Modelling the geoid and sea-surface topography in coastal areas

This paper looks at the relation between the time-averaged level of the sea surface and a gravimertic geoid, as determined in coastal areas. Measurements in local regions can now be accurate enough to demonstrate that the geoid and mean sea level are not even parallel to each other, let alone identical. The accuracy and pattern structure of surface gravity data in some shelf seas is comparable with those on land, so that a marine geoid can be derived from surface data without using satellite altimetry. The geodetic objective is then to combine the two to determine sea surface topography. In principle, gravimetric studies provide the absolute datum so that local oceanographic models on the shelf can be combined with sea surface topography models related to the global ocean circulation. In contrast, sea surface topography information near deep ocean coasts must come from external sources and satellite altimetry used to give the gravity data needed to offset the less good coverage by ship-borne gravimetry.Marine Bouguer anomalies enable two specific problems of gravity anomaly patterns near the continent ocean transition to be overcome. The necessary extension of Stokes' condensation reduction is developed and illustrated along a north-south profile from the Mediterranean across the Cote d'Azur. The effect on gravity of deep ocean water introduces a geoid correction in the form of a dipolar ridge whose amplitude at the shore is about 11 cm. In addition to geostrophic currents, a semi-quantitative model for the thermohaline effects on sea surface topography is discussed in relation to sea level differences between the Atlantic and Mediterranean.In considering appropriate algorithms for local geoid computation, Kirby's Iterative Fourier Combination routine for combining altimetry and surface gravity is extended to account for global sea surface topography. The impact of very fast spherical harmonic analysis algorithms is discussed and a simple physical model is given which explains the short coherence lengths found for the global gravity field. This necessary assumption for any local geoid computation was hitherto purely empirical.Finally, the use of land data such as tide gauges, ellipsoidal heights from GPS, and orthometric heights from first order levelling are reviewed as ways of corroborating geodetic estimates of sea surface topography and its relation to levelling datums. Successful examples are given from southern England.     

A new global topographic-isostatic model

This is a preliminary report of our on-going research on a global topographic-isostatic model. The model comes from a completely new idea — the geoid undulation is the responses of an elastic earth to the topographic mass load. Assuming the topography as a condensed surface mass load, we derive expressions for calculating the vertical displacement, potential and equipotential surface changes, based on the load theory proposed in Sun and Sjöberg (1996). The modeled geoid is composed of three parts: loading potential, surface displacement and mass redistribution. The mass redistribution of the earth compensates to some extent the topography. We mainly calculate and discuss the vertical displacements and equipotential surface changes for three depths: the earth's surface, d = 36 km and the core-mantle boundary. Numerical results show that the displacements at depth 36 km and the earth's surface have the same distribution pattern and magnitude, while the vertical movement of the core-mantle boundary appears much smoother and smaller. The modeled geoid undulations vary between −352 and +555 m. The comparison between the modeled and observed geoid undulations shows that there are strong positive correlations between them, but a compensation only by elastic deformations is not sufficient to explain the observed undulations because of the big difference in magnitude between the two geoids. More geodynamic effects should be considered to better explain the long-wavelength geoid features.     

Deep Geodynamics of the Himalaya Orogeny

DEEP GEODYNAMICS OF THE HIMALAYA OROGENYRFBR( grant 990 56 56 38)     

Study of geoid–quasigeoid separation obtained from terrestrial gravity data and two geopotential models

In this article, separation between the geoid and the quasigeoid was calculated using ground gravity data and the data extracted from two Global Geopotential Models (GGMs). The calculated results were compared together. To do so, the authors used the terrestrial gravity data in a vast region of Iran, comprising 8,245 stations which are kindly put in our disposal by the National Cartographic Center of Iran, as well as two GGMs, namely EGM96 and EGM2008 for comparison. The calculation of the separation for GGMs was performed by iteration method. The results showed that the geoid–quasigeoid separations obtained from the terrestrial data versus the orthometric heights are nonlinear in mountainous areas, whereas they are almost linear in flat regions due to decreasing the values of the topographic potential of the masses between the earth surface and the geoid. On the other hand, in case of GGMs, a positive correlation was observed between the separations and the orthometric heights in both mountainous and flat areas. As the difference between the separations extracted by two methods in mountainous areas—especially in the regions with ragged topography—differs strongly, it is recommended to use the dense gravity and height networks for accurate determination of the geoid–quasigeoid separation in these regions. Finally, we can conclude that the mean values of separation by two global geopotential models (EGM96 and EGM2008) are 21.87 and 21.23 cm, respectively, values which did not differ strongly, whereas this mean value obtained from ground gravity data is 16.10 cm, which differs from the GGMs’ results with approximately 5 cm.     

