Modern Geodesy Research Articles

СОВРЕМЕННЫЕ ВОЗМОЖНОСТИ ЛАЗЕРНОГО СКАНИРОВАНИЯ

In modern geodesy, great emphasis is placed on modern digital technologies for data collection and processing, the maximum presentation of which is possible only in digital form. The article provides an overview of modern methods and technologies for using lasers to capture three-dimensional object data; the basic principles of laser scanners, their components, as well as areas and methods of application of this technology are considered. The advantages of using laser scanning in the implementation of work and the prospects for its development in the future are described.

Potential of cold-atom airborne gravimetry to improve coastal gravity field and quasigeoid modelling

We investigate using the GIRAFE cold-atom gravimeter during an airborne gravity survey for improving gravity field and quasigeoid modelling. The study is conducted over the Bay of Biscay, France. Geoid/quasigeoid determination is usually a major challenge over such coastal areas due to scarce and inconsistent gravity data. In a first step, the GIRAFE dataset is analysed and compared with available surface gravity data as well as with global altimetry models from UCSD and DTU. The comparisons indicate that the DTU model is better than the UCSD model within around 10 km from the coastline. Furthermore, recent satellite altimeter missions significantly improve the altimetry models in coastal areas. A significant bias (− 4.00 mGal) in shipborne data is also found from this comparison. In a second step, eight quasigeoid solutions are calculated to evaluate the contribution of GIRAFE data. This contribution reaches 3 cm in terms of height anomaly for DTU21 while being much larger for UCSDv31 and shipborne data. Finally, the quasigeoid solutions are validated using GNSS-levelling data. The results indicate that using GIRAFE data improves by approximately 50% the quality of quasigeoid models over land near the coast. The highest accuracy, around 1 cm, is achieved when GIRAFE data are merged with refined gravity data. Importantly, the standard deviation is just 1.2 cm when compared with GNSS-levelling points if using only GIRAFE data over marine areas, which is very close to the 1 cm goal of geoid/quasigeoid model determination in modern geodesy. This study thus confirms the benefits of performing airborne gravity survey using quantum sensors.

Damped least squares method for nonlinear mixed additive and multiplicative errors model

Measurement data in the field of modern geodesy contains not only additive errors but also multiplicative errors related to signal strength. The existing models for dealing with mixed additive and multiplicative errors are mainly based on the linear form of unknown parameters and observations, and there are few studies on the nonlinear form of the two. In the parameter estimation method of the nonlinear mixed additive and multiplicative errors model, the initial value of the Gauss–Newton parameter estimation method is selected by previous experience. The initial value determined by this method deviates far from the true value due to a lack of experience, which will lead to inaccurate parameter estimation results. In order to solve this problem, based on the least squares principle and the introduction of the damping factor, this paper deduces the damping least squares parameter solution formula for the parameter estimation of the nonlinear mixed additive and multiplicative errors model. The superiority of the damping least squares algorithm is reflected in the adjustment of the damping factor, taking into account the advantages of the Gauss–Newton method and the steepest descent method, and some weighted selection is obtained in the two algorithms. The calculation and comparative analysis of the simulated cases show that the damped least squares method is more suitable for handling geodetic data with this nonlinear mixed additive and multiplicative errors model when the initial value deviates far from the true value.

Pedagogical approaches in modern geodesy and integrating earth measurement techniques into STEM education

Relevance. In the context of an increasingly dynamic and interconnected world, the integration of geodesy into STEM education has emerged as a crucial domain for nurturing a comprehensive understanding of Earth�s intricate spatial dynamics. Purpose. The purpose of this research is to carry out a comprehensive analysis of pedagogical approaches in modern geodesy and to investigate the process of integrating advanced land surveying methods into the educational structure of Kosovo. Methodology. The study utilizes content analysis, functional and historical approaches, induction, and comparative analysis to examine Kosovo's higher geodesical education, focusing on the University of Prishtina's Geodesy Department from 2003 to 2023. Results. This study highlighted the significance of cultivating a robust geospatial skill set among students to address pressing global challenges and promote sustainable development. This research highlighted the key role of innovative learning strategies and experimental learning methods in improving the landscape of geodesy education. This paper offered a blueprint for designing an inclusive and dynamic curriculum that fostered a profound understanding of geospatial concepts while fostering a culture of scientific inquiry and critical thinking. Conclusions. The research presents the changes in the Department of Geodesy over the years, both in terms of study program accreditation and curriculum adjustments to align with labor market needs. It also highlights the department's participation in European Union projects, which has significantly elevated the quality of education. Keywords: accreditation; curriculum; study program; European projects; students

