Evaluation of GGMs Based on the Terrestrial Gravity Data of Gravity Disturbance and Moho Depthin Afar, Ethiopia

To estimate Moho depth, geoid, gravity anomaly, and other geopotential functionals, gravity data is needed. But, gravity survey was not collected in equal distribution in Ethiopia, as the data forming part of the survey were mainly collected on accessible roads. To determine accurate Moho depth using Global Gravity Models (GGMs) for the study area, evaluation of GGMs is needed based on the available terrestrial gravity data. Moho depth lies between 28 km and 32 km in Afar. Gravity disturbances (GDs) were calculated for the terrestrial gravity data and the recent GGMs for the study area. The model-based GDs were compared with the corresponding GD obtained from the terrestrial gravity data and their differences in terms of statistical comparison parameters for determining the best fit GGM at a local scale in Afar. The largest standard deviation (SD) (36.10 mGal) and root mean square error (RMSE) (39.00 mGal) for residual GD and the lowest correlation with the terrestrial gravity (0.61 mGal) were obtained by the satellite-only model (GO_CONS_GCF_2_DIR_R6). The next largest SD (21.27 mGal) and RMSE (25.65 mGal) for residual GD were obtained by the combined gravity model (XGM2019e_2159), which indicates that it is not the best fit model for the study area as compared with the other two GGMs. In general, the result showed that the combined models are more useful tools for modeling the gravity field in Afar than the satellite-only GGMs. But, the study clearly revealed that for the study area, the best model in comparison with the others is the EGM2008, while the second best model is the EIGEN6C4.

Strategy for the realisation of the International Height Reference System (IHRS)

In 2015, the International Association of Geodesy defined the International Height Reference System (IHRS) as the conventional gravity field-related global height system. The IHRS is a geopotential reference system co-rotating with the Earth. Coordinates of points or objects close to or on the Earth’s surface are given by geopotential numbersC(P) referring to an equipotential surface defined by the conventional valueW0 = 62,636,853.4 m2 s−2, and geocentric Cartesian coordinatesXreferring to the International Terrestrial Reference System (ITRS). Current efforts concentrate on an accurate, consistent, and well-defined realisation of the IHRS to provide an international standard for the precise determination of physical coordinates worldwide. Accordingly, this study focuses on the strategy for the realisation of the IHRS; i.e. the establishment of the International Height Reference Frame (IHRF). Four main aspects are considered: (1) methods for the determination of IHRF physical coordinates; (2) standards and conventions needed to ensure consistency between the definition and the realisation of the reference system; (3) criteria for the IHRF reference network design and station selection; and (4) operational infrastructure to guarantee a reliable and long-term sustainability of the IHRF. A highlight of this work is the evaluation of different approaches for the determination and accuracy assessment of IHRF coordinates based on the existing resources, namely (1) global gravity models of high resolution, (2) precise regional gravity field modelling, and (3) vertical datum unification of the local height systems into the IHRF. After a detailed discussion of the advantages, current limitations, and possibilities of improvement in the coordinate determination using these options, we define a strategy for the establishment of the IHRF including data requirements, a set of minimum standards/conventions for the determination of potential coordinates, a first IHRF reference network configuration, and a proposal to create a component of the International Gravity Field Service (IGFS) dedicated to the maintenance and servicing of the IHRS/IHRF.

A geothermal application for GOCE satellite gravity data: modelling the crustal heat production and lithospheric temperature field in Central Europe

SUMMARY Since the completion of the Gravity field and steady-state Ocean Circulation Explorer mission (GOCE), global gravity models of uniform quality and coverage are available. We investigate their potential of being useful tools for estimating the thermal structure of the continental lithosphere, through simulation and real-data test in Central-Eastern Europe across the Trans-European Suture Zone. Heat flow, measured near the Earth surface, is the result of the superposition of a complex set of contributions, one of them being the heat production occurring in the crust. The crust is enriched in radioactive elements respect to the underlying mantle and crustal thickness is an essential parameter in isolating the thermal contribution of the crust. Obtaining reliable estimates of crustal thickness through inversion of GOCE-derived gravity models has already proven feasible, especially when weak constraints from other observables are introduced. We test a way to integrate this in a geothermal framework, building a 3-D, steady state, solid Earth conductive heat transport model, from the lithosphere–asthenosphere boundary to the surface. This thermal model is coupled with a crust-mantle boundary depth resulting from inverse modelling, after correcting the gravity model for the effects of topography, far-field isostatic roots and sediments. We employ a mixed space- and spectral-domain based forward modelling strategy to ensure full spectral coherency between the limited spectral content of the gravity model and the reductions. Deviations from a direct crustal thickness to crustal heat production relationship are accommodated using a subsequent substitution scheme, constrained by surface heat flow measurements, where available. The result is a 3-D model of the lithosphere characterised in temperature, radiogenic heat and thermal conductivity. It provides added information respect to the lithospheric structure and sparse heat flow measurements alone, revealing a satisfactory coherence with the geological features in the area and their controlling effect on the conductive heat transport.

