Search

This study presents a geophysical-geochemical integrated model of the thermochemical structure of the lithosphere and uppermost mantle along a transect from the Northern Tyrrhenian Sea to the Pannonian Basin, crossing the northern Apennines, the Adriatic Sea, and the Dinarides fold-thrust belt. The objectives are to image crustal thickness variations and characterize the different mantle domains. In addition, we evaluate the topographic response of opposed subductions along this transect and discuss their implications in the evolution of the region. Results show a more complex structure and slightly higher average crustal density of Adria compared to Tisza microplate. Below the Tyrrhenian Sea and Western Apennines, Moho lays at, This work is funded by GeoCAM (PGC2018-095154-B-I00) from the Spanish Government, the Generalitat de Catalunya Grant (AGAUR 2017 SGR 847) and ALORBE (PIE-CSIC-202030E10). WZ is supported by the China Scholarship Council (CSC-201904910470) and EBG by the Spanish Government Grant PRE2019-090524.

The differences between local and reference geopotential values are the fundamental quantities of interest in the geodetic boundary value problem approach for connecting independent height reference frames. The local gravity potential values are usually derived from gravimetric and geometric geoid undulations. In determining the short-wavelength components of the gravimetric geoid, a harmonic or analytical downward continuation of the external harmonic functions of gravity to the geoid is necessary. This study analyses the stability of the Poisson downward continuation technique with respect to varying the spatial resolution of surface gravity data in Ireland in order to estimate an effective grid resolution on this reduction. Results of the study show that the minimum range of 500-m resolution provides an unconditionally stable solution to downward continuation without the need for regularisation of the computation algorithm. In this case, downward continued data contribute from −13 to 12 mm to geoid heights and from −0.128 to 0.118 m2s−2 to local gravity potential value at Malin-Head tide gauge station in Ireland.

In this study, we use seven years of Cryosat-2 data to improve Mean Sea Surface (MSS) and also to estimate Mean Dynamic Topography (MDT) around Australia. Sea Level Anomaly (SLA) map, obtained from Cryosat-2 data, shows substantial spatial striping effects in the areas where annual signal has considerable amplitudes. This signal causes shifts among the SLAs acquired from adjacent tracks since they have collected at different times of the year. In order to mitigate these effects, we used Topex/Poseidon and follow on missions to estimate the seasonal signals in the Cryosat-2 data points. MSSC2 is then estimated by (1) removing these signals from SLAs, (2) averaging in a 0.1° × 0.1° grid cells, and (3) finally adding them to the DTUMSS13. The resultant surface shows good agreement with the MSS estimated by Jason-1 and Jason-2 data in altimetry nominal points. MDTC2 is also estimated in the study area using the MSSC2 and the geoid. It is in good agreement with two widely used global MDT models although showing higher values due to the effect of sea-level rise. When compared to the estimated MDT in tide gauge stations using geodetic data, MDTC2 statistically performs better than the global models.

Shallow layer method (SLM) based on the definition of the geoid can determine the gravity field inside the shallow layer. In this study, the orthometric height of Mount Everest (HME) is calculated based on SLM, in which the key is to construct the shallow layer model. The top and bottom boundaries of the shallow layer model are the natural surface of the Earth and the surface at a certain depth below the reference geoid, respectively. The model-combined strategies to determine the geoid undulation (N) based on SLM are applied to calculate the HME by two approaches: (1) direct calculation by combining N and geodetic height (h); (2) calculation by the segment summation approach (SSA) using the gravity field inside the shallow layer. On December 8, 2020, the Chinese and Nepalese governments announced an authoritative value of 8848.86 m, which is referred to a geoid determined by the International Height Reference System (IHRS) (i.e., the geopotential is 62636853.4 m2s-2). Here, our results (combined strategies (1) EGM2008 and CRUST1.0, (2) EGM2008 and CRUST2.0, (3) EIGEN-6C4 and CRUST1.0, and (4) EIGEN-6C4 and CRUST2.0) are referred to the geoid defined by WGS84 (i.e., the geopotential is 62636851.7 m2s-2). The differences between our results and the authoritative value (8848.86 m) are 0.448 m, −0.009 m, −0.295 m, and −0.741 m by the first approach, and 0.539 m, 0.083 m, −0.214 m, and −0.647 m by the second approach. When the reference surface WGS84 geoid is converted to the IHRS geoid, the differences are 0.620 m, 0.163 m, −0.123 m, and −0.569 m by the first approach, and 0.711 m, 0.225 m, −0.042 m, and −0.475 m by the second approach.

The strong earthquake with magnitude 6.9 occurred offshore at the northernmost edge of the Samos Island and was strongly felt in the north Aegean islands and Izmir metropolitan city. In this study, the effective elastic thicknesses of the lithosphere and seismogenic layer thickness were correlated with each other in order to understand the nature of the earthquakes. We determined that the upper and lower depth limits of seismogenic layer are in a range of 5–15 km, meaning that only the upper crust is mostly involved in earthquakes in the study area. The fact that seismogenic layer and effective elastic thicknesses are close to each other indicates that the earthquake potential may be within the seismogenic layer. Following that, we estimate the stress field from the geoid undulations as a proxy of gravity potential energy in order to analyze the amplitude and orientation of the stress vectors and seismogenic behavior implications. The discrete wavelet transform has been carried out to decompose the isostatic residual gravity anomalies into horizontal, vertical and diagonal detail coefficients. The results delineated edges of gravity anomalies that reveal some previously unknown features.