Extending the margins of marketization: Frontier regions and the making of agro-export markets in northern Ghana

This paper demonstrates how the global commodity chain approach has mutated from a critical tool for studying the production of inequality in the global economy to an instrument of development policy that extends the frontiers of marketization to so-called “peripheries” in the Global South. Taking an outgrower scheme for the global production of organic mangoes in northern Ghana as point of departure, and situating this case study within the broader context of market experiments in the Ghanaian agricultural sector, it develops an account of global capitalism as a diverse, heterogeneous and messy arrangement of local borderlands. As a zone of inclusive exclusion these borderlands are brought into being by an economic discourse which separates the inside of the capitalist world from its supposed outside. The so-called integration of smallholders into global markets relies on exclusionary representations and the forging of new associations. First, economic practices in northern Ghana are portrayed by economists as defective and in doing so determine what lies outside the market. Second, within this “outside” – on which the “inside” actually depends – global capitalism mediated through the market models and rhetoric of international development organizations now literally touches the ground in specific geographical settings. Hence Frontier regions as represented by our case study bear the paradoxical character of the work of economics and are an instructive example for the performative power of economic theories. Marketization is revealed as a complex and socio-technically entangled process full of hidden prerequisites and unforeseen consequences that open up new social spaces of multiple ontological reconfigurations.     

Isostatic geoid anomalies over trenches and island arcs

Altimeter geoid profiles crossing trenches and island arcs typically exhibit a long-wavelength increase in geoidal height approaching the trench which, in many cases, reaches a maximum over the back-arc area. Bathymetry profiles across trenches show a similar regional increase in the mean depth of the ocean floor behind the trench. Filters corresponding to Airy and Pratt models of isostatic compensation were applied to bathymetry profiles crossing seven different trench systems in order to estimate how much of the observed geoid variation in these regions could be attributed to isostatically-compensated ocean-floor topography. The results indicate that short-wavelength, high-amplitude variations in the geoid, which in some cases account for over 50% of the total observed amplitude variation, can be reasonably reproduced assuming a Pratt model of isostatic compensation. An additional component of the geoid arises from the uncompensated outer rise seaward of the trench. It is therefore concluded that a large part of the geoid signal over trenches and island arcs may be related to variations in sea-floor topography. This topographic component should be removed from altimeter geoid profiles before using the data to infer details of the deeper structure of subduction zones.     

Geoid modelling based on EGM08 and recent Earth gravity models of GOCE

In this paper an estimator for geoid is presented and applied for geoid computation which considers the topographic and atmospheric effects on the geoid. The total atmospheric effect is mathematically developed in terms of spherical harmonics to degree and order 2,160 based on a recent static atmospheric density model. Also the contribution of its higher degrees is formulated. Another idea of this paper is to combine one of the recent Earth gravity models (EGMs) of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission with EGM08 and the terrestrial gravimetric data of Fennoscandia in an optimum way. To do so, the GOCE EGMs are compared with the Global Positioning System (GPS)/levelling data over the area for finding the most suited one. This comparison is done in two different ways: with and without considering the errors of the EGMs. Comparison of the computed geoids with the GPS/levelling data shows that a) considering the total atmospheric effect will improve the geoid by about 5 mm, b) GOCO03S is the most suited GOCE EGM for Fennoscandia, c) the errors of some of the GOCE EGMs are optimistic and far from reality. Combination of GOCO03S from degree 120 to 210 and EGM08 for the rest of degrees shows its good quality in these frequencies.     