Reduction of geometric leveling results to a system of normal heights using the global gravity models of the Earth

The possible range of application of models of the Earth’s gravitational field is considered in the article by reducing the results of geometric leveling to a system of normal heights. The accuracy of the global gravity models EGM2008, EIGEN-6C4, GECO on the gravity acceleration differences calculated for the territory of the Republic of Belarus by the results of instrumental gravimetric measurements and obtained from gravity models was estimated. Areas of Belarus are determined for which the gravitational correction for the transition to the system of normal heights will be caused by the deviation of the level surfaces of the normal gravitational field from the actual, and not by the errors of the gravitational models in the form of acceleration of gravity. It is shown that the error of the gravitational correction obtained from the data of gravity models for the territory of Belarus is many times less than the permissible random mean error of geometric leveling of the first class.

LOCAL EVALUATION OF EARTH GRAVITATIONAL MODELS, CASE STUDY: IRAN

Global gravity models are being developed according to new data sets available from satellite gravity missions and terrestrial/marine gravity data which are provided by different countries. Some countries do not provide all their available data and the global gravity models have many vague computational methods. Therefore, the models need to be evaluated locally before using. It is generally understood that the accuracy of global gravity models is enough for local (civil, mining, construction, etc.) projects, however, our results in Iran show that the differences between synthesized values and observation data reach up to ∼300 mGal for gravity anomalies and ∼2 m for geoid heights. Even by applying the residual topographical correction to synthetized gravity anomalies, the differences are still notable. The accuracy of global gravity models for predicting marine gravity anomalies is also investigated in Persian Gulf and the results show differences of ∼140 mGal in coastal areas. The results of evaluating selected global gravity models in Iran indicate that the EIGEN-6C4 achieves the lowest RMS for estimating the geoid heights. EGM08 predicts the closest results to terrestrial gravity anomalies. DIR-R5 GOCE satellite-only model estimates the low-frequency part of gravity field more accurately. The best prediction of marine gravity anomalies is also achieved by EGM08.

Assessment of the GOCE-Based Global Gravity Models in Canada

The aim of this study is to test the first, second and third generation GOCE geoid solutions, obtained from the first 2, 8 and 18-month observations, respectively. These solutions are assessed over Canada and for two sub-regions (the Great Lakes and Rocky Mountains). The Canadian GPS/leveling-derived geoid heights are used as independent control values in the assessment of the GOCE geoid models. The study is conducted in two steps. First, the geoid models are computed from satellite-only models and truncated to different spherical harmonic degrees. These models are compared with the GPS/leveling geoid heights which are reduced to the same spectral band as the satellite models by EGM2008 predicted frequency components higher than the truncation degrees. The results suggest that the GOCE models show a full power of signal up to about spherical harmonic degree 180. Moreover, the second and third generation GOCE models (with the exception of the direct approach models) provide better agreement with the GPS/leveling-derived geoid undulations than the first generation models due to the longer observation period. The second step involves the combination of the two third generation GOCE models with terrestrial data. These models are tested against to the GPS/leveling-derived geoid undulations in full spectrum. EGM2008 global geopotential model and Canadian gravimetric geoid model CGG2005 are also included in the comparisons to measure improvement provided by the GOCE models. The GOCE-combined models yielded GPS/leveling results that are comparable with those obtained from EGM2008 and CGG2005 models. The best comparative results with the combined models give standard deviations of 4.8 cm, 6.0 cm and 12.2 cm for the Great Lakes, Rocky Mountains and Canada, respectively. These results indicate that the third generation GOCE models conform to the Canadian terrestrial gravity data from degrees 90 to 180. The new generation models show evident improvement over the first and second generation models.