The aim of the current investigation is to determine an alternative geoid model for Africa using the shallow-layer method. The shallow-layer method, following the basic definition of the geoid, differs essentially from the traditional geoid determination techniques (Stokes and Molodensky) that it doesn’t need real gravity data. It comes from the definition of the geoid. Here, the shallow-layer method is used to determine a 5′ × 5′ geoid model for Africa covering the latitudes between −36°N and 39°N and longitudes from −20°E to 53°E The Earth Gravitational Model (EGM2008), the global topographic model (DTM2006.0), the global crustal model (CRUST1.0) and the Danish National Space Center data set (DNSC08) global models have been used to construct and define the shallow layer and its interior structure. A combination of prism and tesseroid modelling methods have been utilized to determine the gravitational potential produced by the shallow-layer masses. The validation and tests of the computed shallow-layer geoid have been done at two different levels. First, a comparison between the computed shallow-layer geoid and the recently developed AFRgeo2019 gravimetric geoid for Africa (based on real gravity data) has been carried out. Second, a comparison of the computed shallow-layer geoid with several geoid models computed using different global geopotential models has been performed. The results show that the computed shallow-layer geoid behaves similarly to those determined by the global geopotential models. Differences between the shallow-layer and the AFRgeo2019 gravimetric geoids are generally small (below 0.5 m) at most of the African continent

This research presents the results for analyses done to five geopotential global models (GGM), comparing them with ground data from GNSS and leveling in heterogenic zones from the geodetic perspective, in Chile and Spain. While the official and complete implementation of the International Height Reference Frame (IHRF) has not yet been established, the vertical geodetic system of many countries is not calculated on a global scale; instead, it is calculated by the variation of relative heights between one or more local tide gauges, such as in the case of Spain and Chile. This aspect creates regional and specific altimetry data, which disables the use of GGM to directly obtain the orthometric height of the vertical reference system (VRS) from the GNSS heights. Global models currently reach centimetric precision due to their high resolution but are directly incompatible for a local level. To solve this, we expose in this article the contrast between geometric geoidal undulation (ellipsoidal heights and orthometric data from the leveling networks in Spain and Chile) with the geoidal undulation in more recent models and higher resolution: Earth Gravitational Model 2008 (EGM08), European Improved Gravity model of the Earth by New techniques (EIGEN6C4), Gravity Observation Combination (GOCO05C), Experimental Gravity Field Model (XGM2016), and Ultra-High Resolution Global Geopotential Model (SGG-UGM), adjusting the residual between both referential heights by different parametric models and polynomials of determined order. Once evaluated, their geoidal undulations are combined with GNSS/leveling data from the corresponding VRS to generate a correcting surface, which is also known as a hybrid geoid, resulting in a model of optimal adjustment for the combination of five parameters of the EIGEN-6C4 with orthometric heights and ellipsoids of both Chile and Spain. The results show 2–3 cm precisions, which were statistically analyzed to determine the suitability for use. The final products are three grids of independent hybrid geoids, one for northern Spain and two for Chile (central and north), which allow continuous access to the VRS of each country using the GNSS's full potential until the IHRF is available and ready for use.

Mapping seafloor geomorphology is a complex task requiring the integration of advanced cartographic technologies and high-resolution spatial data. This paper provides a comparative geomorphological analysis of the Hellenic Trench (HT) and the Pliny Trench (PT) located in the Eastern Mediterranean Sea, southern Greece. These trenches were formed as a result of the tectonic plate subduction in the Eastern Mediterranean Sea: the northward motion of the African and Arabian plates, complicated by the regional geological settings, such as active faults and earthquakes, which resulted in their different geomorphological forms and bathymetric shapes. Technically, this paper presents an example of the advanced scripting mapping by scripting the cartographic toolset of Generic Mapping Tools (GMT), which performs mapping through shell scripts. The maps are based on the high-quality topographic, geological and geophysical data: GEBCO, EGM96, geoid, and marine free-air gravity fields. The GMT builds upon the modules used for data processing. The region was subsetted by ‘grdcut’, analysed by the Geospatial Data Abstraction Library (GDAL) (gdalinfo utility), and visualized by ‘grdimage’. Two segments of the trenches formed in a condition of varying geological and geophysical settings, have been modelled, visualized and compared, as representative cross-sections. As a result of the automated digitizing, spatial interpolation and sequential aggregating of GMT codes, the segments of the cross-sections were represented. The HT (Ionian segment) has an asymmetric one-sided shape; a steepness of 56.8° on the NE side and 7° on the SW flank. The PT has a more symmetric view; a steepness of 42.14° on its NW flank and 26.66° on its SE flank. The PT has a clear peak of the depths at -2600 to -2800 m and the most representative data range at -5000 to -6000 m. The HT has a bimodal data distribution with two peaks. The most frequent data for HT is -3200 m to -3400 m. Compared to PT, the HT is deeper. The histogram shows the peak of data for HT in the interval between -3200 to -3400 m (135 samples) while the PT shows the peak of data in the interval at -2600 to -2800 m (310 samples). Besides, 105 samples of the HT have depths exceeding 4000 m, while only 20 samples were recorded for PT in the same interval. This paper contributes to the geomorphological studies of the general Eastern Mediterranean Sea region, particularly relating to regional seafloor mapping of the Hellenic and Pliny trenches., Mapiranje geomorfologije morskoga dna složen je zadatak koji zahtijeva integraciju naprednih kartografskih tehnologija i prostornih podataka visoke rezolucije. Ovaj rad donosi usporednu geomorfološku analizu Helenskoga i Plinijskoga jarka smještenih u istočnome Sredozemlju, na jugu Grčke. Te su strukture nastale kao rezultat podvlačenja tektonske ploče, tj. kretanja afričke i arapske ploče prema sjeveru, usložnjenoga regionalnim geološkim postavkama poput aktivnih rasjeda i potresa, što je rezultiralo njihovim različitim geomorfološkim oblicima i batimetrijom. Prikazano je njihovo napredno kartiranje primjenom alata Generic Mapping Tools (GMT), koji koriste programske skripte. Karte se temelje na visokokvalitetnim topografskim, geološkim i geofizičkim podatcima, kao što su GEBCO, EGM96, geoid te gravitacijsko polje na razini mora. GMT se nadovezuje na module koji se koriste za obradu podataka. Područje je podijeljeno skriptom grdcut, a na temelju podataka iz zbirke apstraktnih geoprostornih podataka (GDAL) (skripta gdalinfo), te je na kraju vizualizirano (skripta grdimage). Dva dijela jarka oblikovana su u različitim geološkim i geofizičkim postavkama te su uspoređeni njihovi reprezentativni presjeci. Kao rezultat automatizirane digitalizacije, prostorne interpolacije i sekvencijalnoga agregiranja GMT kodova predstavljeni su segmenti presjeka. Helenski jarak (jonski segment) ima asimetričan jednostrani oblik, nagiba 56,8° na sjeveroistočnoj i 7° na jugozapadnoj strani. Plinijski je jarak simetričniji, nagiba 42,14° na SZ i 26,66° na JI boku. Plinijski jarak ima jasno izraženo tjeme od –2600 do –2800 m, a najreprezentativniji su podatci na –5000 do –6000 m. Helenski jarak ima bimodalnu distribuciju podataka s dvama tjemenima, a najčešće su dubine od –3200 do –3400 m. Taj je jarak dublji. Histogram prikazuje okupljanje podataka od –3200 do –3400 m, dok Plinijski (135 uzoraka) prikazuje maksimalne vrijednosti od –2600 do –2800 m (310 uzoraka). Osim toga, 105 uzoraka Helenskoga jarka ima dubine veće od –4000 m, dok je u istome intervalu za Plinijski zabilježeno samo 20 uzoraka. Članak doprinosi geomorfološkim studijama regije istočnoga Sredozemnog mora općenito i regionalnomu mapiranju morskoga dna, posebno Helenskoga i Plinijskoga jarka.

