scholarly journals Lithospheric stress, strain and displacement changes from GRACE-FO time-variable gravity: case study for Sar-e-Pol Zahab Earthquake 2018

2020 ◽  
Vol 223 (1) ◽  
pp. 379-397
Author(s):  
Mehdi Eshagh ◽  
Farzam Fatolazadeh ◽  
Robert Tenzer
Keyword(s):  
Gravity Field ◽  
Elastic Shell ◽  
Lower Boundary ◽  
Stable Solution ◽  
Temporal Variations ◽  
Stress Strain ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Long Wavelength ◽  
Ill Posed

SUMMARY Temporal variations in the Earth's gravity field can be used for monitoring of lithospheric deformations. The network of continuously operating gravity stations is required for this purpose but a global coverage by such network is currently extremely sparse. Temporal variations in long-wavelength part of the Earth's gravity field have been, however, observed by two satellite missions, namely the Gravity Recovery And Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO). These satellite gravity observations can be used to study long-wavelength deformations of the lithosphere. Consequently, considering the lithosphere as a spherical elastic shell and solving the partial differential equation of elasticity for it, the stress, strain and displacement inside the lithosphere can be estimated. The lower boundary of this shell is assumed to be stressed by mantle convection, which has a direct relation to the Earth's gravity field according to Runcorn's theory. Changes in gravity field lead to changes in the sublithospheric stress and the stress propagated throughout the lithosphere. In this study, we develop mathematical models in spherical coordinates for describing the stress propagation from the sublithosphere through the lithosphere. We then organize a system of observation equations for finding a special solution to the boundary-value problem of elasticity in the way that provides a stable solution. In contrast, models presented in previously published studies are ill-posed. Furthermore, we use constants of the solution determined from the boundary stresses to determine the strain and displacements leading to these stresses, while in previous studies only the stress has been considered according to rheological properties of the lithosphere. We demonstrate a practical applicability of this theoretical model to estimate the stress–strain redistribution caused by the Sar-e-Pol Zahab 2018 earthquake in Iran by using the GRACE-FO monthly solutions.

scholarly journals Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)

2020 ◽  
Vol 12 (12) ◽  
pp. 2066
Author(s):  
Alessandra Borghi ◽  
Riccardo Barzaghi ◽  
Omar Al-Bayari ◽  
Suhail Al Madani
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Data ◽  
Independent Set ◽  
Geoid Undulation ◽  
Height Anomaly ◽  
Geoid Model ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Long Wavelength

In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)).

scholarly journals An improved test of the general relativistic effect of frame-dragging using the LARES and LAGEOS satellites

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Ignazio Ciufolini ◽  
Antonio Paolozzi ◽  
Erricos C. Pavlis ◽  
Giampiero Sindoni ◽  
John Ries ◽  
...  
Keyword(s):  
General Relativity ◽  
Gravity Field ◽  
Temporal Variations ◽  
Gravity Field Model ◽  
Earth’S Gravity Field ◽  
Frame Dragging ◽  
Earth Gravity ◽  
Gravity Field Determination ◽  
General Relativistic ◽  
Static Part

Abstract We report the improved test of frame-dragging, an intriguing phenomenon predicted by Einstein’s General Relativity, obtained using 7 years of Satellite Laser Ranging (SLR) data of the satellite LARES (ASI, 2012) and 26 years of SLR data of LAGEOS (NASA, 1976) and LAGEOS 2 (ASI and NASA, 1992). We used the static part and temporal variations of the Earth gravity field obtained by the space geodesy mission GRACE (NASA and DLR) and in particular the static Earth’s gravity field model GGM05S augmented by a model for the 7-day temporal variations of the lowest degree Earth spherical harmonics. We used the orbital estimator GEODYN (NASA). We measured frame-dragging to be equal to $$0.9910 \pm 0.02$$0.9910±0.02, where 1 is the theoretical prediction of General Relativity normalized to its frame-dragging value and $$\pm 0.02$$±0.02 is the estimated systematic error due to modelling errors in the orbital perturbations, mainly due to the errors in the Earth’s gravity field determination. Therefore, our measurement confirms the prediction of General Relativity for frame-dragging with a few percent uncertainty.

