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Evolution of stress fields during the supercontinent cycle

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Geodesy and Geodynamics 2022年第4期13卷 363-375页

作者： Alexander Bobrov Alexey Baranov robert tenzer Schmidt Institute of Physics of the Earth Russian Academy of SciencesMoscowRussia Institute of Earthquake Prediction Theory and Mathematical Geophysics Russian Academy of SciencesMoscowRussia Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic UniversityHong KongChina

We investigate the evolution of stress fields during the supercontinent cycle using the 2D Cartesian geometry model of thermochemical convection with the non-Newtonian rheology in the presence of floating deformable continents.In the course of the simulation,the supercontinent cycle is implemented several times.The number of continents considered in our model as a function of time oscillates around 3.The lifetime of a supercontinent depends on its dimension.Our results suggest that immediately before a supercontinent breakup,the over-lithostatic horizontal stresses in it(referring to the mean value by the computational area)are tensile and can reach-250 MPa.At the same time,a vast area beneath a supercontinent with an upward flow exhibits clearly the over-lithostatic compressive horizontal stresses of 50-100 МРа.The reason for the difference in stresses in the supercontinent and the underlying mantle is a sharp difference in their viscosity.In large parts of the mantle,the over-lithostatic horizontal stresses are in the range of±25 MPa,while the horizontal stresses along subduction zones and continental margins are significantly larger.During the process of continent-to-continent collisions,the compressive stresses can approximately reach 130 MPa,while within the subcontinental mantle,the tensile over-lithostatic stresses are about-50 MPa.The dynamic topography reflects the main features of the su-percontinent cycle and correlates with real ones.Before the breakup and immediately after the disin-tegration of the supercontinent,continents experience maximum uplift.During the supercontinent cycle,topographic heights of continents typically vary within the interval of about±1.5 km,relatively to a mean value.Topographic maxima of orogenic formations to about 2-4 km are detected along continent-to-continent collisions as well as when adjacent subduction zones interact with continental margins.

关键词： Supercontinent cycle Floating deformable continents Thermochemical convection Horizontal stresses Dynamic topography

ETH-GQS: An estimation of geoid-to-quasigeoid separation over Ethiopia

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Geodesy and Geodynamics 2022年第1期13卷 31-37页

作者： Ephrem Y.Belay Walyeldeen Godah Malgorzata Szelachowska robert tenzer Ethiopian Space Science and Technology Institute Addis Ababa Ethiopia Centre of Geodesy and Geodynamics Institute of Geodesy and Cartography(IGiK)WarsawPoland Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic UniversityHong KongChina

The determination of accurate orthometric or normal heights remains one of the main challenges for the geodetic community in Ethiopia.These heights are required for geodetic and geodynamic scientific research as well as for extensive engineering applications.The main objective of this study is to estimate the geoid-to-quasi geoid separation(GQS)in Ethiopia(ETH-GQS).Such separation would be required for the conversion between geoid and quasigeoid models,which is mandatory for the determination of accurate geodetic heights in mountain regions.The airborne free-air gravity anomalies and the topo-graphic information retrieved from the SRTM3(Shuttle Radar Topography Mission of a spatial resolution 3 arc-second)digital elevation model were used to compute the ETH-GQS model according to the Sjoberg's strict formula for the geoid-to-quasigeoid separation.The ETH-GQS was then validated using GNSS-levelling data as well as geoid heights determined from different Global Geopotential Models(GGMs),namely the EGM2008,EIGEN-6C4 and GECO.The results reveal that the standard deviation of differences between the geoid heights obtained from the EIGEN-6C4 model and the geometric geoid heights obtained from GNSS-levelling data were improved by~75%(i.***.from~24 to~6 cm)when considering GQS values obtained from the ETH-GQS.

关键词： Geoid-to-quasigeoid separation GNSS-Levelling Ethiopian vertical control network Orthometric and normal heights Airborne gravity data

A numerical model for the gravimetric recovery of sub-lithospheric mantle structures

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Geodesy and Geodynamics 2020年第2期11卷 85-96页

作者： robert tenzer The Department of Land Surveying and Geo-Informatics The Hong Kong Polytechnic University181 Chatham Road SouthHong KongChina

