The tensor invariants (or invariants of tensors) for gravity gradient tensors (GGT, the second-order derivatives of the gravitational potential (GP)) have the advantage of not changing with the rotation of the corresponding coordinate system, which were widely applied in the study of gravity field (e.g., recovery of global gravity field, geophysical exploration, and gravity matching for navigation and positioning). With the advent of gravitational curvatures (GC, the third-order derivatives of the GP), the new definition of tensor invariants for gravitational curvatures can be proposed. In this contribution, the general expressions for the principal and main invariants of gravitational curvatures (PIGC and MIGC denoted as I and J systems) are presented. Taking the tesseroid, rectangular prism, sphere, and spherical shell as examples, the detailed expressions for the PIGC and MIGC are derived for these elemental mass bodies. Simulated numerical experiments based on these new expressions are performed compared to other gravity field parameters (e.g., GP, gravity vector (GV), GGT, GC, and tensor invariants for the GGT). Numerical results show that the PIGC and MIGC can provide additional information for the GC. Furthermore, the potential applications for the PIGC and MIGC are discussed both in spatial and spectral domains for the gravity field.

How to cite: Deng, X.-L., Shen, W.-B., Yang, M., and Ran, J.: Tensor Invariants for Gravitational Curvatures, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-312, https://doi.org/10.5194/egusphere-egu21-312, 2020.

The problem of determining the height anomaly in a local area of the radius ψ₀ using gravity disturbances and gravity anomalies is discussed. The influence of the far zone, as usually, is approximately taken into account using the global gravity field model and the truncation coefficients Q_n (ψ₀) introduced by M.S. Molodensky [1]. The modification Q_n⁰(ψ₀) by O.M. Ostach [2] of these coefficients is described. They provide - in contrast to the original coefficients - the continuity of the used integral transform kernel Ker⁰ (ψ) in the whole its definition domain. As a consequence, the modified coefficients decrease faster compared to the original ones with an increase of the degree n (frequency). It reduces the error of the far zone influence. Coefficients are interpreted as Fourier coefficients of the outer part of the kernel when it is decomposed into the orthogonal system of nonnormalized Legendre polynomials. The relationship between Q_n (ψ₀) and Q_n⁰(ψ₀) is indicated. In the frequency domain, the expression for the truncated kernel ΔKer⁰ (ψ) of the integral transform used (Stokes or Hotine-Koch) differs from the corresponding full kernel by a multiplier, which is proposed to be called the frequency characteristic of the kernel truncation operator onto the inner zone of radius ψ₀.

In local modeling, when describing the details of the "useful signal", it is advisable to use approximation by means of spherical radial basis functions (SRBF) instead of traditional integration due to their good spatial localization [3, 4]. The procedure of constructing scaling functions and corresponding wavelets is briefly described. New scaling functions, based on the above-mentioned concept of frequency characteristic of the kernel truncation operator onto the inner zone of the radius ψ_o, are proposed. To prove the effectiveness of these scaling functions, numerical experiments were conducted. Both gravity anomalies Δg and disturbances δg were used as input data. The results of the calculations showed a high accuracy of recovering height anomalies from gravity anomalies. Besides, introduction of frequency characteristic of kernel truncation of corresponding integral transform onto the inner zone allows to cut off implicit influence of far zone. Known scaling functions that do not use this frequency characteristic lead, as experiments have shown, to biased results.

References:

How to cite: Sugaipova, L. and Neyman, Y.: On frequency response of Stokes and Hotine-Koch integral transforms in calculation of height anomaly in the local area by means of SRBF, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-500, https://doi.org/10.5194/egusphere-egu21-500, 2021.

