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Several geoid models have been developed to convert geodetic heights measured by the Global Navigation Satellite Systems (GNSS) to heights in the Hong Kong Principal Datum (HKPD). Although gravity measurements were used to compile these geoid models, heights of levelling benchmarks in HKPD were determined from precise spirit levelling measurements but without involving gravity data. To address these inconsistencies, the orthometric heights of HKPD levelling benchmarks were determined from levelling and gravity data. Moreover, the new geoid model HKGEOID-2022 was computed and fitted with the geometric geoid heights at GNSS-levelling benchmarks derived from newly determined orthometric heights. Numerical procedures used to prepare the HKGEOID-2022 geoid are discussed in this study. A gravimetric geoid was computed adopting the KTH method. A systematic bias between the gravimetric and geometric geoid heights at GNSS-levelling benchmarks was modelled and reduced by applying a 7-parameter similarity transformation. The accuracy analysis revealed that the resulting detailed geoid model HKGEOID-2022 fits the geometric geoid heights with a standard deviation of ±2.2 cm. This accuracy is compatible with the estimated uncertainties of GNSS measurements as well as with the expected accuracy of a newly developed geoid model, both at the level of approximately ±1–2 cm., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

Mapping of the Moho geometry could serve as an effective tool for visualization of the tectonic features/processes and their interactions beneath a region of interest. In this study, we employed a high-resolution (25′′×25′′ grid) tailored Bouguer gravity data to explore the mechanisms of tectonism beneath a highly rifted continental plate of the Southeastern Nigeria. Hence, we separated the Bouguer gravity data into shallow (high-pass) and deep (low-pass) gravity signals before carrying out gravimetric inversion. To obtain suitable estimates of gravimetric inversion parameters (reference depth and density contrast), we numerically computed and stochastically evaluated a seismically and our gravimetrically determined crustal thickness until a minimum RMS of their differences was achieved. Our obtained crustal thickness data range from 22 to 36 km with a stochastically determined optimal reference depth of 26 km and density contrast of 0.45gcm-3. The crustal thickness map reveals a dense magmatic feature traversing the central portion of the study area in northeastern, southeastern, and southwestern directions leading to the thinning of the crust in those regions. We have been also able to refine and depict the lateral extent of the different sub-basins, ridges, crustal architecture, and the geophysical processes (magmatism, faulting/fracturing, mantle uplift, crustal thinning/thickening) of continental separation within the study area from our crustal thickness map. Considering the fine-scale discontinuity and continuity of tectonism revealed in our crustal thickness map, we conclude that a narrowing of two or more conjugate plates might have mainly occasioned those visible and complex geophysical phenomena., The 28th IUGG General Assembly (IUGG2023) (Berlin 2023)

This paper deals with the validation of gravity gradients measured by GOCE using terrestrial data measured in the Czech Republic and Slovakia. In our study, we test the quality of the official GOCE Level 2 product called GRD_SPW_2 and GOCE + Geoxplore II. These are gravitational gradients in a local north-oriented frame at a regular grid at mid-altitude corresponding to the GOCE orbit. These gradients are continued to the points on the Earth's surface at which the gravity measurements were performed and then transformed into gravity failures using the spectral combination method. Since the satellite data contain only band limited information about the Earth's gravity field, a direct comparison with the values ​​measured on the Earth's surface would be incorrect. Therefore, before comparing, we removed from the teresetrial gravity data a shortwave component corresponding to the spherical degrees 250-2190 from the global gravitational potential model EGM2008 and degrees above 2190 were calculated using a residual terrain model.