The tectonic–geodynamic characteristics of the North African–Arabian region are complicated by the interaction of numerous factors. To study this interaction, we primarily used satellite gravimetric data (retracked to the Earth’s surface), which has been acknowledged as a powerful tool for tectonic–geodynamic zoning. The applied polynomial averaging of gravity data indicated the presence of a giant, deep quasi-ring structure in the Eastern Mediterranean, the center of which is located under the island of Cyprus. Simultaneously, the geometrical center of the revealed structure coincides with the Earth’s critical latitude of 35°. A quantitative analysis of the obtained gravitational anomaly made it possible to estimate the depth of the upper edge of the anomalous body as 1650‒1700 km. The GPS vector map coinciding with the gravitational trend indicates counterclockwise rotation of this structure. A review of paleomagnetic data on the projection of the discovered structure into the Earth’s surface also confirms its counterclockwise rotation. Analysis of the geoid anomalies map and seismic tomography data commonly prove the presence of this deep anomaly. The structural and geodynamic characteristics of the region and paleobiogeographic data are consistent with the proposed physical–geological model. Comprehensive analysis of petrological, mineralogical, and tectonic data suggests a relationship between the discovered deep structure and near-surface processes. The deep structure also sheds light on specific anomalous effects in the upper layer of the crust, including the high-intensity Cyprus gravitational anomaly, counterclockwise rotation of the Mesozoic terrane belt, configuration of the Sinai Plate, and asymmetry of sedimentary basins along continental faults.

The study presents an analysis of the sediment thickness compared with bathymetric and geophysical settings in the Bay of Bengal and Andaman Sea, Indian Ocean. It uses a combination of the high-resolution data: topographic GEBCO, satellite and marine gravity anomalies, EGM2008 geoid and GlobSed to visualize the correlation between relief, gravity and trends in continent-ocean sediment transport. The results include thematic maps and 3D model showing increased sediment thickness in the Bengal Fan (8,0 to 8,2 km) in NE direction with maximum in Ganges Fan (16,2 km), and southward decrease in the Andaman Sea from Irrawaddy river mouth (6-7 km) to the Strait of Malacca (1-2 km). All maps and 3D model have been plotted by Generic Mapping Tools (GMT) cartographic scripting toolset version 6.0.0.

Forward gravity field modelling requires high accurate determination of the topographic potential on the surface of the Earth’s ellipsoid. Since the topography is recently known with high resolution, the determination of the harmonic analysis of the topographic ellipsoidal potential should be carried-out to an ultra-high degree. The paper presents a direct technique to determine the harmonic analysis of the ellipsoidal potential to an ultra-high degree. The detailed derivation of the developed expressions is given. The proposed technique can be used to compute the harmonic analysis of the topographic potential of the whole Earth or for a local/regional window. This has a great advantage when using the proposed technique for local/regional geoid determination within the window remove–restore technique (Abd-Elmotaal and Kuhtreiber, Phys Chem Earth Part A 24(1):53–59, 1999, J Geod 77(1–2):77–85, 2003). The developed technique has been compared to existing global solutions for the ellipsoidal topographic potential and it shows quite good agreement. Local tests for the developed technique proved that it works very well.

The aim of this work is the determination of the parameters of Earth’s triaxiality through a geometric fitting of a triaxial ellipsoid to a set of given points in space, as they are derived from a geoid model. Starting from a Cartesian equation of an ellipsoid in an arbitrary reference system, we develop a transformation of its coefficients into the coordinates of the ellipsoid center, of the three rotation angles and the three ellipsoid semi-axes. Furthermore, we present different mathematical models for some special and degenerate cases of the triaxial ellipsoid. We also present the required mathematical background of the theory of least-squares, under the condition of minimization of the sum of squares of geoid heights. Also, we describe a method for the determination of the foot points of the set of given space points. Then, we prepare suitable data sets and we derive results for various geoid models, which were proposed in the last fifty years. Among the results, we report the semi-axes of the triaxial ellipsoid of geometric fitting with four unknowns to be 6378171.92 m, 6378102.06 m and 6356752.17 m and the equatorial longitude of the major semi-axis –14.9367 degrees. Also, the parameters of Earth’s triaxiality are directly estimated from the spherical harmonic coefficients of degree and order two. Finally, the results indicate that the geoid heights with reference to the triaxial ellipsoid are smaller than those with reference to the oblate spheroid and the improvement in the corresponding rms value is about 20 per cent.

A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m−3 for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.

