A method for describing the uncertainty in geophysical models

Geophysical models are more and more complex and can describe, in a very careful way, the geodynamical processes. These models depend on several geometrical and physical parameters, which characterize the models behaviour. These parameters are not errorless since they are known with some uncertainties. Thus, model predictions are affected by these parameter uncertainties. Usually, the model errors are not taken into account and are not propagated to the estimated quantities. This can cause improper hypothesis testing when geodetic data and model predictions are compared. In this paper, a method is presented which allows considering the model errors through the definition of the spatial covariance function of the model. A simulation is set up to prove the method feasibility

The worldwide physical height datum project

AbstractThe definition of a common global vertical coordinate system is nowadays one of the key points in Geodesy. With the advent of GNSS, a coherent global height has been made available to users. The ellipsoidal height can be obtained with respect to a given geocentric ellipsoid in a fast and precise way using GNSS techniques. On the other hand, the traditional orthometric height is not coherent at global scale. Spirit levelling allows the estimation of height increments so that orthometric heights of surveyed points can be obtained starting from a benchmark of known orthometric heights. As it is well known, this vertical coordinate refers to the geoid, which is assumed to be coincident to the mean sea level. By means of a tide gauge, the mean sea level is estimated and thus a point of known orthometric height is defined. This assumption, which was acceptable in the past, became obsolete given the level of precision which is now required. Based on the altimetry observation, one can precisely quantify the existing discrepancy between geoid and mean sea level that can amount to 1 ÷ 2 m at global scale. Therefore, different tide gauges provide biased estimates of the geoid, given the discrepancy between this equipotential surface and the mean sea level. Also, in the last years, another vertical coordinate was used, the normal height that was introduced in the context of the Molodensky theory. In this paper, a review of the existing different height systems is given and the relationships among them are revised. Furthermore, an approach for unifying normal height referring to different tide gauges is presented and applied to the Italian test case. Finally, a method for defining a physical height system that is globally coherent is discussed in the context of the definition of the International Height Reference System/Frame, a project supported by the Global Geodetic Observing System of the International Association of Geodesy (IAG). This project was established in 2015 during the XXVI IAG General Assembly in Prague as described in IAG Resolution no. 1 that was presented and adopted there

GNSS methods in dam monitoring: case studies and future perspectives

GNSS receivers are nowadays commonly used in monitoring applications, e.g. in estimating crustal and infrastructure deformations. This is basically due to the recent improvements in GNSS instruments and methodologies that allow high precision positioning, 24h availability, semiautomatic data processing. In this paper, we use GNSS technique to monitor dam deformation behaviour comparing results with outcomes from pendulum observations that thanks to their reliability and high accuracy can be considered as reference. The study has been carried out for two dams in Sardinia: the Genna Is Abis on Rio Cixerri, and the Eleonora D’Arborea called also Cantoniera dam. Appropriate analytical models of dam deformation depending on time, reservoir water level, air and water temperature have been estimated using pendulum data (for Genna Is Abis dam) and GNSS data (for Cantoniera dam). Both reference models were able to properly fit respectively pendulum data and GNSS data, with standard deviation of residuals lower than one millimeter. Furthermore the Genna Is Abis reference deformation model deduced by pendulum was compared with estimated displacement from GNSS observations and standard deviation of the residuals was still lower than one millimeter. For the send model estimated at Cantoniera dam the comparison with pendulum data gave residual with mean around zero and standard deviation of lower than two millimiter. These encouraging outcomes open new perspectives in the study of deformations of structures that foresee the GNSS technique as complementary monitoring instrumentation especially for medium-long time intervals

Vision-Based Georeferencing of GPR in Urban Areas

Ground Penetrating Radar (GPR) surveying is widely used to gather accurate knowledge about the geometry and position of underground utilities. The sensor arrays need to be coupled to an accurate positioning system, like a geodetic-grade Global Navigation Satellite System (GNSS) device. However, in urban areas this approach is not always feasible because GNSS accuracy can be substantially degraded due to the presence of buildings, trees, tunnels, etc. In this work, a photogrammetric (vision-based) method for GPR georeferencing is presented. The method can be summarized in three main steps: tie point extraction from the images acquired during the survey, computation of approximate camera extrinsic parameters and finally a refinement of the parameter estimation using a rigorous implementation of the collinearity equations. A test under operational conditions is described, where accuracy of a few centimeters has been achieved. The results demonstrate that the solution was robust enough for recovering vehicle trajectories even in critical situations, such as poorly textured framed surfaces, short baselines, and low intersection angles

Experimental Charge Density of α-Glycine at 23 K

The electrostatic properties of crystals of α-glycine have been obtained from extensive X-ray diffraction data collected at approximately 23 K and carefully processed, including corrections for scan truncation losses, anisotropic extinction, and multiple reflection. From a multipole parameterization of the X-ray intensities we have obtained an unusually precise - and we are confident, accurate - model of the total electron distribution in the crystal including the topological features, atom and group charges, the dipole moment for the glycine zwitterion, electrostatic potentials, electric field gradients at the nucleii of the three hydrogen atoms of the ammonium group, and intermolecular electrostatic energies within the crystal. We have also calculated the total interaction energies involving the six distinct types of intermolecular pairings and examined these energies in terms of the molecular arrangement

THE COMPUTATION OF THE GEOID MODEL IN THE STATE OF SÃO PAULO USING TWO METHODOLOGIES AND GOCE MODELS

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes’ integral through the Fast Fourier Transform - FFT and Least Squares Collocation – LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes’ integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT

On the connection of the Ecuadorian Vertical Datum to the IHRS

In this work, the determination of the discrepancy between the Ecuadorian Vertical Datum (EVD) and the International Height Reference System (IHRS) is presented. The vertical offset was estimated at the EVD based on the fixed geodetic boundary value problem approach. The focus of the experiment was the determination of the anomalous potential in the EVD, which in turn enable determination of the respective geopotential value. Taking a geopotential space-based approach, two estimates of the EVD offset with respect to the IHRS were obtained that amount to −1.51 and −1.61m2/s2

OFFSET EVALUATION OF THE ECUADORIAN VERTICAL DATUM RELATED TO THE IHRS

Considering the definition of the International Height Reference System (IHRS) in the geopotential space (Resolution 1/2015, International Association of Geodesy - IAG), among the present main objectives of the international geodetic community is the materialization of IHRS around the world. One fundamental task for this is the offset determination of each national vertical datum related to the IHRS. In this manuscript we establish the relationship between the Ecuadorian Vertical Datum (EVD) and the IHRS in the geopotential space following the foundations of the Resolution 1/2015 IAG. Gravity data, heights from the Ecuadorian Fundamental Vertical Network, Global Geopotential Models and Digital Elevation Models were used in the computations. Based on the Least Squares Collocation method, empirical covariance functions and spectral decomposition techniques, we realized the modelling of the geopotential in the study region (4° x 4° centered in the La Libertad tide gauge, Ecuador). Based on the referred approaches, we solved the free Geodetic Boundary Value Problem for determining the discrepancy of the EVD related to the IHRS. An offset of approximately 29 cm ± 3 cm was estimated for the W0 - W0i relation when the GO_CONS_GCF_2_DIR_R5 model was used in the modeling of the medium and long wavelengths of the terrestrial gravity field, and approximately 43 cm ± 3 cm when the EIGEN6C4 model was used