It is a well-known fact that the long-wavelength terrestrial geoid undulations are mainly attributed to deep mantle density heterogeneities,while more detailed features in the geoid geometry are associated with the topography and the lithospheric density structure.To enhance a gravitational signature of mantle density heterogeneities below the lithosphere,the gravitational contributions of topography and lithospheric density heterogeneities should be modelled and subsequently removed from Earth’s gravity field.The refined gravity field obtained after this numerical procedure is more suitable for a recovery of a mantle density structure(below the lithosphere).Following this idea,methods for a spherical harmonic analysis and synthesis of gravity field and lithospheric density structures are presented,and a theoretical relation between gravity field and mass density structure is formulated.Since a gravimetric recovery of inner density structure has a non-unique solution,we propose an alternative method based on a conversion of seismic velocities to mass densities.A forward modelling approach is then employed to find the mantle density configuration that generates the gravitational field that best approximates the corresponding refined gravitational field obtained from observed gravity field after subtracting the gravitational signal of the lithosphere.

关键词： Asthenosphere Crust Gravity field Lithosphere Mantle

Theoretical Deficiencies of Isostatic Schemes in Modeling the Crustal Thickness along the Convergent Continental Tectonic Plate Boundaries

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Journal of Earth Science 2016年第6期27卷 1045-1053页

作者： robert tenzer Mohammad Bagherbandi School of Geodesy and Geomatics Wuhan University Division of Geodesy and Geoinformatics Royal Institute of Technology (KTH) Department of Industrial Development IT and Land ManagementUniversity of G?vle

The results of global and regional studies often show significant disagreement between the Moho depths determined using seismic and isostatic models. In this study, we estimate the differences between these two models in central Eurasia. The Vening Meinesz-Moritz （VMM） inverse problem of isostasy is utilized to determine the isostatic Moho depths. The estimated VMM Moho depths are then corrected for the sediment density contrast. The application of this correction improves the agreement between the isostatic and seismic Moho models. The existing discrepancies between the isostatic and seismic models are finally modeled by applying the non-isostatic correction, which accounts for the unmodelled mantle density heterogeneities and other geodynamic processes, which are not taken into account in classical isostatic models. Our results reveal that the non-isostatic correction still cannot fully describe mechanisms affecting the Moho geometry along the convergent continent-tocontinent tectonic plate boundaries occurring beneath Himalayas despite an overall good performance of the applied method.

关键词： crust gravity Himalaya isostasy Moho interface Tibetan Plateau.

Global spectral model of the geoid

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Geodesy and Geodynamics 2017年第1期8卷 24-33页

作者： robert tenzer The Key Laboratory of Geospace Environment and Geodesy School of Geodesy and GeomaticsWuhan University

The coefficients of the Global Gravitational Models （GGMs） define the external gravitational field of the Earth. In many geoscience applications and gravity interpretations these coefficients are routinely used to represent the geoid surface and related gravitational field quantities without taking into consideration the internal convergence domain for computing the gravitational field inside the Earth＇s masses. In this study we discuss this issue and present the numerical approach for computing the gravitational field quantities on the geoid. The proposed numerical approach utilizes spectral expressions for the gravi- metric forward modelling of topographic mass density distribution and the indirect gravimetric modelling of mass density heterogeneities inside the geoid. In the numerical realization we demonstrate that for precise applications the differences between the potential values computed at the topographic surface and on the geoid should be taken into consideration especially in mountainous regions with complex geology as well as in polar regions, where these differences in absolute values reach 40 m2 s-2 （or more）, which translates into vertical displacements between the geoid and the quasigeoid of about 4m,

关键词： Density Eart hGravity Topography

Optimum choice of parameters and numerical schemes for a regional gravimetric Moho recovery

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Geodesy and Geodynamics 2019年第6期10卷 417-429页

作者： Samurdhika Rathnayake robert tenzer Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic University

Despite practical limitations of isostatic theories to model the Moho geometry are well-known,gravimetric methods are often used in terrestrial studies of crustal structure in regions with a low seismic data coverage.Moreover,these methods are indispensable in planetary studies.Various gravimetric methods have been proposed.The Airy and Pratt theories are defined based on adopting a local compensation mechanism.The Vening Meinesz theory assumes a regional isostatic flexural model.The Vening Meinesz regional isostatic model generally describes a respond of the lithosphere to a load more realistically than the Airy model over continents.The Pratt method,on the other hand,better describes a compensation mechanism of the oceanic lithosphere.The application of a particular isostatic model also depends on applied numerical procedures,parameters for inversion,input data specifications,and many other aspects.In this study,we address some basic aspects by applying local and regional isostatic models for a Moho recovery.We also conduct a spectral analysis to assess a spectral resolution of gravity data that is optimal for a Moho recovery.Furthermore,we inspect the influence of low-degree spherical harmonics of gravity field on a Moho geometry.Gravimetric results are validated using seismic data at the European plate.Our results confirm a better performance of a regional compensation principle.We also demonstrate that a different thickness of the oceanic and continental crustal thickness should be taken into account as a priori information.Spectral analysis indicates that gravity data used for a Moho inversion should optimally have a spatial resolution between degrees 60 to 180.Results also show that low-degree spherical harmonics do not modify significantly the Moho geometry,particularly over regions with a relatively homogenous structure of deep mantle.