The need for dense and accurate gravity data cannot be overemphasised in the development of a precise gravimetric geoid model. Unfortunately, the field observations required are costly, and labour-intensive hence the need to ascertain via numerical simulations the appropriate field specifications before embarking on them. This paper presents an experimental study on the gravimetric data specifications (spatial resolution and data accuracy) required for achieving decimetre-level accuracy geoid using the conventional Stokes' Remove Compute Restore (RCR) method in Nigeria. A two-step solution approach was used in this study. The steps were determination of the (i) effect of data spacing by a comparative assessment of computation results obtained by using gravity data at four user determined intervals and (ii) effect of observation accuracy by numerical simulation using error propagation analysis. The data intervals (3′×3′, 5′×5′, 10′×10′ and 20′×20′) were selected from a combination of 1815 terrestrial FA anomaly points merged with EGM2008 derived FA anomaly covering the study area. Also, observational errors investigated were 0 mGal, 0.1 mGal, 0.5 mGal, 1 mGal and 5 mGal. The study was conducted in Nigeria having a total land area of approximately 923,768 km2. The study established that gravimetric geoid accuracy improves substantially as the spatial resolution and accuracy of the gravity data improves. Also, the study identified that data spacing contributes more to the overall geoid error than data accuracy. In addition, the study observed that hilly regions should have denser data spacing than plain areas. Within the test region, a data spacing of 3′×3′ with gravity observational errors 5 mGal was found to produce an acceptable gravimetric geoid. The produced gravimetric geoid had a pre-fit Root Mean Square Error (RMSE) of 15.6 cm when compared with GNSS-Levelling data at 27 stations located evenly across the study area.

Optimizing the combined horizontal and vertical accuracy of the well-known Global Digital Elevation Models (GDEMs) of various resolutions for each country and region especially in Iraq's mountainous areas is still questionable. All the three GDEMs, approximately, have the same vertical accuracy with the Root Mean Square (RMSE) of ±7.3 m, ±7.6 m and ±6.5 m via 12 fixed Ground Control Points (GCPs) for the Advanced Land Observation Satellite Phased Array L-band Synthetic Aperture Radar (ALOS PALSAR 12.5 m), the Shuttle Radar Topographic Mission (SRTM 30 m) and the TerraSAR-X (the name of twin satellites) add-on for Digital Elevation Measurement (TanDEM-X 90 m) GDEMs respectively. Moreover, the percentage of outliers that are greater or smaller than ±10 m detection of the height extraction from both the ALOS PALSAR and SRTM Digital Elevation Models (DEMs) contains 16.7% and for TanDEM-X was 25%. In this paper, the special DEM is derived using 2123 handheld GPS points for Sulaymaniyah Governorate, Kurdistan region, Iraq. The height extraction by discarding the outliers of 58% gives the RMSE of ±8.0 m in the case of adding geoid heights (N) to the ellipsoidal heights (h) via the Earth Gravitational Model 2008 (EGM2008) and ±5.6 m without adding N. It is expected that the derived DEMs will give more accurate results both horizontally and vertically in the mountainous areas when GPS observations are intensified. The horizontal accuracy is validated through extracting hierarchy stream types of the watershed map from the DEMs for higher than 100 pixels length. The ALOS PALSAR DEM extracted more numbers of stream orders than others. Finally, based on the criteria of RMSE, outlier detection, and the number of extracted stream orders, the ALOS PALSER DEM is regarded as the optimal GDEM in comparison with the close accuracy of both the TanDEM-X and SRTM DEM.

Marine gravity anomalies are essential data for determining coastal geoid, investigating tectonics and crustal structures, and offshore explorations. The objective of this study is to present a methodology for estimating marine gravity anomalies from CryoSat-2 and Saral/AltiKa satellite altimeter data for the Gulf of Tonkin of Vietnam with a high-resolution 2′ × 2′ grid. A total of 15,665 sea surface height (SSH) grid points, including derived from the Cryosat-2 (6842 grid points) and Saral/AltiKa (8823 grid points) satellite altimeter data were used. Then, the remove-restore technique and the crossover adjustment algorithm were used to remove the long-wavelength geoid height, the mean dynamic topography , and time-varying sea-surface topography . The residual geoid heights were used to determine the residual gravity anomalies using the Least-Squares Collocation method, whereas the Earth Geopotential Model was employed to restore the long-wavelength gravity anomalies . GPS/leveling and tidal gauge of 31 tidal stations were used for assessing and choosing the best Earth Geopotential Model and Mean Dynamic Topography models for the study area (EIGEN6C4 and DTU15MDT models). The accuracy of the final marine gravity anomaly result was assessed using 56,978 marine gravity points, which were distributed in the study area. The result showed that the standard deviation between the satellite-derived gravity anomalies and checked points is ± 3.36 mGal, indicating good accuracy. After improving with ship-measured gravity anomalies, the accuracy of satellite-derived marine gravity anomaly improves to ± 2.63 mGal. The results of this research are useful for geodetic and geophysical applications in the region. 2020 COSPAR. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/)

GNSS observations are a common solution for outdoor positioning around the world for coarse and precise applications. However, GNSS produces geodetic heights, which are not physically meaningful, limiting their functionality in many engineering applications. In Costa Rica, there is no regional model of the geoid, so geodetic heights (h) cannot be converted to physically meaningful orthometric heights (H). This paper describes the computation of a geoid model using the Stokes-Helmert approach developed by the University of New Brunswick. We combined available land, marine and satellite gravity data to accurately represent Earth's high frequency gravity field over Costa Rica. We chose the GOCO05s satellite-only global geopotential model as a reference field for our computation. With this combination of input data, we computed the 2020 Regional Stokes-Helmert Costa Rican Geoid (GCR-RSH-2020). To validate this model, we compared it with 4 global combined geopotential models (GCGM): EGM2008, Eigen6C-4, GECO and SGG-UM-1 finding an average difference of 5 cm. GECO and SGG-UM-1 are more similar to the GCR-RSH-2020 based on the statistics of the difference between models and the shape of the histogram of differences. The computed geoid also showed a shift of 7 cm when compared to the old Costa Rican height system but presented a slightly better fit with that system than the other models when looking at the residuals. In conclusion, GCR-RSH-2020 presents a consistent behaviour with the global models and the Costa Rican height systems. Also, the lowest variance suggests a more accurate determination when the bias is removed.