scholarly journals GRAVITY ANOMALY ASSESSMENT USING GGMS AND AIRBORNE GRAVITY DATA TOWARDS BATHYMETRY ESTIMATION

2016 ◽  
Vol XLII-4/W1 ◽  
pp. 287-297
Author(s):  
A. Tugi ◽  
A. H. M. Din ◽  
K. M. Omar ◽  
A. S. Mardi ◽  
Z. A. M. Som ◽  
...  
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Airborne Gravity ◽  
Satellite Gravity ◽  
Earth’S Gravity Field ◽  
Explorer Mission ◽  
Satellite Gravity Missions

The Earth’s potential information is important for exploration of the Earth’s gravity field. The techniques of measuring the Earth’s gravity using the terrestrial and ship borne technique are time consuming and have limitation on the vast area. With the space-based measuring technique, these limitations can be overcome. The satellite gravity missions such as Challenging Mini-satellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity-Field and Steady-State Ocean Circulation Explorer Mission (GOCE) has introduced a better way in providing the information on the Earth’s gravity field. From these satellite gravity missions, the Global Geopotential Models (GGMs) has been produced from the spherical harmonics coefficient data type. The information of the gravity anomaly can be used to predict the bathymetry because the gravity anomaly and bathymetry have relationships between each other. There are many GGMs that have been published and each of the models gives a different value of the Earth’s gravity field information. Therefore, this study is conducted to assess the most reliable GGM for the Malaysian Seas. This study covered the area of the marine area on the South China Sea at Sabah extent. Seven GGMs have been selected from the three satellite gravity missions. The gravity anomalies derived from the GGMs are compared with the airborne gravity anomaly, in order to figure out the correlation (R<sup>2</sup>) and the root mean square error (RMSE) of the data. From these assessments, the most suitable GGMs for the study area is GOCE model, GO_CONS_GCF_2_TIMR4 with the R<sup>2</sup> and RMSE value of 0.7899 and 9.886 mGal, respectively. This selected model will be used in the estimating the bathymetry for Malaysian Seas in future.

scholarly journals DIONYSOS SATELLITE OBSERVATORY AND HIGHER GEODESY LABORATORY: HISTORY AND PERSPECTIVES

2017 ◽  
Vol 50 (2) ◽  
pp. 1091
Author(s):  
A. Marinou ◽  
D. Anastasiou ◽  
X. Papanikolaou ◽  
D. Paradissis ◽  
V. Zacharis
Keyword(s):  
Gravity Field ◽  
Temporal Variations ◽  
Technological Advance ◽  
Satellite Geodesy ◽  
Research Needs ◽  
Reference Systems ◽  
Earth’S Gravity Field ◽  
Wide Range

Dionysos Satellite Observatory and Higher Geodesy Laboratory have been in operation since the 60s and their main objective is to fulfill academic and research needs, determined through the ongoing scientific and technological advance in the field of geodesy. They are involved in all scientific domains related to the determination of earth’s size and figure, as well as its temporal variations. Their field of expertise is Satellite Geodesy, (spanning a wide range of applications like reference systems, tectonic geodesy, etc.), as well as the study of the geoid and earth's gravity field.

scholarly journals ANALYSIS OF ISOSTATICALLY-BALANCED CORTICAL MODELS USING MODERN GLOBAL GEOPOTENTIAL MODELS

2017 ◽  
Vol 23 (4) ◽  
pp. 623-635
Author(s):  
Claudia Infante ◽  
Claudia Tocho ◽  
Daniel Del Cogliano
Keyword(s):  
Gravity Field ◽  
Temporal Variations ◽  
Geoid Height ◽  
Geological Structure ◽  
Earth’S Gravity Field ◽  
Isostatic Equilibrium ◽  
Geopotential Models ◽  
Show Evidence ◽  
Residual Geoid ◽  
Cortical Models