We presents local gravity field modelling in a spatial domain using the finite element method (FEM). FEM as a numerical method is applied for solving the geodetic boundary value problem with oblique derivative boundary conditions (BC). We derive a novel FEM numerical scheme which is the second order accurate and more stable than the previous one published in [1]. A main difference is in applying the oblique derivative BC. While in the previous FEM approach it is considered as an average value on the bottom side of finite elements, the novel FEM approach is based on the oblique derivative BC considered in relevant computational nodes. Such an approach should reduce a loss of accuracy due to averaging. Numerical experiments present (i) a reconstruction of EGM2008 as a harmonic function over the extremely complicated Earth’s topography in the Himalayas and Tibetan Plateau, and (ii) local gravity field modelling in Slovakia with the high-resolution 100 x 100 m while using terrestrial gravimetric data.

[1] Macák, Z. Minarechová, R. Čunderlík, K. Mikula, The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy. Tatra Mountains Mathematical Publications. Vol. 75, no. 1, 63-80, (2020)

How to cite: Macák, M., Minarechová, Z., Čunderlík, R., and Mikula, K.: Stable finite element method for solving the oblique derivative boundary value problems in geodesy, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2614, https://doi.org/10.5194/egusphere-egu21-2614, 2021.

Similarly as in other branches of engineering and mathematical physics, a transformation of coordinates is applied in treating the geodetic boundary value problem. It offers a possibility to use an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. In our case the Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth and thus also the solution domain substantially differ from a sphere or an oblate ellipsoid of revolution, even if optimally fitted. The situation becomes more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. Applying tensor calculus the Laplace operator is expressed in the new coordinates. However, its structure is more complicated in this case and in a sense it represents the topography of the physical surface of the Earth. The Green’s function method together with the method of successive approximations is used for the solution of the geodetic boundary value problem expressed in terms of the new coordinates. The structure of iteration steps is analyzed and if useful and possible, it is modified by means of integration by parts. Subsequently, the iteration steps and their convergence are discussed and interpreted, numerically as well as in terms of functional analysis.

How to cite: Holota, P. and Nesvadba, O.: Laplacian structure mirroring surface topography in determining the gravity potential by successive approximations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11729, https://doi.org/10.5194/egusphere-egu21-11729, 2021.

The total station-based QDaedalus system, developed in 2014 by ETH Zurich in Switzerland, incorporates a charge-coupled device (CCD) camera in support of daytime geodetic and nighttime astrogeodetic observations. The successful realization of astrogeodetic observations has resulted in astrogeodetic vertical deflection (VD) data collection in Germany, Italy, Hungary, Australia, and Turkey. Astrogeodetic observations carried out in Munich, Germany were used to determine the precision and accuracy of the newly installed QDaedalus system, which was found to be ~0.2 arcseconds for both the North-South (N-S) and East-West (E-W) VD components. In this study, 10 benchmark observations in the Munich region were also used to assess the quality of three global gravity field models—Global Gravitation Model Plus (GGMplus), Earth Residual Terrain Modelled 2160 (ERTM2160) and Earth Gravitational Model 2008 (EGM2008)—through comparison with the QDaedalus observations. The results of these comparisons between the predicted and observed VD data are: (i) The GGMplus predicted VD values were found to be closer to the observed VDs, with the differences for both the N-S and E-W VD components being ~0.2″, and reaching a maximum of 0.3″ and 0.4″ for the N-S and E-W components, respectively; (ii) The ERTM2160 predicted values were also found to be closer to the observed VDs, with differences of 0.4″ or less for the N-S component, with the exception of one benchmark (BM 8), and 0.2″ or less for the E-W component, with the exception of one benchmark (BM 9); and, (iii) When the predicted VDs computed using EGM2008 were analysed, we found that they were less accurate than the predicted GGMplus and ERTM2160 values. Therefore, the maximum differences between the observed and EGM2008 predicted VD data were for 0.9″ N-S and 1.8″ for E-W. Finally, we conclude with a comparison of the results of this Munich Region study with the results of a prior QDaedalus study, which was conducted in Istanbul (Albayrak et al. 2020), to assess the accuracy of the EGM2008 and GGMplus models.