The primary task of the IAG Sub-Commission on Gravity and Geoid in Africa is the development of the vertical reference surface (the geoid) for the entire African continent. For the practical solution of this boundary value problem, the available, arbitrarily distributed boundary data (gravity values) must be interpolated onto a regular grid for numerical reasons. In this paper it is explained in detail how to create this grid from the irregularly distributed point-gravity data. It is worth mentioning that this gravity database is not only used for geoid computation; it is also a stand-alone product used in earth sciences, as it reflects interesting geophysical signals. The gravity data available in this project are land and shipborne point gravity values as well as altimetry-derived gravity anomaly data. One challenge of preparing the homogeneous grid of gravity anomalies is caused by the inhomogeneous distribution of the observations and a lot of data gaps, especially on land. At these data gaps, gravity anomalies are provided on a so-called underlying grid from the GOCE DIR_R5 global reference model. One challenge in the framework of the least-squares prediction technique used is the determination of an empirical covariance function representing the behaviour of the irregularly distributed data points and the individual weights of the land, shipborne, and altimetry data and the underlying grid entering the process. A sophisticated filtering of the available gravity data is carried out to meet this challenge. The preprocessed data from the remove step are predicted to an equiangular $$5^{'} \times 5^{'}$$ grid. Finally, a consistent restore step leads to the AFRGDB_V2.2 gravity database. The precision of the developed gravity database has been studied to assess the quality of the new product. The new AFRGDB_V2.2 gravity database is compared to the preceding one (AFRGDB_V2.0), which was generated using the window remove-restore technique.

The Istanbul GPS Triangulation Network (IGTN) and the Istanbul Levelling Network (ILN), established in 2006, provide data for the determination of a local GNSS/levelling geoid model. These networks' measurements were done separately on both the Asian and European sides of the Bosphorus Strait in the vicinity of Istanbul. To connect these regions for those networks, a Valley Cross Levelling (VCL) data set, acquired in 1986 and 2004, was used. The use of this VCL data set was challenging in calculating the Istanbul geoid model, primarily because of its errors. In this study, this challenge was overcome through newly collected VCL data in 2010, allowing for the readjustment of the ILN and the newly collected VCL data set. The Istanbul geoid model was computed using soft computing techniques including the adaptive-network-based fuzzy inference system (ANFIS) and the artificial neural networks (ANNs). The resulting Istanbul GNSS/levelling geoid model is shown to be more reliable when compared with the model computed using conventional interpolation techniques. (C) 2020 Institute of Seismology, China Earthquake Administration, etc. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.

During the last few years, the determination of high-resolution global gravity field has gained momentum due to high-accuracy satellite-derived observations and development of forward gravity modelling. Forward modelling computes the global gravitational field from mass distribution sources instead of actual gravity measurements and helps improving and complementing the medium to high-frequency components of the global gravity field models. In this study, we approximate the global gravity potential of the Earth’s upper crust based on ellipsoidal approximation and a mass layer concept. Such an approach has an advantage of spectral methods and also avoids possible instabilities due to the use of a sequence of thin ellipsoidal shells. Lateral density within these volumetric shells bounded by confocal lower and upper shell ellipsoids is used in the computation of the ellipsoidal harmonic coefficients which are then transformed into spherical harmonic coefficients on the Earth’s surface in the final step. The main outcome of this research is a spectral representation of the gravitatioal potential of the Earth’s upper crust, computed up to degree and order 3660 in terms of spherical harmonic coefficients (ROLI_EllApprox_SphN_3660). We evaluate our methodology by comparing this model with other similar forward models in the literature which show sub-cm agreement in terms of geoid undulations. Finally, EIGEN-6C4 is augmented by ROLI_EllApprox_SphN_3660 and the gravity field functionals computed from the expanded model which has about 5 km half-wavelength spatial resolution are compared w.r.t. ground-truth data in different regions worldwide. Our investigations show that the contribution of the topographic model increases the agreement up to ~ 20% in the gravity value comparisons.

The determination of the gravimetric geoid is based on the magnitude of the gravity observed at the topographic surface of the Earth. In order to satisfy Laplace’s equation, the masses between the surface of the Earth and the geoid must be removed or shifted inside the geoid. Then the gravity values have to be reduced to the geoid, forming the boundary values on the boundary surface. Gravity reduction techniques using unclassified Digital Terrain Models (DTM) usually presume that negative elevations are reserved for ocean stations. In case of Qattara Depression, the elevations are negative, i.e., below sea level. This leads to an obvious error in the topographic-isostatic reduction using, for example, TC-program employing unclassified DTM by assuming water masses filling the depression instead of air, besides computing at the non-existing sea level instead of computing at the actual negative topography. The aim of this paper is to determine the effect of Qattara Depression on gravity reduction and geoid computation, as a prototype of the effect of the unclassified land depressions on gravity reduction and geoid determination. The results show that the effect of Qattara Depression on the gravity reduction reaches 20 mGal and is restricted only to the depression area, while its effect on the geoid exceeds 1 m and has a regional effect which extends over a distance of about 1000 km.

