区域重力地改的精度问题基础上，提出了系统差概念，并推荐一种新的计算方法，即把测点高程平移法和节点高程插值法有机地结合起来实现地改，通过理论模型和实例计算，表明该方法计算精度优于节点高程插值法和测点高程平移法。