Albayrak, M., Hirt, C., Guillaume, S., Halicioglu, K., Özlüdemir, M.T., Shum, C.K., 2020. Quality assessment of global gravity field models in coastal zones: a case study using astrogeodetic vertical deflections in Istanbul, Turkey, Studia Geophysica et Geodaetica, 64(3), 306–329. doi: 10.1007/s11200-019-0591-2

How to cite: Albayrak, M., Hirt, C., Guillaume, S., Shum, C., Bevis, M., Zeray Öztürk, E., and Bildirici, I. Ö.: Validations of Three Global Gravity Field Models Using the QDaedalus System Observed Astrogeodetic Vertical Deflections in the Munich Region, Germany, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-128, https://doi.org/10.5194/egusphere-egu21-128, 2020.

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational potential or gravitational gradients with uniform quality and a near-global coverage. More than three years of the outstanding measurements resulted in two levels of data products (Level 1b and Level 2), six releases of global gravitational models (GGMs), and several grids of gravitational gradients (see, e.g., ESA-funded GOCE+ GeoExplore project or Space-wise GOCE products). The grids of gravitational gradients represent a step between gravitational gradients measured directly along the GOCE orbit and data directly from GGMs. One could use grids of gravitational gradients for geodetic as well as for geophysical applications. In this contribution, we are going to validate the official Level 2 product GRD_SPW_2 by terrestrial gravity disturbances and GNSS/levelling over two test areas located in Europe, namely in Norway and former Czechoslovakia (now Czechia and Slovakia). GRD_SPW_2 product contains all six gravity gradients at satellite altitude from the space-wise approach computed only from GOCE data for the available time span (r-2, r-4, and r-5) and provided on a 0.2 degree grid. A mathematical model based on a least-squares spectral weighting will be developed and the corresponding spectral weights will be presented for the validation of gravitational gradients grids. This model allows us to continue downward gravitational gradients grids to an irregular topographic surface (not to a mean sphere) and transform them into gravity disturbances and/or geoidal heights in one step. Before we compared results obtained by spectral downward continuation, we had to remove the high-frequency part of the gravitational signal from terrestrial data because in gravitational gradients measured at GOCE satellite altitude is attenuated. To do so we employ EGM2008 up to d/o 2160 and the residual terrain model correction (RTC) has been a) interpolated from ERTM2160 gravity model, b) synthesised from dV_ELL_Earth2014_5480_plusGRS80, c) calculated from a residual topographic model by forward modelling in the space domain.  

How to cite: Pitoňák, M., Šprlák, M., Ophaug, V., Omang, O., and Novák, P.: Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting   , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1112, https://doi.org/10.5194/egusphere-egu21-1112, 2021.

Model-based hydrodynamic leveling allows transferring heights between tide gauges by means of model-derived mean water level (MWL) differences between them. In this study, we aim to exploit the technique to improve the quality of the European Vertical Reference Frame (EVRF). In doing so, the candidate tide gauges must fulfill two criteria. First, they must be connected to the Unified European Leveling Network (UELN). Second, the hydrodynamic model to be used should be capable of resolving the local MWL at the tide gauge locations. The latter can be very challenging as some tide gauges are located in areas with complicated hydrodynamic processes. To identify which tide gauges have the largest impact on the quality of the EVRF, we conducted geodetic network analyzes. Here we used all tide gauges within 10 km of UELN height markers. Moreover, we assumed to have access to a hydrodynamic model covering all European seas, or alternatively regional models for separate basins, providing the MWLs with uniform precision. Our results indicate a reduction of the mean propagated standard deviation of the adjusted heights between 20% to 40% compared to the UELN-only solution. The magnitude of the improvement depends on the setup of the experiment and the selected noise level for model-derived MWL differences. Detailed analysis shows that we already obtain a significant improvement (>20%) by adding only a limited number of hydrodynamic leveling connections. Moreover, we found that the tide gauges located in the countries with the most UELN height markers are most profitable in terms of improvement. The impact hardly depends on the tide gauges' geographic location, which shows the method's freedom and flexibility in selecting the tide gauges.

How to cite: Afrasteh, Y., Slobbe, C., Verlaan, M., Sacher, M., Klees, R., Guarneri, H., Keyzer, L., Pietrzak, J., Snellen, M., and Zijl, F.: Towards tide gauges selection for model-based hydrodynamic leveling connections; with application to assess the potential impact on the quality of the European Vertical Reference Frame, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12598, https://doi.org/10.5194/egusphere-egu21-12598, 2021.