Based on the concept of Global Position System (GPS)/leveling, the satellite altimetry leveling (SAL) is first proposed to evaluate the marine geoid. SAL is derived by the difference among the mean sea surface (MSS), mean dynamic ocean topography (MDT), and leveling origin. In this study, (1) the original satellite altimetry data are processed to infer the vertical deflection and gravity anomaly, (2) the Chinese coastal marine geoids (CMG) are determined by using the different methods (including Molodensky, least square collocation, Stokes formula, and two-dimensional fast Fourier transformation (FFT) with the vertical deflection and gravity anomaly data), (3) CMG are evaluated by using the results from above different methods, the Gravity field and steady-state Ocean Circulation Explorer (GOCE) gravity potential model (GGPM), and SAL. The results show that (1) CMG from the Molodensky method has the highest precision by using vertical deflection data, (2) the accuracy of CMG indicate good consistency between the SAL and GGPM, (3) SAL can be used as a new method for assessing marine geoid. Keywords: Satellite altimetry leveling, Marine geoid, Vertical deflection, Gravity anomaly

The problem of determining small tangential mass forces in the Earth lithosphere is formulated. It is shown that the current state in understanding the shape of The Earth's physical surface and data on its geoid allow us to determine deviations of the vertical line from the normal to the Earth's surface on the scale of averaging in the first hundreds of kilometers. It is established that for large areas of lithospheric plates, systematic unidirectional deviations of the vertical line from the normal to the surface are observed. Small tangential mass forces calculated from these data are of the order n 10–4 G/cm3. If there is a stable surface gradient over areas of the first thousand kilometers (the oceanic part of the lithospheric plates) tangential mass forces can create additional compressive or tensile horizontal stresses of the order of 10–15 MPa. These forces, summed up by the depth of the lithosphere, are able to overcome the level of tangential stresses of 0.2–0.3 MPa at its bottom, and therefore they can be considered as a source of plate motion.

In this study, we compare six commonly used methods for the downward continuation of airborne gravity data. We consider exact and noisy simulated data on grids and along flight trajectories and real data from the GRAV-D airborne campaign. We use simulated and real surface gravity data for validation. The methods comprise spherical harmonic analysis, least-squares collocation, residual least-squares collocation, least-squares radial basis functions, the inverse Poisson method and Moritz’s analytical downward continuation method. We show that all the methods perform similar in terms of surface gravity values. For real data, the downward continued airborne gravity values are used to compute a geoid model using a Stokes-integral-based approach. The quality of the computed geoid model is validated using high-quality GSVS17 GPS-levelling data. We show that the geoid model quality is similar for all the methods. However, the least-squares collocation approach appears to be more flexible and easier to use than the other methods provided that the optimal covariance function is found. We recommend it for the downward continuation of GRAV-D data, and other methods for second check.

Geophysical data from open sources are widely used as support of integrated analysis in regional geologic studies in seismically active areas, such as Mexico. High seismicity with repetitive earthquakes occurs in areas of the subduction zones formed during the tectonic evolution and correlates with geophysical anomalous fields. This paper investigates the correspondence between the geophysical, topographic and seismic setting of Mexico using Generic Mapping Tools (GMT) scripting toolset for data processing. The approach for automated mapping using GMT console and shell scripts is presented as an advanced cartographic method aimed to get insights into in the geology and geophysics of Mexico. The data were obtained from open source high-resolution datasets: GEBCO, EGM-2008, satellite-derived gravity, EMAG2 magnetic anomaly and IRIS seismic database. The correspondence between the geological and geophysical data of Mexico has been verified through the comparison between the thematic maps, regional distribution of gravity anomalies and locations of earthquakes. Seven new maps are performed on geologic, geophysical, topographic and seismic data. Seismic mapping is presented for the period of 2007-2021 demonstrating events with magnitude from 1.5 to 7.2. The impact of tectonic processes that formed Middle American Trench and active Trans-Mexican Volcanic Belt on high regional seismicity with intensive earthquakes is explored. The study finds that GMT is an effective tool for high-quality mapping and cartographic analysis. The IRIS data can be used for geologic analysis of Mexico. Dados geof��sicos de fontes abertas s��o amplamente usados como suporte de an��lise integrada em estudos geol��gicos regionais em ��reas sismicamente ativas, como o M��xico. Alta sismicidade com terremotos repetitivos ocorre em ��reas das zonas de subduc����o formadas durante a evolu����o tect��nica e se correlaciona com campos an��malos geof��sicos. Este artigo investiga a correspond��ncia entre o cen��rio geof��sico, topogr��fico e s��smico do M��xico usando o conjunto de ferramentas de script Generic Mapping Tools (GMT) para processamento de dados. A abordagem para mapeamento automatizado usando o GMT e scripts de shell �� apresentada como um m��todo cartogr��fico avan��ado com o objetivo de obter insights sobre a geologia e a geof��sica do M��xico. Os dados foram obtidos de conjuntos de dados de alta resolu����o de c��digo aberto: GEBCO, EGM-2008, gravidade derivada de sat��lite, anomalia magn��tica EMAG2 e banco de dados s��smico IRIS. A correspond��ncia entre os dados geol��gicos e geof��sicos do M��xico foi verificada atrav��s da compara����o entre os mapas tem��ticos, distribui����o regional de anomalias gravitacionais e localiza����es de terremotos. Sete novos mapas s��o realizados em dados geol��gicos, geof��sicos, topogr��ficos e s��smicos. O mapeamento s��smico �� apresentado para o per��odo de 2007-2021 demonstrando eventos com magnitude de 1,5 a 7,2. O impacto dos processos tect��nicos que formaram a trincheira da Am��rica Central e o cintur��o vulc��nico transmexicano ativo na alta sismicidade regional com terremotos intensos �� explorado. O estudo concluiu que o GMT �� uma ferramenta eficaz para mapeamento e an��lise cartogr��fica de alta qualidade. Os dados IRIS podem ser usados para an��lises geol��gicas do M��xico.