青藏高原及邻区大地水准面异常场源结构

以青藏高原及邻区地形、地震层析成像、沉积层底面、Moho面及岩石层底面资料为基础 ,讨论了由地形起伏、地球内部各界面以及物质密度不均匀引起的大地水准面异常的计算方法 ,正演计算出青藏高原及邻区岩石圈内部物质不均匀产生的大地水准面异常 ,并把从全阶大地水准面异常中扣除正演模拟得到的岩石圈大地水准面异常与不同阶次波段的大地水准面进行比较 ,以寻求表示青藏高原及邻区地幔物质不均匀的大地水准面异常球谐函数的最佳阶次。结合地震层析成像资料分析结果得出 ,表示青藏高原及邻区下地幔、上地幔及岩石圈物质不均匀的大地水准面异常球谐函数的阶次范围分别为 2 6阶 ,7 60阶和 61 3 60阶。     

Using Newton's law and geophysical bounds on mass density contrast to ensure consistency between gravity and height data

In this paper we advocate the use of Newton's law of gravitational attraction to ensure perfect consistency between gravity and height data. Starting with the absolute gravity on the topography we decompose this signal into a number of quantities associated with physics of the system. To model gravitational attraction from topography we use DTM and Newton's law of gravitational attraction. A residual part of the gravity signal is interpreted as inconsistency between gravity and heights. In the paper we discuss a method by which such inconsistency (at least in principle) can be decomposed into a “gravity error” and a “terrain error”. In practice such separation is not possible because the two types of error are nearly 100% correlated. The inconsistency can be interpreted as a measure of ambiguity of the gravity-terrain models which are consistent with a set of measured/interpolated data. We discuss the influence of such ambiguity on the accuracy of the geoid for the investigated area of Jutland, Denmark.     

Spatial analysis of anthropogenic impact on karst geomorphology (Slovenia)

The objective of this contribution is analyzing, visualizing, interpreting and discussing the impacts of anthropogenic influences on karst geomorphology through various geomorphologically based environmental indicators. The primary data sources are digital terrain models (DTMs) as continuous surface data, supported by aerial photographs, satellite images, topographic maps and databases of natural and anthropogenic features. The sources are supplemented by written information about surface changes and in situ inspections. Spatial analyses as quantitative methods in combination with enhanced visualizations as qualitative methods performed in a geographical information system (GIS) on different data sets are introduced as an important methodology. This enables explaining many anthropogenic influences on the terrain surface (landform), which were not perceived before by classical surveying techniques and verifications.     

Mass anomalies and the structure of the earth

Details of the Earth's geoid and gravity fields are summarized and examined. A set of 9274 centerpoints of 5 ° cubes (referred to as bloblets) represents subducted slab locations. This set, developed from reconstructed plate history, was provided by the first author of Lithgow-Berttelloni et. al. [1998] and is the best available estimate of locations of subduction material in the Earth's mantle. Two global mass solutions offered here utilize 1) only those bloblets in the outer 800 km, and 2) only those bloblets in the outer 1400 km. Since each bloblet location represents the center of a 5-degree cube [a larger volume than appropriate for a fragment of subducted lithosphere] it was necessary in the 800 km depth limit model to reduce their density to 0.004 grams/cc, and by increasing bloblet density six times at 797.5 km depth to simulate the piling up of slab material beneath the 670 km boundary. The 1400 km depth limit model [commensurate with evidence of slab penetration into the lower mantle from seismic tomography] required estimating densities for the bloblets at nine different mantle depths. An additional four point-masses at 3000 km depth (to simulate CMB topography, unrelated to dynamic topography) completes the mass models. Both these models show reasonable agreement to patterns and magnitudes for degrees 2–10, 3–10, 4–10, 2–3, 3, and 2 geoid fields with both geometric and hydrostatic flattening. These models support an assessment that topography at the core mantle boundary (CMB) may be produced by processes within the core rather than from within the mantle. Possible causes for the CMB topography are discussed.     