Time-variable strain and stress rates induced by Holocene glacial isostatic adjustment in continental interiors

In continental interiors, tectonically-driven deformation rates are low, often to the point where they are undetectable with modern geodesy. However, a range of non-tectonic surface processes, particularly relating to hydrological, cryospheric, and sedimentological mass changes, can produce strain-rates which on geologically-short timescales are substantially greater than those produced by tectonics. Here, we illustrate the problem that such transient strain rates may pose in low-strain environments by considering the impact that the growth and decay of the Fennoscandian and Laurentian ice sheets over the Holocene had on Europe and North America respectively. Induced deformation extended far beyond the periphery of the ice sheets, with the potential to impact on seismicity rates thousands of kilometres south of the maximum ice extent. We consider how the modelled non-tectonic deformation would have interacted with several known active fault systems, including the European Cenozoic Rift System and the New Madrid fault system. In low strain continental interiors, seismic hazard assessment – crucial for the long-term planning of critical infrastructure, including nuclear waste disposal – is often dependent on sparse information from observational and historical seismicity, and from paleoseismological studies of surface fault systems. We recommend that for a more complete seismic hazard assessment, the impact of non-tectonic transients should be considered – both in the context of the role such transients may have played in recent seismicity, and the role they may play in seismicity to come. Whilst such consideration has previously been given to the direct impact on glacial loading in areas directly glaciated, we show that it should also be considered much more broadly.

Reference Gravity Frame in Latin America

With the development of the ballistic gravimeter in the late 80s, the efforts to establish reliable absolute gravity reference around the world became a reality. The need for the so-called International Terrestrial Gravity Reference Frame (ITGRF[1]) to substitute the IGSN 71 (International Gravity Standardization Net 1971) is one of the demands of modern Geodesy. In that context, the Laboratório de Topografia e Geodesia, Escola Politécnica da Universidade de São Paulo (LTG/EPUSP), Brazil, started in 2013, with the acquisition of the A10 no 32 (A10-032) absolute gravimeter, a large number of campaigns to measure gravity acceleration in the states of São Paulo, Minas Gerais, Paraná and abroad. The gravimeter was purchased by Instituto Geográfico e Cartográfico (IGC), state of São Paulo. After eight years of operation under the coordination of the Centro de Estudos de Geodesia(CENEGEO) and with the support of different institutions, a total of five national Gravity Reference (GR) was established: Argentina, Brazil, Costa Rica, Ecuador and Venezuela. The present efforts are the selection of a set of local GR in the different countries of Latin America and a possible contribution to the ITGRF.[1] The ITGRS/F acronyms were approved by IAG JWG 2.1.1 in April 2022, replacing the former IGRS/F acronyms.

Mining High-Resolution KH-9 Panoramic Imagery to Determine Earthquake Deformation: Methods and Applications