International audience; This paper presents the GRASS GIS-based thematic mapping of Antarctica using scripting approach and associated datasets on topography and geophysics. The state-ofthe art in cartographic development points at two important aspects. The first one comprises shell scripting promoted repeatability of the GIS technique, increased automatization in cartographic workflow, and compatibility of GRASS with Python, PROJ and GDAL libraries which enables advanced geospatial data processing: converting formats, re-projecting and spatial analysis. The second aspect is that data visualization greatly influences geologic research through improving the interpretation between the Antarctic glaciation and surface. This includes the machine learning algorithms of image classification enabling to distinguish between glacier and non-glacier surfaces through automatically partitioning data and analysis of various types of surfaces. Presented detailed maps of Antarctic include visualized datasets from the ETOPO1, GlobSed, EGM96 and Bedmap2 projects. The grids include bed and surface elevation, ETOPO1-based bathymetry and topography, bed, ice and sediment thickness, grounded bed uncertainty, subglacial bed elevation, geoid undulations, ice mask grounded and shelves. Data show the distribution of the present-day glacier, geophysical fields and topographic landforms for analysis of processes and correlations between the geophysical and geological phenomena. Advances in scripting cartography are significant contributions to the geological and glaciological research. Processing high-resolution datasets of Southern Ocean retrieved by remote sensing methods present new steps in automatization of the digital mapping, as presented in this research, and promotes comprehensive monitoring of geological, permafrost and glacial processes in Antarctica. All maps have been plotted using GRASS GIS version 7.8. with technical details of scripts described and interpreted.

The radial viscosity of the mantle is generally thought to increase by ∼10–100 times from the upper to lower mantle with a putative, abrupt increase at 660 km depth. Recently, a low viscosity channel (LVC) between 660 and 1,000 km has been suggested. We conduct a series of time-dependent flow models with viscosity either increasing or decreasing at 660 km depth while tracking slab structure, state-of-stress, and geoid. We find that a LVC will lower the amplitude of long wavelength (>5,000 km) geoid highs over slabs, with amplitudes

Previous studies mainly focused on second- and third-order gravitational potential gradients that these values are already measurable or that appropriate measurement principles are being developed. Although the higher-order (i.e. the order is larger than or equal to four) gravitational potential gradients cannot be observed now, with the development of science and technology, it will be hoped to measure these parameters in the future. Once the values of higher-order gradients are observable, they can express the higher frequency of the Earth’s gravity field and have the higher sensitivity to the shallower structures of the Earth’s subsurface, which will be applied for the global and regional gravity field modelling and geoid determination in geodesy and the mass density mapping of the subsurface and shallower structures in geophysics. In this paper, the higher-order gravitational potential gradients in spherical coordinates are focused on by tensor analysis. Firstly, the rule of the covariant derivative of a tensor is revised based on Casotto and Fantino (2009). Secondly, the general expressions for the natural components of the fourth-order up to seventh-order gravitational potential gradients are derived based on the revised rule. Specifically, we derive the expressions for physical components of the fourth-order gravitational potential derivatives as an example. Thirdly, Laplace’s equation with a uniform tesseroid using the spherical integral kernels has been applied to validate these newly derived expressions’ correctness. The expressions for the physical components of higher-order gradients up to m order can theoretically be derived based on this paper’s research results.

Author(s): Yu, Yao; Sandwell, David T; Gille, Sarah T; Boas, Ana Beatriz Villas | Abstract: SUMMARY The Ice, Cloud and land Elevation Satellite 2 (ICESat-2) laser altimetry mission, launched in September 2018, uses six parallel lidar tracks with very fine along-track resolution (15nm) to measure the topography of ice, land and ocean surfaces. Here we assess the ability of ICESat-2 ocean data to recover oceanographic signals ranging from surface gravity waves to the marine geoid. We focus on a region in the tropical Pacific and study photon height data in both the wavenumber and space domain. Results show that an ICESat-2 single track can recover the marine geoid at wavelengths g20nkm which is similar to the best radar altimeter data. The wavelength and propagation direction of surface gravity waves are sometimes well resolved by using a combination of the strong and weak beams, which are separated by 90nm. We find higher than expected power in the 3–20nkm wavelength band where geoid and ocean signals should be small. This artificial power is caused by the projection of 2-D surface waves with ∼300nm wavelengths into longer wavelengths (5–10nkm) because of the 1-D sampling along the narrow ICESat-2 profile. Thus ICESat-2 will not provide major improvements to the geoid recovery in most of the ocean.

The signal content and error level of recent GOCE-based high resolution gravity field models is assessed by means of signal degree variances and comparisons to independent GNSS-levelling geoid heights. The signal of the spherical harmonic series of these models is compared to the pre-GOCE EGM2008 model in order to identify the impact of GOCE data, of improved surface and altimetric gravity data and of modelling approaches. Results of the signal analysis show that in a global average roughly 80% of the differences are due to the inclusion of GOCE satellite information, while the remaining 20% are contributed by improved surface data. Comparisons of the global models to GNSS-levelling derived geoid heights demonstrate that a 1 cm geoid from the global model is feasible, if there is a high quality terrestrial gravity data set available. For areas with less good coverage an accuracy of several centimetres to a decimetre is feasible taking into account that GOCE provides now the geoid with a centimetre accuracy at spatial scales of 80 to 100 km. Comparisons with GNSS-levelling geoid heights also are a good tool to investigate possible systematic errors in the global models, in the spirit levelling and in the GNSS height observations. By means of geoid height differences and geoid slope differences one can draw conclusions for each regional data set separately. These conclusions need to be considered for a refined analysis e.g. to eliminate suspicious GNSS-levelling data, to improve the global modelling by using full variance-covariance matrices and by consistently weighting the various data sources used for high resolution gravity field models. The paper describes the applied procedures, shows results for these geoid height and geoid slope differences for some regional data sets and draws conclusions about possible error sources and future work to be done in this context.