Odhadujeme elastickou tloušťku kontinentální litosféry pomocí dvou přístupů, které kombinují regionální izostatický princip podle Vening Meinesz-Moritz (VMM) s isostatickými modely pružnosti formulovanými na základě řešení diferenciálních rovnic pro tenký elastický plášť s a bez uvažování zakřivení elastického pláště. Abychom modelovali odezvu litosféry na zátěž realističtěji, uvažujeme také heterogenity hustoty litosféry. Výsledné výrazy popisují funkční vztah mezi veličinami gravitačního pole a mechanickými vlastnostmi litosféry, jmenovitě Youngovým modulem a Poissonovým poměrem, které jsou vypočteny z modelů seismické rychlosti před odhadem efektivní tloušťky litosféry. Naše numerická studie v centrální Eurasii ukazuje, že oba výsledky mají podobný prostorový vzor, ​​přestože vykazují i ​​některé velké lokalizované rozdíly v důsledku nezohlednění zakřivení elastického pláště. Výsledky ukazují, že cratonické útvary severočínské a tarimské krátery, turánské platformy a části sibiřského kráteru jsou charakterizovány maximální tloušťkou litosférické vrstvy. Na druhé straně indický Craton se jasně neprojevuje. Minima elastické tloušťky typicky odpovídají místům aktivních kontinentálních tektonických okrajů, hlavních orogenů (Tibet, Himaláje a části středoasijského orogenního pásu) a rozšířené kontinentální kůry. Tato zjištění obecně podporují hypotézu, že tektonicky aktivní zóny a orogeny mají relativně malou litosférickou sílu, což má za následek významnou reakci litosféry na různé tektonické zátěže ve srovnání s velkou litosférickou silou cratonických útvarů. We estimate the elastic thickness of a continental lithosphere by using two approaches that combine the Vening Meinesz-Moritz (VMM) regional isostatic principle with isostatic flexure models formulated based on solving flexural differential equations for a thin elastic shell with and without considering a shell curvature. To model the response of the lithosphere on a load more realistically, we also consider lithospheric density heterogeneities. Resulting expressions describe a functional relation between gravity field quantities and mechanical properties of the lithosphere, namely Young's modulus and Poisson's ratio that are computed from seismic velocity models in prior of estimating the lithospheric elastic thickness. Our numerical study in central Eurasia reveals that both results have a similar spatial pattern, despite exhibiting also some large localized differences due to disregarding the shell curvature. Results show that cratonic formations of North China and Tarim Cratons, Turan Platform as well as parts of Siberian Craton are characterized by the maximum lithospheric elastic thickness. Indian Craton, on the other hand, is not clearly manifested. Minima of the elastic thickness typically correspond with locations of active continental tectonic margins, major orogens (Tibet, Himalaya and parts of Central Asian Orogenic Belt) and an extended continental crust. These findings generally support the hypothesis that tectonically active zones and orogens have a relatively small lithospheric strength, resulting in a significant respond of the lithosphere on various tectonic loads, compared to a large lithospheric strength of cratonic formations.

V tomto príspevku sa diskutuje o regionálnom modelovaní tiažových porúch na strednej geocentrickej sfére blížiacej sa k Zemi v oblasti strednej Európy zo satelitných gravitačných gradientov. Hlavným cieľom tejto štúdie je preskúmať tri numerické prístupy na zníženie vplyvu vzdialených zón pri riešení inverznej gradiometrickej úlohy. Prvý prístup je založený na modifikácii integrálnych vzorcov, t.j., individuálne riešime príspevky v blízkej a vzdialenej zóne. Druhý prístup je jednoduchá modifikácia prvého scenára vyhladením meraných gravitačných gradientov pomocou gravitačného účinku topografických hmôt. V poslednom prístupe, ktorý sa tu nazýva tretí scenár, uplatňujeme dodatočnú úpravu vyhladením gravitačných gradientov o referenčný globálny geopotenciálny model. Pri všetkých troch prístupoch odhadujeme tiažové poruchy každého zo štyroch dobre meraných gravitačných gradientov oddelene, ako aj ich kombinácie. Naše regionálne riešenia gravitačných polí sú založené na gravitačných gradientoch GOCE EGG TRF 2 meraných v období od 1. novembra 2009 do 11. januára 2010. Ako celková referencia bol zvolený model EGM2008. Najlepšia zhoda z týmto modelom bola dosiahnutá pomocou druhého prístupu a komponentu Tzz (RMS 4,4 mGal). In this contribution we discuss a regional recovery of gravity disturbances at the mean geocentric sphere approximating the Earth over the area of Central Europe from satellite gravitational gradients. The main aim of the presented study is to investigate three numerical approaches for reducing the far zone effect for solving an inverse problem. The initial approach is based on the modification of the integral formulas, i. e., we are solving individually the near- and distant-zone contributions. The second approachis a simple modification of the first scenario by reducing measured gravitational gradients for gravitational effects of topographic masses. In the last approach called herein as the third scenario, we apply additional modification by reducing gravitational gradients for the reference global geopotential model. In all three approaches we estimate the gravity disturbances from each of the four well-measured gravitational gradients separately as well as from their combination. Our regional gravity field solutions are based on the GOCE EGG TRF 2 gravitational gradients collected within the period from November 1 2009 until January 11 2010. As an overall reference we choose EGM2008. The best fit, in terms of RMS (4.4 mGal), is achieved using a second approach and Tzz.