In data mining, outliers can lead to misleading interpretations of statistical results, particularly in deformation monitoring based on fluctuations and disturbances simulated by numerical models for the analysis of deformations. Therefore, outlier filtering cannot be ignored in data standardization. However, it is not likely that a filtering algorithm is efficient for every data pattern. We investigate five outlier filtering algorithms using MATLAB® (Release 2020a): moving average, moving median, quartiles, Grubbs, and generalized extreme Studentized deviation (GESD) to select the optimal algorithms applied for GNSS time series data. This study is conducted on two types of data used for ionosphere disturbance analysis in the region of the Ring of Fire and crustal deformation monitoring in Germany, one showing seasonal time series patterns and the other presenting the trend models. We apply the simple random sampling method that ensures the principles of unbiased surveying techniques. The optimal algorithm selection is based on the sensitivity of outlier detection and the capability of the central tendency measures. The algorithm robustness is also tested by altering random outliers but maintaining the standard distribution of each dataset. Our results show that the moving median algorithm is most sensitive for outlier detection because it is robust statistics and is not affected by anomalies; followed in turn by quartiles, GESD, and Grubbs. The outlier filtering capability of the moving average algorithm is least efficient, with a percentage of outlier detection below 20% compared to the moving median (corresponding 95% probability). In deformation analysis, disturbances on numerical models are often the basis for motion assessment, while these anomalies are smoothed by moving median filtering. Hence, the quartiles algorithm can be considered in this case. Overall, the moving median is best suited to filter outliers for seasonal and trend time series data; in particular, for deformation analysis, the optimal solution is applying the quartiles or extending the threshold factor and the sliding window of the moving median.

Keywords: Outlier filtering, Time series, Deformation analysis, Moving median, Quartiles, MATLAB.

How to cite: Le Thi, N., Männel, B., Jarema, M., Krishna Seemala, G., Heki, K., and Schuh, H.: Selection of an optimal algorithm for outlier detection in GNSS time series, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1598, https://doi.org/10.5194/egusphere-egu21-1598, 2021.

Best integer equivariant (BIE) estimators provide minimum mean squared error (MMSE) solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Their accuracy is therefore always better or the same as that of Integer Least-Squares (ILS) estimators and Best Linear Unbiased Estimators (BLUEs).

Current theory is based on using BIE for the multivariate normal distribution. In this contribution this will be generalized to the contaminated normal distribution and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution. In addition a GNSS real-data based analysis is carried out to demonstrate the universal MMSE properties of the BIE estimators for GNSS-baselines and associated parameters.

Keywords: Integer equivariant (IE) estimation · Best integer equivariant (BIE) · Integer Least-Squares (ILS) . Best linear unbiased estimation (BLUE) · Multivariate contaminated normal · Multivariate t-distribution . Global Navigation Satellite Systems (GNSSs)

How to cite: Teunissen, P.: Theory of best integer equivariant estimation for contaminated normal and multivariate t-distribution with applications, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2027, https://doi.org/10.5194/egusphere-egu21-2027, 2021.

The individual space geodetic techniques have different advantages and disadvantages. For instance, the global observing network of Very Long Baseline Interferometry (VLBI) consists of much fewer stations with a poorer distribution than the one of Global Navigation Satellite Systems (GNSS). In a combination thereof, this fact can be compensated, mainly to the benefit of the former.