关键词： Crust Gravity Moho inversion Isostasy

The application of a gravimetric forward modelling of the lithospheric structure for an estimate of the average density of the upper asthenosphere

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Geodesy and Geodynamics 2019年第4期10卷 265-275页

作者： Wenjin Chen robert tenzer School of Geomatics Science and Technology Nanjing Tech UniversityNanjingChina Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic UniversityHong KongChina

The average density of 3300 kg m-3 is often attributed for the asthenosphere. In this study, we inspect this value by estimating the average value of the(upper) asthenosphere based on applying the gravimetric forward modelling of major known lithospheric density structures. The LITHO1.0 global seismic model of the lithospheric density structure is used for this purpose, while considering that the lithosphere-asthenosphere boundary(LAB) is rheological, conventionally taken at the 1300C isotherm,above which the mantle behaves in a rigid fashion and below which it behaves in a ductile fashion.According to our result, the average density of the upper asthenosphere is roughly 3400 kg m-3. This density value closely agrees with the corresponding average value 3371 kg m-3 computed based on an empirical density model provided in the Preliminary Reference Earth Model(PREM), while using the LITHO1.0 LAB depth data. We also demonstrate that the sub-lithospheric mantle gravity map exhibits mainly a thermal signature. The most prominent features in this gravity map are mid-oceanic spearing ridges marked by gravity lows, while oceanic subductions in the West Pacific are characterized by the most pronounced gravity highs.

关键词： Asthenosphere Density Forward modelling Gravity Lithosphere

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

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Geodesy and Geodynamics 2017年第4期8卷 260-272页

作者： Xinyu Xu Yongqi Zhao Tilo Reubelt robert tenzer School of Geodesy and Geomatics Wuhan University 129 Luoyu Road Wuhan 430079 China Key Laboratory of Geospace Environment and Geodesy Ministry of Education 129 Luoyu Road Wuhan 430079 China Institute of Geodesy University of Stuttgart Geschwister-Scholl-Str. 24D 70174 Stuttgart Germany

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

关键词： Earth＇s gravity field Geopotential model Gravity gradient Validation SateLlite-to-satellite tracking

Water storage variations in the Poyang Lake Basin estimated from GRACE and satellite altimetry

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Geodesy and Geodynamics 2016年第2期7卷 108-116页

作者： Yang Zhou Shuanggen Jin robert tenzer Jialiang Feng School of Environment and Chemical Engineering Shanghai UniuersityShanghai 200444China Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China School of Geodesy and Geomatics Wuhan UniuersityWuhan 430079China

The Gravity Recovery and Climate Experiment（GRACE） satellite mission provides a unique opportunity to quantitatively study terrestrial water storage（TWS） variations. In this paper,the terrestrial water storage variations in the Poyang Lake Basin are recovered from the GRACE gravity data from January 2003 to March 2014 and compared with the Global Land Data Assimilation System（GLDAS） hydrological models and satellite altimetry. Furthermore, the impact of soil moisture content from GLDAS and rainfall from the Tropical Rainfall Measuring Mission（TRMM） on TWS variations are investigated. Our results indicate that the TWS variations from GRACE, GLDAS and satellite altimetry have a general consistency. The TWS trends in the Poyang Lake Basin determined from GRACE, GLDAS and satellite altimetry are increasing at 0.0141 km^3/a, 0.0328 km^3/a and 0.0238 km^3/a,respectively during the investigated time period. The TWS is governed mainly by the soil moisture content and dominated primarily by the precipitation but also modulated by the flood season of the Yangtze River as well as the lake and river exchange water.

关键词： Gravity Recovery and Climate Experiment（GRACE） Satellite altimetry Terrestrial water storage variations Poyang Lake Basin