We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measurements from the GNS Science gravity database (onshore). The GGM coefficients are taken from EIGEN-GRACE02S complete to degree 65 of spherical harmonics. The topographic heights are generated from the 1×1 arc-sec detailed digital terrain model (DTM) of New Zealand and from the 30×30 arc-sec global elevation data of SRTM30_PLUS V5.0. The least-squares analysis is applied to combine the gravity and GPS-levelling data using a 7-parameter model. The fit of the KTH geoid model with GPS-levelling data in New Zealand is 7 cm in terms of the standard deviation (STD) of differences. This STD fit is the same as the STD fit of the NZGeoid2009, which is the currently adopted official quasigeoid model for New Zealand. Naujosios Zelandijos geoido modelio vertinimas KTH metodu Santrauka.Stokholmo Karališkajame technologijos institute (KTH) sukurtu metodu apskaičiuotas naujas Naujosios Zelandijos ir kontinentinio šelfo geoido modelis. Taikoma Stokso integralo mažiausiųjų kvadratų modifikacija, įvertinant paklaidas ir jų nevertinant bei ieškant optimalių stochastinių sprendinių. Modifikuotas Bruno ir Stokso integralas sieja regioninius žemyninius gravimetrinius duomenis su globaliuoju geopotencialo modeliu (GGM). Gravimetriniam geoidui gauti skaičiuojamos keturios papildomos pataisos: topografinės situacijos ir atmosferos tiesioginės ir netiesioginės įtakos, redukcijos įtakos ir Stokso integralo taikymo sferiniam paviršiui. Gravimetrinis geoido modelis apskaičiuotas pagal du duomenų rinkinius:DNSC08 jūrinių gravimetrinių duomenų bazėje (šelfas) esančias altimetriniu metodu nustatytas sunkio pagreičio anomalijas ir žemyninės dalies gravimetrinių matavimų duomenis iš GNS gravimetrinės duomenų bazės (pakrantė). GGM koeficientai imti išEIGEN-GRACE02S modelio sferinių iki 65 laipsnio harmonikų. Topografiniai aukščiai sugeneruoti iš Naujosios Zelandijos 1×1 sekundės detaliojo skaitmeninio reljefo modelio ir iš 30×30 sekundžių globaliojo aukščių modelioSRTM30_PLUSV5.0. Gravimetriniams irGPSniveliacijos duomenims sujungti taikytas mažiausiųjų kvadratų 7 parametrų metodas. KTH metodu sudaryto geoido modelio vidutinė kvadratinė paklaida 7 cm. Tai sutampa suNZGeoid2009 geoido modelio, taikomo Naujoje Zelandijoje, tikslumu. Reikšminiai žodžiai: geoidas,gravimetrija,mažiausiųjų kvadratų metodas,Stokso integralas,UDK 528.21. Оценка модели геоида Новой Зеландии с применением метода КТН Резюме.Модель геоида континентального шельфа Новой Зеландии построена с применением метода, созданного в Королевском технологическом институте Стокгольма. Данный метод основан на модификации решения интеграла Стокса методом наименьших квадратов с оценкой или без оценки погрешностей и поиском оптимальных статистических решений. Модифицированный интеграл БрунаСтокса объединяет региональные надземные гравиметрические данные с глобальной геопотенциальной моделью (GGM).Для определения гравиметрического геоида вычисляются дополнительные поправки прямого и косвенного влияния топографии и атмосферы, редукции и применения проблемы Стокса для сферической поверхности. Гравиметрическая модель геоида вычисляется на основе двух баз данных: альтиметрическим методом определенных аномалий силы тяжести в базе морских гравиметрических данных DNSC08 (шельф) и надземной части гравиметрических измерений из базы данных GNS. Коэффициенты GGM взяты из сферических гармоник до 65 степени модели EIGENGRACEO2S. Топографические высоты сгенерированы из детальной цифровой модели рельефа Новой Зеландии с сеткой 1×1 секунду и из глобальной модели высот SRTM30_PLUSv5.0 с сеткой 30×30 секунд. Для объединения гравиметрических и GPSнивелирных данных применялся метод наименьших квадратов с 7 параметрами. Среднеквадратическая погрешность модели геоида, созданной по методу КТН, равна 7 см. Точность аналогична точности применяемой в Новой Зеландии модели геоида NZGeoid2009. Ключевые слова:геоид,гравиметрия,способ наименьших квадратов,интеграл Стокса,УДК 528.21. First published online: 15 Apr 2011