Earthquake deformation is crucial for understanding fault kinematics. Modern earthquakes (moment magnitude $M_{w} ≥ 6$ ) have been well documented by geodetic techniques, such as radar interferometry and image correlation with unprecedented accuracy. Nonetheless, many large ( $M_{w} ≥ 7$ ) historical earthquakes remain unexplored due to a lack of preearthquake data. In this article, we provide the first study of using Hexagon KeyHole-9 (KH-9) panoramic imagery to investigate historical earthquakes. We propose patch-based orthorectification and test the method from analog experiments with unmanned aerial vehicle (UAV) photographs. Using the 2013 $M_{w}$ 7.7 Balochistan as a case example, we demonstrate that KH-9 images can be used to retrieve meter-scale horizontal deformation. The displacements, derived from correlating KH-9 (preearthquake) and Sentinel-2 (postearthquake) images, are comparable with published studies. Applying the method to the 1981 $M_{w}$ 7.1 Sirch earthquake, we succeed to measure NS strike-slip motion (up to 5.9 ± 1.6 m) along the 1981 rupture and find that most of the accumulated strain energy may be released by motion along a 25-km-long segment of the Gowk fault. The southward propagation of the rupture may be prevented by the earlier $M_{w}$ 6.6 Golbaf earthquake that released most of the accumulated strain in the south. The rapid decay of slip in the north seems to be associated with a 3-km-long, 1-km-wide step-over, which may have dissipated a large fraction of seismic energy. The KH-9 panoramic images show great potential for determining horizontal deformation, providing useful information about historical earthquakes that occurred before the era of modern geodesy.

SOME FEATURES OF CURRENT TECHNOGENIC MOVEMENTS OF THE EARTH’S CRUST

We describe the history of studying the current crustal movements by various methods and discuss technogenic effects recorded at large water-reservoir zones and mineral deposits in Siberia. Initially, classical surveying techniques aimed to obtain high-accuracy ground-based measurements of height, tilt and direction. Modern geodesy techniques and methods for measuring absolute gravity are now available to investigate displacement, deformation, tilt and other phenomena taking place on the Earth’s surface. These methods are used to estimate kinematic parameters of the crust areas (e.g. rates of subsidence and horizontal movements) and to monitor fluid motions in mineral deposits. Such data are critical for ensuring a proper management of the mineral deposits. In this article, we analyse technogenic processes observed in the Ust Balyk oil-gas field, the Zapolyarny gas deposit, the water-reservoir zone at the Sayano-Shushenskaya hydroelectric power station (SSHPS) on the Yenisei river, and large open-pit mines in the Kuzbass basin. Our analysis is based on surface displacement rates estimated from the data collected in different periods of observations at large man-made facilities. In the study of the hydro technical objects, we estimated the displacement rates at 5.0 mm per year. In the northern areas of the West Siberian petroleum basin, subsidence rates amounted to 20–25 mm per year in the early 2000s. These estimates were supported by the high-accuracy gravity measurements showing an increase up to 6–7 microGal per year in the oil-gas field development areas. We assess a possibility of triggering effects related to weak seismicity due to a high stress accumulation rate (1 KPa per hour) in the SSHPS area. A connection between earth tides and catastrophic events, such as gas emissions in high amounts on mining sites, is discussed. Having analysed the surface monitoring records taken in South Primorye in September 2017, we conclude that underground nuclear explosions in North Korea in this period did not cause any significant displacement of the surface in this most southerly region of the Russian Far East territories.

On determination of the geoid from measured gradients of the Earth's gravity field potential

The geoid is an equipotential surface of the static Earth's gravity field which plays a fundamental role in definition of physical heights related to the mean sea level (orthometric heights) in geodesy and which represents a reference surface in many geoscientific studies. Its determination with the cm-level accuracy or better, in particular over dry land, belongs to major tasks of modern geodesy. Traditional data and underlined theory have significantly been affected in recent years by rapid advances in observation techniques. This study reviews gradients of the disturbing gravity potential, both currently available and foreseen, and systematically discusses mathematical models for geoid determination based on gradient data. Fundamentals required for geoid definition and its estimation from measured potential gradients are shortly reviewed at the beginning of the text. Then particular mathematical models based on solutions to boundary-value problems of the potential theory, which include both integral transforms and integral equations, are formulated. Properties of respective integral kernel functions are demonstrated and discussed. With the new mathematical models introduced, new research topics are opened which must be resolved in order to allow for their full-fledged applicability in geoid modelling. Stochastic modelling is also discussed which estimates gradient spatial resolution and accuracy required for geoid modelling with the cm-level accuracy. Results of stochastic modelling suggest that the cm-geoid can be estimated using available gradient data if related problems, namely reduction of gradient data for gravitational effects of all masses outside the geoid and their downward continuation, are solved at the same level of accuracy.