The sensitivity level provides information on the detection capacity of observing stations based on undetectable gross errors in a geodetic network solution. Furthermore, sensitivity can be understood as the minimum value of the undetectable gross errors by hypothesis testing. The location of the station in the network and the total weight of its observations contribute to the sensitivity levels thereof. Also, the total observation number of a radio source and the quality of the observations are critical for the sensitivity levels of the radio sources. Besides these criteria, a radio source having a larger structure index has a larger sensitivity level. In this study, it is investigated whether the sensitivity levels of VLBI stations in the CONT14 campaign improve by combination with GNSS. The combination was done at the normal equation level using 153 GNSS stations in total, 17 VLBI radio telescopes, and local ties at 5 co-located stations which are ONSA-ONSALA60, NYA1-NYALES20, ZECK-ZELENCHK, MATE-MATERA, and HOB2-HOBART26 during the CONT14 campaign spanning 15 days. To evaluate the observations of GNSS and VLBI, the software of EPOS8 and VieVS@GFZ (G2018.7, GFZ, Potsdam, Germany) were used respectively. In the VLBI-only solution, FORTLEZA shows the poorest sensitivity level compared to the other VLBI radio telescopes. As a result of the combination with GNSS, it can be seen that the sensitivity levels of FORTLEZA improved by about 60% in all sessions of CONT14. It can be concluded that VLBI stations, which are poorly controlled by the other radio telescopes in the network, can be supported by the other space geodetic techniques to improve the overall quality of the solution.

How to cite: Küreç Nehbit, P., Glaser, S., Balidakis, K., Sakic, P., Heinkelmann, R., Schuh, H., and Konak, H.: Improving the sensitivity levels generated from hypothesis testing by combining VLBI with GNSS data, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3116, https://doi.org/10.5194/egusphere-egu21-3116, 2021.

The classification of vertical displacements and the estimation of a local geometric geoid model and coordinate transformation were recently solved by the L² support vector machine and support vector regression. The L^p quasi-norm SVM and SVR (0<p<1) is a non-convex and non-Lipschitz optimization problem that has been successfully formulated as an optimization model with a linear objective function and smooth constraints (LOSC) that can be solved by any black-box computing software, e.g., MATLAB, R and Python. The aim of this talk is to show that interior-point based algorithms, when applied correctly, can be effective for handling different LOSC-SVM and LOSC-SVR based models with different p values, in order to obtain better sparsity regularization and feature selection. As a comparative study, some artificial and real-life geoscience datasets are used to test the effectiveness of our proposed methods. Most importantly, the methods presented here can be used in geodetic classroom teaching to benefit our undergraduate students and further bridge the gap between the applications of geomatics and machine learning.

How to cite: Wong, J. C. F. and Yu, T. F.: Lp LOSC-Support Vector Machines for Regression Estimation and their Application to Geomatics, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1765, https://doi.org/10.5194/egusphere-egu21-1765, 2021.

Global mean sea level is rising at an increasing rate. It is expected to cause more frequent extreme events on coastal sites. The main sea level monitoring systems are conventional tide gauges and satellite altimeters. However, tide gauges are few and satellite altimeters do not work well near the coasts. Ground-based GNSS Reflectometry (GNSS-R) is a promising alternative for coastal sea level measurements. GNSS-R works as a bistatic radar, based on the use of radio waves continuously emitted by GNSS satellites, such as GPS and Galileo, that are reflected on the Earth’s surface. The delay between reflected and direct signals, known as interferometric delay, can be used to retrieve geophysical parameters, such as sea level. One advantage of ground-based GNSS-R is the slant sensing direction, which implies the reflection points can occur at long distances from the receiving antenna. The higher is the receiving antenna and the lower is the satellite elevation angle, the longer will be the distance to the reflection point. The geometrical modeling of interferometric delay, in general, adopts a planar and horizontal model to represent the reflector surface. This assumption may be not valid for far away reflection points due to Earth’s curvature. It must be emphasized that ground-based GNSS-R sensors can be located at high altitudes, such in lighthouses and cliffs, and GNSS satellites are often tracked near grazing incidence and even at negative elevation angles. Eventually, Earth’s curvature would have a significant impact on altimetry retrievals. The osculating spherical model is more adequate to represent the Earth’s surface since its mathematical complexity is in between a plane and an ellipsoid. The present work aims to quantify the effect of Earth’s curvature on ground-based GNSS-R altimetry. Firstly, we modeled the interferometric delay for each plane and sphere and we calculated the differences across the two surface models, for varying satellite elevation and antenna altitude. Then, we developed an altimetry correction in terms of half of the rate of change of the delay correction with respect to the sine of elevation. We simulated observation scenarios with satellite elevation angles from zenith down to the minimum observable elevation on the spherical horizon (negative) and antenna altitudes from 10 m to 500 m. We noted that due to Earth’s curvature, the reflection point is displaced, brought closer in the x-axis and bent downward in the y-axis. The displacement of the reflection point increases the interferometric delay. Near the planar horizon, at zero elevation, the difference increases quickly and so does the altimetry correction. Finally, considering a 1-cm altimetry precision threshold to sea-level measurements, we observed that the altimetry correction for Earth’s curvature is needed at 10°, 20°, and 30° satellite elevation, for an antenna altitude of 60 m, 120 m, and 160 m, respectively.