The NKG2015 geoid model covers the Nordic and Baltic countries and has been computed based on the least-squares modification of Stokes’ formula with additive corrections method. New and precise terrestrial, airborne and shipborne gravimetric measurements, the recent global gravity model of the gravity field and steady-state ocean circulation explorer (GOCE) and detailed digital terrain models over each territory have been used for computing this new geoid model. Some estimates for the error of this model have been roughly presented by comparing it with the global navigation satellite system (GNSS) data over each country. In this paper, our goal is to have a closer look at the relative error of this model by performing some statistical tests and finding the proper corrective surface for absorbing the systematic errors over each country. Our main assumption is realisticity of the errors of GNSS/levelling data and we will investigate its consequences in estimating the error of the geoid model. Our results show that the 4-parameter corrective surface is suitable for modelling the systematic trends of the differences between the gravimetric and GNSS geoid heights in Sweden, Denmark and Finland, but a filtered discrepancies by a confidence interval of 95% should be used for Sweden. A 7-aparameter model is suitable for the filtered discrepancies with the confidence interval of 95% in Norway. Based on the selected corrective surface and our newly developed regional iterative variance estimator, the confidence interval for the error of NKG2015 geoid model in Sweden, Denmark and Norway yielded 0-6.5 mm, 1.8-5.2 mm, 14.8-17.7 mm, respectively with a confidence level of 95%. We could not estimate the geoid error in Finland because the given error of the GNSS/levelling heights is significantly larger than the size of residuals. Based on the selected corrective surfaces and our presented local variance estimator, the average error of geoid becomes 3.6, 2.4, 8.8 and 5.8 mm with a confidence interval of 68%, respectively, over Sweden, Denmark, Norway and Finland.

Different modification methods and software programs were developed to obtain accurate local geoid models in the past two decades. The quantitative effect of the main factors on the accuracy of local geoid modeling is still ambiguous and has not been clearly diagnosed yet. This study presents efforts to find the most influential factors on the accuracy of the local geoid model, as well as the amount of each factor's effect quantitatively. The methodology covers extracting the quantitative characteristics of 16 articles regarding local geoid models of different countries. The Statistical Package of Social Sciences (SPSS) software formulated a strong multiple regression model of correlation coefficient r = 0.999 with a high significance coefficient of determination R2 = 0.997 and adjusted R2 = 0.98 for the required effective factors. Then, factor analysis is utilized to extract the dominant factors which include: accuracy of gravity data (40%), the density of gravity data (25%) (total gravity factors is 65%), the Digital Elevation Model (DEM) resolution (16%), the accuracy of GPS/leveling points (10%) and the area of the terrain of the country/state under the study (9%). These results of this study will assist in developing more accurate local geoid models. Keywords: Accuracy of local geoid model, Multiple regression model, Influence factors

We present a three-dimensional (3D) density model of northern Andaman subduction zone (10°–15°N) constructed through joint modelling of satellite free-air gravity and geoid anomalies with constraints from previous studies. This novel modelling approach utilizes geoid and gravity anomalies simultaneously to better resolve the structure of inadequately known part of the subduction zone. The density model suggests: • A contrasting situation of subducting Indian plate, mapped up to a depth of ∼180 km in the southern part, and almost missing in the north of the study region. • Dip of the Benioff zone and the width of the accretionary prism decreases from south to north. • Nature of the overriding plate varies from oceanic to semi-continental towards the north. • Moho depth is relatively higher under the seamounts and 90°E ridge. The change in the subduction geometry is probably due to the subducting aseismic ridge, difference in the sediment influx and variation in the convergence rates. The absence of the subducting slab in the north is probably caused due to tearing between northern Andaman in the south and Burmese Arc in the north.

We present the official land uplift model NKG2016LU of the Nordic Commission of Geodesy (NKG) for northern Europe. The model was released in 2016 and covers an area from 49° to 75° latitude and 0° to 50° longitude. It shows a maximum absolute uplift of 10.3 mm/a near the city of Umea in northern Sweden and a zero-line that follows the shores of Germany and Poland. The model replaces the NKG2005LU model from 2005. Since then, we have collected more data in the core areas of NKG2005LU, specifically in Norway, Sweden, Denmark and Finland, and included observations from the Baltic countries as well. Additionally, we have derived an underlying geophysical glacial isostatic adjustment (GIA) model within NKG as an integrated part of the NKG2016LU project. A major challenge is to estimate a realistic uncertainty grid for the model. We show how the errors in the observations and the underlying GIA model propagate through the calculations to the final uplift model. We find a standard error better than 0.25 mm/a for most of the area covered by precise levelling or uplift rates from Continuously Operating Reference Stations and up to 0.7 mm/a outside this area. As a check, we show that two different methods give approximately the same uncertainty estimates. We also estimate changes in the geoid and derive an alternative uplift model referring to this rising geoid. Using this latter model, the maximum uplift in Umea reduces from 10.3 to 9.6 mm/a and with a similar reduction ratio elsewhere. When we compare this new NKG2016LU with the former NKG2005LU, we find the largest differences where the GIA model has the strongest influence, i.e. outside the area of geodetic observation. Here, the new model gives from − 3 to 4 mm/a larger values. Within the observation area, similar differences reach − 1.5 mm/a at the northernmost part of Norway and − 1.0 mm/a at the north-western coast of Denmark, but generally within the range of − 0.5 to 0.5 mm/a.

The paper presents a modified formulation of least-squares collocation. This residual least-squares collocation (RLSC) includes a remove–compute–restore procedure with a high-resolution global geopotential model (GGM) and a topographic gravitational potential model. In contrast to previous approaches, in RLSC, the remaining input residuals are modeled with error covariance matrices instead of signal covariance matrices. Therefore, we include the full variance–covariance information of a high-resolution GGM, namely the XGM2016, to the procedure. The included covariance matrices are anisotropic and location-dependent and enable a realistic error modeling of a target area. This fact represents an advantage over covariance matrices derived from signal degree variances or empirical covariance fitting. Additionally, due to the stochastic modeling of all involved components, RLSC provides realistic accuracy estimates. In a synthetic closed-loop test case with a realistic data distribution in the Andes we demonstrate the advantages of RLSC for regional geoid modeling and quantify the benefit which results mainly from a rigorously handled high-resolution GGM. In terms of root mean square deviations from the true reference solution, RLSC delivers an improvement of about 30% compared to a standard LSC approach, where the benefit is particularly pronounced in areas with a sparse data distribution. This improved performance, together with the fact that the resulting stochastic error estimates better reflect the true errors, might be an important aspect for the application of RLSC to derive gravity potential values and their uncertainties at reference stations of the international height reference system.