On the question of definition of the subject area of research in the specialty "Geodesy and land surveying"

The article discusses the content of the subject area of research introduced in 2015 in Ukraine specialty "Geodesy and Land Management" as a set of all subjects, the properties of which and the relationship between which should be considered in the relevant scientific theory. Based on the established practice of research work, as well as international approaches to determining the subject of modern geodesy and land management, it is proposed to identify five subsets of research areas (specializations): geodesy and cartography; geoinformatics and aerospace research of the Earth; land cadastre; land management; land management. For each of the subsets of the subject area of research, a detailed description of the subject orientation is proposed, which allows to specify the context and content of the relevant research.

The impact of precipitation on state of the slopes surface and thermal activity of the mine waste dump – preliminary study

Precipitation, especially with a high intensity, affects the condition of mining waste dumps. The article presents the results of research aimed at determining the impact of rain on water erosion on the slopes of a coal waste dump and its thermal state. Preliminary tests of the condition of two slopes of the coal waste dump in Libiąż (Poland) undertaken in the frameworks of the TEXMIN project was carried out using modern geodesy techniques (low-ceiling photogrammetry and TLS terrestrial laser scanning). The current geometry of the slope surface was faithfully reproduced in the form of a cloud of points with known coordinates x, y, z. The thermal state within the analyzed slopes of the dump was also assessed. Based on thermography studies and measurements of temperature and gas concentrations inside the object, two zones of thermal activity were located on one of the examined slopes. The test results constitute the initial state against which the results of further tests will be compared. This will allow to determine the influence of precipitation on the amount of water erosion and the thermal state of the dump in a specific time period.

A Multi-Observation Least-Squares Inversion for GNSS-Acoustic Seafloor Positioning

Monitoring deformation on the seafloor is a major challenge for modern geodesy and a key to better understanding tectonic processes and assess related hazards. The extension of the geodetic networks offshore can be achieved by combining satellite positioning (GNSS) of a surface platform with acoustic ranging to seafloor transponders. This approach is called GNSS-Acoustic (GNSS-A). The scope of this work is to provide a tool to identify and quantify key points in the error budget of such experiment. For this purpose, we present a least-squares inversion method to determine the absolute position of a seafloor transponder array. Assuming the surface platform is accurately positioned by GNSS, the main observables are the two-way travel time in water between the transponders on the seafloor and the surface platform acoustic head. To better constrain transponder positions, we also consider the baseline lengths and the relative depth-differences between different pairs of them. We illustrate the usefulness of our forward modeling approach and least-square inversion by simulating different experimental protocols (i.e., platform trajectories, with or without information on the distance and depth between transponders). We find that the overall accuracy of a GNSS-A experiment is significantly improved with additional information about the relative depths of the instruments. Baseline lengths also improve the accuracy, but only when combined with depth differences. The codes in Python3 used in this article are freely available online.

3D Modelling of Earth Kinematics in Palestine for GNSS and Geodetic Time-Dependent Positioning

The use of GNSS technologies for precise point positioning enabled the calculations for single-point observations or relative positioning of long baselines. The GNSS absolute and relative positioning techniques can be implemented between points within different tectonic plates, while the classical surveying methods start from local reference/triangulation points to near points within a few kilometers. The definition of the kinematic models of the earth has become an important role in GNSS measurements techniques and networks adjustment methods based on international terrestrial reference frames (ITRF), where the reference points can be located in different continents and tectonic plates. Thus, the position calculations in the ITRF systems are time-dependent. To satisfy the requirements of land and cadastral surveying, the bidirectional transformation between classical geodetic networks and GNSS global, regional and local networks is nowadays a primary requirement in modern geodesy. While the classical networks were defined locally assuming a static earth system, the ITRF coordinates by GNSS techniques are defined globally and directly affected by earth kinematics including plate tectonics and local crustal movements. However, Palestine has a special kinematic situation because it is located at the border between two plates; Nubia/Sinai plate and the Arabia plate along the Jordan valley line. Thus, the result is unsteady surface kinematics all over the country, which has a longitudinal shape parallel to the Jordan valley rift. Using the IGS/EUREF stations and GNSS stations data that are freely available on the internet, varying positional velocities were calculated in both magnitude and direction using years of daily available GNSS raw observations. The GNSS precise observation techniques have proven that the points of the classical networks were subjected to a kinematic situation over the years. Therefore, the Palestinian geodetic network has to be revised for kinematic effects for the integration with the modern GNSS positioning. In this work, the effect of surface movements is included in the calculations between the different ITRF coordinate systems and the classical geodetic network of Palestine. To achieve the required transformations between ITRF and the classical network, a velocities model was established and tested utilizing GIS raster interpolation. The accuracy of the modeled velocities could support 1cm in static or real-time GNSS positioning. This made it possible for the integration between geodetic measurements between different time epochs.