How to cite: Almeida Junior, V. H., Matsuoka, M. T., and Geremia-Nievinski, F.: Impact of Earth's curvature on coastal sea level altimetry with ground-based GNSS Reflectometry, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8511, https://doi.org/10.5194/egusphere-egu21-8511, 2021.

Observing coastal sea-level change from satellite altimetry is challenging due to land influence on the estimated sea surface height (SSH), significant wave height (SWH), and backscatter. In recent years specialized algorithms have been developed which allow retrieving meaningful estimates up to the coast. Among these, the Spatio Temporal Altimetry Retracker (STAR) has introduced a novel approach by partitioning the total return signal into individual sub-signals which are then processed leading to a point-cloud of potential estimates for each of the three parameters which tend to cluster around the true values, e.g., the real sea surface. The original STAR algorithm interprets each point-cloud as a weighted directed acyclic graph (DAG). The spatio-temporal ordering of the potential estimates induces a layering, and each layer is fully connected to the next. The weights of the edges are based on a chosen distance measure between the connected vertices. The STAR algorithm selects the final estimates by searching the shortest path through the DAG using forward traversal in topological order. This approach includes the inherent assumption that neighboring SSHs etc. should be similar. However, a drawback of the original STAR approach is that each of the point clouds for the three parameters can only be treated individually since the applied standard shortest path approach can not handle multiple edge weights. Therefore, the output of the STAR algorithm for each parameter does not necessarily correspond to the same sub-signal. To overcome this limitation, we propose to employ a multicriteria approach to find a final estimate that takes the weighting of two or three point-clouds into account resulting in the multicriteria Spatio Temporal Altimetry Retracking (mSTAR) framework. An essential difference between the single and the multicriteria shortest path problems is that there is no single optimal solution in the latter. We call a path Pareto-optimal if there is no other path that is strictly shorter for all criteria. Unfortunately, the number of Pareto-optimal paths can be exponential in the input size, even if the considered graph is a DAG. A simple and common approach to tackle this complexity issue is to use the weighted sum scalarization method, in which the objective functions are weighted and combined to a single objective function, such that a single criteria shortest path algorithm can find a Pareto-optimal path. Varying the weighting, a set of Pareto-optimal solutions can be obtained. However, it is in general not possible to find all Pareto-optimal paths this way. In order to find all Pareto-optimal paths, label-correcting or label-setting algorithms can be used. The mSTAR framework supports both scalarization and labeling techniques as well as exact and approximate algorithms for computing Pareto-optimal paths. This way mSTAR is able to find multicriteria consistent estimates of SSH, SWH, and backscatter.

How to cite: Oettershagen, L., Uebbing, B., Charfreitag, J., Mutzel, P., and Kusche, J.: mSTAR: Multicriteria Spatio Temporal Altimetry Retracking, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9504, https://doi.org/10.5194/egusphere-egu21-9504, 2021.

The nature, the age and probably first of all the magnitude of driving forces of plate motion since long are a subject of scientific debates and it cannot be regarded as clarified even today.

The physical basis of recent plate tectonics is characterized by interaction between plates by viscous coupling to a convecting mantle.  Authors are going to demonstrate that changes in the Earth's axial rotation can affect the movement of tectonic plates, and the phenomenon of tidal friction is able to shift the lithospheric plates.