Abstract: The knowledge of the Earth's gravity field and its temporal variations is the main goal of the dedicated gravity field missions CHAMP, GRACE and GOCE. Since then, several global geopotential models (GGMs) have been released. This paper uses geoid heights derived from global geopotential models to analyze the cortical features of the Tandilia structure which is assumed to be in isostatic equilibrium. The geoid heights are suitably filtered so that the structure becomes apparent as a residual geoid height. Assuming that the geological structure is in isostatic equilibrium, the residual geoid height can be assimilated and compared to the isostatic geoid height generated from an isostatically compensated crust. The residual geoid height was obtained from the EGM2008 and the EIGEN-6C4 global geopotential models, respectively. The isostatic geoid was computed using the cortical parameters from the global crustal models GEMMA and CRUST 1.0 and from local parameters determined in the area under study. The obtained results make it clear that the isostatic geoid height might become appropriate to validate crustal models if the structures analyzed show evidence of being in isostatic equilibrium.

scholarly journals On the joint inversion of SGG and SST data from the GOCE mission

2003 ◽  
Vol 1 ◽  
pp. 87-94 ◽  
Author(s):  
P. Ditmar ◽  
P. Visser ◽  
R. Klees
Keyword(s):  
Gravity Field ◽  
Joint Inversion ◽  
Normal Matrix ◽  
Nuisance Parameters ◽  
Design Matrix ◽  
Explicit Computation ◽  
Gravity Gradiometry ◽  
Satellite Gravity Gradiometry ◽  
Satellite Gravity ◽  
Earth’S Gravity Field

Abstract. The computation of spherical harmonic coefficients of the Earth’s gravity field from satellite-to-satellite tracking (SST) data and satellite gravity gradiometry (SGG) data is considered. As long as the functional model related to SST data contains nuisance parameters (e.g. unknown initial state vectors), assembling of the corresponding normal matrix must be supplied with the back-substitution operation, so that the nuisance parameters are excluded from consideration. The traditional back-substitution algorithm, however, may result in large round-off errors. Hence an alternative approach, back-substitution at the level of the design matrix, is implemented. Both a stand-alone inversion of either type of data and a joint inversion of both types are considered. The conclusion drawn is that the joint inversion results in a much better model of the Earth’s gravity field than a standalone inversion. Furthermore, two numerical techniques for solving the joint system of normal equations are compared: (i) the Cholesky method based on an explicit computation of the normal matrix, and (ii) the pre-conditioned conjugate gradient method (PCCG), for which an explicit computation of the entire normal matrix is not needed. The comparison shows that the PCCG method is much faster than the Cholesky method.Key words. Earth’s gravity field, GOCE, satellite-tosatellite tracking, satellite gravity gradiometry, backsubstitution

scholarly journals Rigidity of elastic shell of rubber-cable belt during displacement of cables relatively to drum

2019 ◽  
Vol 109 ◽  
pp. 00005 ◽  
Author(s):  
Ivan Belmas ◽  
Peter Kogut ◽  
Dmytro Kolosov ◽  
Volodymyr Samusia ◽  
Serhii Onyshchenko
Keyword(s):  
Elastic Layer ◽  
Strain State ◽  
Elastic Shell ◽  
Lower Boundary ◽  
Efficiency Coefficient ◽  
Shear Forces ◽  
Stress Strain ◽  
Rubber Layer ◽  
Stress Strain State

Analytical dependencies for determining the rigidity and parameters of a stress-strain state of a rubber layer located between the cables and the drum from their mutual shear are established in a closed form. A method of determining the dispersion of deviation of calculated displacements from established values of elastic shell material is developed. Obtained results allow considering the shape of an elastic layer of rubber, estimate the level of reliability of the results when calculating a stress-strain state of rubber-cable tractive elements from the shear of cables relatively to the drum. Established dependencies can be used for determining a stress-strain state of a layer of elastic material, caused by shear of cables relatively to the drum of a machine, and formulating the condition of strength of a rubber-cable tractive element loaded with shear forces on a drum. Possibility of determination of a lower boundary of the efficiency coefficient in a process of interaction of a rubber-cable rope (belt) with pulleys and drums, both driving and driven, lined with elastic materials and with hard operating surfaces, allows improving the accuracy of calculations of drives of lifting and transporting machines with such executing elements.

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