Robust Prediction Algorithm Based on a General EIV Model for Multiframe Transformation

In modern geodesy, there are cases in which the target frame is unique and there is more than one source frame. Helmert transformations, which are extensively used to solve transformation parameters, can be separately solved between the target frame and one of the source frames. However, this is not globally optimal, even though each transformation is locally optimal on its own. Additionally, this also generates the problem of multiple solutions in the noncommon station of the target frame. Moreover, least squares solutions can cause estimation value distortion, with a gross error existing in observations. Thus, in this paper, Helmert transformations among three frames, that is, one target frame and two source frames, are studied as an example. A robust prediction algorithm based on the general errors-in-variables prediction algorithm and the robust estimation is derived in detail and is applied to achieve multiframe total transformation. Furthermore, simulation experiments were conducted and the results validated the superiority of the proposed total transformation method over classical separate approaches.

High-precision two-phase laser rangefinder PFSD-1,2

Performing high-precision linear measurements is one of the main tasks of modern engineering geodesy. Consequently, the development and creation of high-precision laser rangefinders and refractometers with a relative measurement error of not more than 3.10-7, becomes an urgent scientific and technical problem. Wide theoretical and experimental studies in the problem laboratory of geodetic measurements of NUACA have accumulated a sufficient amount of experimental results for the construction of modern high-precision light meter with the determination of the residual part of the phase cycle with an error of 0.03-0.05 mm. The article discusses issues related to improving the accuracy of linear measurements developed in the NUACA of high-precision light rangefinder. A two-phase modulation measurement method is proposed, when signals shifted by 180° are formed optically using a phase plate at λ/2. This modulation method of linear measurements provided the phase error of linear measurements mφ = 0.03-0.05 mm. The article also discusses the issue of reducing the modulation power. For this purpose, it is proposed to install a high-quality buffer Q-resonator between the high-quality light modem and the low-quality microwave oscillator.

USING OF LASER SCANNING IN GEODETIC HIGHWAYS SURVEYS

In modern geodesy, laser scanning is a rapidly evolving technology that allows you to automate work processes, as well as provide the most accurate research results. Laser scanning systems have emerged relatively recently. Despite this, they quickly becam

Определение параметров вектора Эйлера

Improving the accuracy of points coordinates determination from geodetic networks with the use of modern space geodesy techniques (GPS, SLR, VLBI, DORIS) identified factors that were earlier considered as insignificant. Such factors include the movement of tectonic plates. This made possible the transition from the static coordinate system model to the kinematic one. For the effect of the tectonic plates movement on the points coordinates you must know kinematic parameters of the tectonic plates movement – the Euler vector parameters – angular velocity of the tectonic plates rotation and the poles rotation coordinates (latitude and longitude) of tectonic plates. Many modern kinematic models of tectonic plates are used observations, performed by geophysical methods, to estimate kinematic parameters of the tectonic plates movement. The article presents the algorithm that allows to estimate the parameters of the tectonic plates movement from mathematical processing of geodetic measurements carried out at points distributed over the surface of tectonic plates. Based on the presented algorithm the EULER program was developed in the algorithmic FORTRAN language, which was experimentally tested. The analysis results showed that the parameters of the Euler vector obtained by the EULER program are in good agreement with the results obtained by using ITRF 2005 and ITRF 2008 models.