The tidal friction regulates the length of day (LOD)and consequently also the rotational energy of the Earth. It can be investigated with the use of total tidal energy_, which can be determined as a sum of three energies (energy of axial rotation of the Earth, Moon’s orbital energy around the common centre of mass and the mutual potential energy). It was found that during the last 3 Ga the Earth lost 33% of its rotational energy. The LOD 0.5Ga BP (before present) was ~21 h. This means that the rotational energy loss rate was 4.1 times higher during the Pz (Phanerozoic, from 560 Ma BP to our age) than earlier in the Arch (Archean, 4 to 2.5 Ga BP) and Ptz (Proterozoic 2.5 to0.56 Ga BP). The low-velocity zone (LVZ) at 100-200 km depth interval, close to the boundary between the lithosphere and the asthenosphere characterized by a negative anomaly of shear wave velocities. Consequently, the LVZ can result in a decoupling effect. Tidal friction brakes the lithosphere and the part of the Earth below the asthenosphere with different forces. By model calculation, we show that this force difference is sufficient to move the tectonic plates along the Earth’s surface.  

Reference: Varga P., Fodor Cs., 2021. About the energy and age of the plate tectonics, Terra Nova. (in print) https://doi.org/10.1111/ter.12518

How to cite: Fodor, C. and Varga, P.: Modelling moving force of tectonic plates with the use of length of day variation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8401, https://doi.org/10.5194/egusphere-egu21-8401, 2021.

Earth deformation caused by the tidal redistribution of ocean mass is governed by the material properties of Earth's interior. Surface displacements induced by ocean tidal loading can exceed several centimeters over periods of hours. The rich spectrum of elastic and gravitational responses of the solid Earth produced by the load tides are predominantly sensitive to crust and upper-mantle structure, and inverting load-tide observations for Earth structure can complement independent constraints inferred from seismic tomography and Earth's body tides. 

Global Navigation Satellite Systems (GNSS) record the load-tide displacements with sub-millimeter precision and at high temporal resolution on the order of minutes. Recent studies have demonstrated agreement between predicted and GNSS-observed oceanic load tides in several regions worldwide to a similar level of accuracy. However, residuals between load-tide observations and predictions, which have been limited to spherically symmetric models for Earth structure, exhibit spatially coherent patterns that cannot be fully explained by random measurement or tide-model error and therefore present key opportunities to refine our understanding of Earth's 3-D structure at depths important to mantle convection and plate tectonics. 

Here, we present a novel numerical approach based on a preconditioned conjugate-gradient solver and the spectral-element method to investigate the sensitivities of Earth's load tides to 3-D variations in elastic Earth structure, including ellipticity, topography, and lateral contrasts in elasticity, density and crustal thickness. We leverage and extend the Salvus high-performance library to include gravitational physics and to solve quasi-static problems. High-order shape transformations and adaptive mesh refinement allow us to capture the spatial heterogeneity of the ocean tides with kilometer resolution as well as the large scale of exterior domain, which is needed to model the gravitational potential at reasonable computational cost. We perform a series of benchmark tests to verify the 3-D numerical-modeling approach against established quasi-analytical methods for modeling load-induced Earth deformation (LoadDef software). We then compute the sensitivities of load-induced surface displacements to 3-D Earth structure in two ways: (1) direct comparison of predicted surface displacements computed using 1-D and 3-D Earth models, and (2) direct computation of derivatives of surface displacements with respect to density and elasticity structure using the adjoint method.

Additional high-impact applications of the surface-load modeling capabilities include: quantifying seasonal fluctuations in mountain snowpack, tracking the depletion of groundwater reservoirs during periods of drought, improving constraints on ocean-tide models and refining the load-tide corrections employed in GNSS signal processing.

How to cite: Martens, H. R., Boehm, C., van Driel, M., and Khan, A.: Load-Tide Sensitivity to 3-D Earth Structure, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3636, https://doi.org/10.5194/egusphere-egu21-3636, 2021.