Interpolation for geochemical surface reconstruction incorporating topographic catchment definitions

Geochemical surfaces are reconstructed by interpolating geochemical measurements obtained from stream-water and stream-sediment samples. The geographical region that influences (and therefore is represented by) the value of a geochemial sample is its topographic catchment area. However, standard convention is to treat and to record the stream sample in the database as a point location, and to reconstruct geochemical surfaces utilizing conventional point interpolation procedures. These interpolation procedures assume, generally, that a data point exerts geographical influence away from itself in all directions, and that influence declines with distance away from that data point. Conventional interpolation procedures are poorly suited for reconstructing geochemical surfaces from stream samples; they do not take into account the true geographic area that geochemical sample points represent (topographic catchments). In this paper we propose a method of interpolation which assumes that data points are representative of their topographic catchment areas. Experimental data indicates that a surface reconstruction procedure which preserves the areal character of geochemical samples provides results more meaningful than surfaces reconstructed using more conventional interpolation techniques.     

地球体地势起伏的大地构造学(英文)

地球体的一般几何形态及其表面的地势起伏,都与地球地形的全球对称以及与由全球地震层析X射线摄影法推导出的深部构造相关联。在西太平洋中,星球地势起伏的对称受到破坏,那里的地球体表面受到抬升。这一区域表现有特殊的岩石圈构造,而且显而易见地是,在后冈瓦纳地球各向异性膨胀一收缩的背景下,自晚中生代以来,这里的构造圈已发生了一些最为重要的变化。     

Eastern Mediterranean gravity potential and the Hellenic subduction process

Tornographic images of the Mediterranean upper mantle P-wave velocity structure have been used to analyse the gravity potential in the vicinity of the Hellenic subduction zone. The velocity anomalies are assumed to be proportional to density variations according to Birch's law. The effect of the topography on the geoid in the region is also calculated. The results indicate that the upper mantle geoid signal probably has significant amplitudes of several metres, but it correlates poorly with the observed geoid. The geoid calculated from topography correlates well, but has an amplitude that is too large in comparison with the observed geoid. The results show that an improved understanding of the Hellenic subduction zone geoid requires refinement of the Moho topography, so that the effect of this topography can be separated from the upper mantle signature.     

Toward a 10' resolution geoid for South America: a comparison study

Since the creation of the Sub-Commission for the Geoid in South America (SCGSA) in 1993, many efforts have been carried out in the different countries in order to improve the geoid computations. The validation of the gravity data in Brazil, Uruguay, Argentina and Chile has improved many of the gravity surveys in those countries. GPS observations carried out on benchmarks of the geometric levelling have been facilitated by the SIRGAS (Geocentric Reference System for South America) project and can contribute for testing the gravimetric determination of the geoid. Several countries made available GPS data for SCGSA like Brazil, Argentina, Venezuela and Chile. The Digital Terrain Model (DTM) has been improved considerably in Brazil and Argentina. A great number of topographic maps has been digitized to generate a DTM grid of 3′ resolution (DTM3). New gravity surveys in the Amazonas region have been in progress along Rio Negro and its tributaries. Many different organizations in most of the countries in South America have been involved with local or national geoid computations. This fact has brought attention to the data in several countries facilitating the efforts for a continental geoid. All these activities are strongly supported by Geophysical Exploration Technology (GETECH) — University of Leeds. The objective envisaged at the moment is to produce a 10′ resolution geoid for South America using FFT and to compare the result with that of the numerical integration of the modified Stokes integral.     

Analogue modelling of relief dynamics

Natural landscape analysis and numerical modelling point to a lack of physical data on relief dynamics. Experimental modelling is therefore an interesting approach for obtaining physical information on eroded systems with runoff transportation and topographic incision. The main technical challenge, in reproducing regional topography at the laboratory scale, is to obtain mm-scale incisions and a limitation of the smoothing action of diffusive transport processes. An experimental design using newly developed rain making apparatus and silica as a model material, satisfies the required conditions, and allows simulation of geomorphic instabilities. An example of “plateau instability” modelling is presented to illustrate the suitability of this experimental procedure.     