Normal gravity field in relativistic geodesy

Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, VLBI, SLR, and GNSS have achieved an unprecedented level of accuracy in measuring coordinates of the reference points of the ITRF and the world height system. The main geodetic reference standard is a normal gravity field represented in the Newtonian gravity by the field of a Maclaurin ellipsoid. The present paper extends the concept of the normal gravity field to the realm of general relativity. We focus our attention on the calculation of the first post-Newtonian approximation of the normal field that is sufficient for applications. We show that in general relativity the level surface of the uniformly rotating fluid is no longer described by the Maclaurin ellipsoid but is an axisymmetric spheroid of the forth order. We parametrize the mass density distribution and derive the post-Newtonian normal gravity field of the rotating spheroid which is given in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce the post-Newtonian multipolar expansion of the metric tensor given in terms of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy. Finally, we derive the post-Newtonian generalization of the Somigliana formula for the gravity field on the reference ellipsoid.

Current state of art of satellite altimetry

Abstract One of the fundamental problems of modern geodesy is precise defi nition of the gravitational fi eld and its changes in time. This is essential in positioning and navigation, geophysics, geodynamics, oceanography and other sciences related to the climate and Earth’s environment. One of the major sources of gravity data is satellite altimetry that provides gravity data with almost 75% surface of the Earth. Satellite altimetry also provides data to study local, regional and global geophysical processes, the geoid model in the areas of oceans and seas. This technique can be successfully used to study the ocean mean dynamic topography. The results of the investigations and possible products of altimetry will provide a good material for the GGOS (Global Geodetic Observing System) and institutions of IAS (International Altimetry Service). This paper presents the achievements in satellite altimetry in all the above disciplines obtained in the last years. First very shorly basic concept of satellite altimetry is given. In order to obtain the highest accuracy on range measurements over the ocean improved of altimetry waveforms performed on the ground is described. Next, signifi cant improvements of sea and ocean gravity anomalies models developed presently is shown. Study of sea level and its extremes examined, around European and Australian coasts using tide gauges data and satellite altimetry measurements were described. Then investigations of the phenomenon of the ocean tides, calibration of altimeters, studies of rivers and ice-sheets in the last years are given.

Goce derived geoid changes before the Pisagua 2014 earthquake

The analysis of space – time surface deformation during earthquakes reveals the variable state of stress that occurs at deep crustal levels, and this information can be used to better understand the seismic cycle. Understanding the possible mechanisms that produce earthquake precursors is a key issue for earthquake prediction. In the last years, modern geodesy can map the degree of seismic coupling during the interseismic period, as well as the coseismic and postseismic slip for great earthquakes along subduction zones. Earthquakes usually occur due to mass transfer and consequent gravity variations, where these changes have been monitored for intraplate earthquakes by means of terrestrial gravity measurements. When stresses and correspondent rupture areas are large, affecting hundreds of thousands of square kilometres (as occurs in some segments along plate interface zones), satellite gravimetry data become relevant. This is due to the higher spatial resolution of this type of data when compared to terrestrial data, and also due to their homogeneous precision and availability across the whole Earth. Satellite gravity missions as GOCE can map the Earth gravity field with unprecedented precision and resolution. We mapped geoid changes from two GOCE satellite models obtained by the direct approach, which combines data from other gravity missions as GRACE and LAGEOS regarding their best characteristics. The results show that the geoid height diminished from a year to five months before the main seismic event in the region where maximum slip occurred after the Pisagua Mw = 8.2 great megathrust earthquake. This diminution is interpreted as accelerated inland-directed interseismic mass transfer before the earthquake, coinciding with the intermediate degree of seismic coupling reported in the region. We highlight the advantage of satellite data for modelling surficial deformation related to pre-seismic displacements. This deformation, combined to geodetical and seismological data, could be useful for delimiting and monitoring areas of higher seismic hazard potential.