TOPO-OZ: Insights into the various modes of intraplate deformation in the Australian continent

As the fastest, lowest, flattest and amongst the most arid of continents, Australia preserves a unique geomorphic record of intraplate tectonic activity, evidencing at least three distinct modes of surface deformation since its rapid northward drift commenced around 43 million years ago. At long wavelengths (several 1000s km) systematic variations in the extent of Neogene marine inundation imply the continent has tilted north–down, southwest–up. At intermediate-wavelengths (several 100s km) several undulations of ~ 100–200 m amplitude have developed on the 1–10 myr timescale. At still shorter wavelengths (several 10s km), fault related motion has produced local relief at rates of up to ~ 100 m/myr over several million years. The long-wavelength, north–down tilting can be related to a dynamic topographic effect associated with Australia's northward drift from the geoid low, dynamic topography low now south of the continent to the geoid high, dynamic topography low centred above the south-east Asian and Melanesian subduction zones. The short wavelength, fault-related deformation is attributed in time to plate-wide increases in compressional stress levels as the result of distant plate boundary interactions and, in space, in part to variations in the thermal structure of the Australian lithosphere. At the intermediate wavelengths, transient, low amplitude undulations can be ascribed to either lithospheric buckling or the development of instabilities in the thermal boundary layer beneath the lithosphere. In the latter case, topographic asymmetries suggest the Australian lithosphere is moving north with respect to the mantle beneath, providing a unique attribution to the progressive alignment of seismic anisotropy and absolute plate motion observed near the base of the Australian lithosphere.     

On the role of heat flow, lithosphere thickness and lithosphere density on gravitational potential stresses

Gravitational potential stresses (GPSt) are known to play a first-order role in the state of stress of the Earth's lithosphere. Previous studies focussed mainly on crust elevation and structure and little attention has been paid to modelling GPSt using realistic lithospheric structures. The aim of the present contribution is to quantify gravitational potential energies and stresses associated with stable lithospheric domains. In order to model realistic lithosphere structures, a wide variety of data are considered: surface heat flow, chemical depletion of mantle lithosphere, crustal thickness and elevation. A numerical method is presented which involves classical steady-state heat equations to derive lithosphere thickness, geotherm and density distribution, but additionally requires the studied lithosphere to be isostatically compensated at its base. The impact of varying surface and crustal heat flow, topography, Moho depth and crust density on the signs and magnitudes of predicted GPSt is systematically explored. In clear contrast with what is assumed in most previous studies, modelling results show that the density structure of the mantle lithosphere has a significant impact on the value of the predicted GPSt, in particular in the case of thick lithospheres. Using independent information from the literature, the method was applied to get insights in the state of stress of continental domains with contrasting tectono-thermal ages. The modelling results suggest that in the absence of tectonic stresses Phanerozoic and Proterozoic lithospheres are spontaneously submitted to compression whereas Archean lithospheres are in a neutral to slightly tensile stress state. These findings are in general in good agreement with global stress measurements and observed geoid undulations.     

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.     

地面重力数据结合GPS/水准数据精化兴城物探实验区大地水准面

区域大地水准面的确定是GPS测量常需解决的问题。目前确定大地水准面的方法主要包括重力法、GPS水准几何法及组合法,其中组合法因其精度和可靠性都较高,常用于计算高精度区域大地水准面。高精度的大地水准面模型是组合法确定区域大地水准面的关键。在我国,EGM2008全球重力场模型精度和分辨率均高于此前的所有模型,研究基于该模型的组合法大地水准面精化具有重要的实践意义。笔者以吉林大学兴城教学实习基地物探实验区为例,基于实测重力数据、EGM2008重力场模型和GPS水准数据,采用组合法精化了区域大地水准面,比较了组合法大地水准面模型和无重力实测数据的几何法大地水准面模型的精度差异,分析了该方法在物探测量中的适用性。结果表明,实验区组合法大地水准面模型精度最高达到1.2 cm,并且误差分布区间较小,总体上精度和可靠性高于对比的几何方法,并且组合法和几何法获取的两种大地水准面模型均能满足大比例尺物探测量要求。EGM2008模型精度较高,故平坦地区使用组合法时,高密度的实测重力数据可能带来高频扰动,有可能降低EGM2008重力场模型本身的精度,所以重力数据采集过程中要顾及重力点的密度和空间分布。本文方法更适用于地形复杂的地区。