The Oblique Mercator (OM) has been the runt in the family of conformal coordinate projection where its particular attribute of arbitrary orientation has been largely ignored. It is proposed that the Oblique Mercator, as a conformal projection, is well-suited to bridge the gap between a conventional north-oriented projection and the family of engineering grids that are unit-scaled and arbitrarily oriented improve the management of coordinate reference systems (CRS) between GIS and CAD/BIM software that has been, and remains, a significant cause of inefficiency for engineering design and construction, and for plane surveying. Issues relating to the selection of an optimal set of HOM projection parameters are discussed, including a new method to transform an existing engineering grid into an optimised HOM grid.

A major motivation of precise geoid computation is to adopt it as a national vertical datum or as an alternative vertical reference surface to aid surveyors in calculating physical heights using the Global Navigation Satellite System (GNSS). There exist several methods of geoid computation, and only one particular method is generally used to calculate the national geoid model irrespective of the size and topographical landforms of the country. The validation of the developed geoid models is done with the complete GNSS-leveling data set. In such a case, it is hard to claim the consistency in the precision of the developed geoid model throughout the country. This study aims to identify the consistency of the geoid models over India computed using the three approaches primarily followed in Curtin University of Technology (CUT), the University of New Brunswick (UNB), and the Royal Institute of Technology (KTH). Three analyses have been done on the calculated geoid models: (1) clusterwise validation with the GNSS-leveling data, (2) intermodel comparison for the whole study area, and (3) intermodel comparison for Indian states and Union Territories (UT) only. The GNSS-leveling validation results show that the standard deviations of differences for all the methods are within a range of +/- 0.01 m with the exception of Uttar Pradesh West with the UNB method. However, inter-model comparison shows that the mean (meters) and standard deviation (meters) of the differences between the pairs (CUT-UNB), (CUT-KTH), and (KTH-UNB) are 0.241 +/- 0.854, -0.133 +/- 0.498, and 0.374 +/- 1.239, respectively, with maximum difference sometimes exceeding 5 m. There is only one UTand four states for which the mean value is within (-0.20 m, 0.20 m) and standard deviation <= +/- 0.05 m for all the three pairs. Therefore, the analysis shows that it is difficult to calculate a precise national geoid model using any one method alone and a strategy is required to merge various regional precise geoid models or methods to develop a consistently precise national geoid model. (C) 2023 American Society of Civil Engineers.

We describe the [somewhat tedious] process of digitising from a 1955 report that lists over 1000 vertical deflections in India and some surrounding countries. It involved error-checking with closed-loop tests and resolution of an ambiguity surrounding the meridional vertical deflection at the Kalianpur origin of the datum. We transformed these Kalianpur coordinates to geodetic coordinates on geocentric datum to compute absolute vertical deflections. However, due to many changes to the Everest spheroid due to different feet to metre conversions and readjustments of the Kalianpur datum, we were restricted to using the abridged Molodensky transformation parameters for the 1975 Kalianpur datum and Everest 1956 spheroid based on only seven common points from the WGS84 technical manual. We compared these transformed absolute vertical deflections with EGM2008 and GGMplus (for both models: meridional standard deviation: ∼±2″; prime vertical standard deviation: ∼±3″), showing that the effort of digitisation and scrutiny of historical geodetic data is indeed worthwhile.

V tejto štúdií používame Newtonov integrál v spektrálnej oblasti na riešenie dvoch geodetických/geofyzikálnych úloh pre Mesiac, viď [1].V prvej úlohe odhadneme hustotu mesačnej kôry (inverzný problém).Využívame model gravitačného poľa GL1500E určený družicovou misiou GRAIL a topografiu zo senzora LOLA na odhad: 1) konštantnej, 2) laterálne premenlivej a 3) priestorovo premenlivej hustoty mesačnej kôry.V druhej úlohe vypočítame modely mesačného gravitačného poľa odvodené z týchto troch zložení mesačnej kôry (priamy problém) do stupňa 2519 (zodpovedajúceho priestorovému rozlíšeniu 2,2 km na rovníku).Nakoniec testujeme naše nové modely, ako aj najnovšie a nezávislé priame modely gravitačného poľa, s oficiálnymi produktami družicovej misie GRAIL úrovne 1B a úrovne 2. Naše globálne modely gravitačného poľa

Since 2006, several different groups have computed geoid and/or quasigeoid (quasi/geoid) models for the Auvergne test area in central France using various approaches. In this contribution, we compute and compare quasigeoid models for Auvergne using Curtin University of Technology’s and the Swedish Royal Institute of Technology’s approaches. These approaches differ in many ways, such as their treatment of the input data, choice of type of spherical harmonic model (combined or satellite-only), form and sequence of correction terms applied, and different modified Stokes’s kernels (deterministic or stochastic). We have also compared our results with most of the previously reported studies over Auvergne in order to seek any improvements with respect to time [exceptions are when different subsets of data have been used]. All studies considered here compare the computed quasigeoid models with the same 75 GPS-levelling heights over Auvergne. The standard deviation for almost all of the computations (without any fitting) is of the order of 30–40 mm, so there is not yet any clear indication whether any approach is necessarily better than any other nor improving over time. We also recommend more standardisation on the presentation of quasi/geoid comparisons with GPS-levelling data so that results from different approaches over the same areas can be compared more objectively.

While the link between groundwater extraction and land subsidence is well documented, observations of land uplift associated with groundwater replenishment are less so. In the Perth Basin, Western Australia, a programme of managed aquifer recharge (MAR) commenced in August 2017 and is designed to sustain levels of hydraulic head in aquifers valuable for extraction. Space-based TerraSAR-X satellite radar measurements were used to capture the first 3.5 years of MAR, providing an insight into the evolution of ground uplift in the Perth Basin that is spatially and temporally related to the MAR injection volumes and the injection-induced changes in hydraulic head. Significantly, the X-band InSAR has spatial coverage around the single injection point, and the time series begins prior to the start of the injection, rather than a generalised study of ground surface and aquifer change from multiple groundwater recharge contributions. This enables the observed ground uplift to be correlated with the time of initial injection, pause, then resumption with increased volumes. The X-band InSAR identified maximum displacements of up to 20±3 mm in the vicinity of the injection bores, but which subside when injection is paused. The spread of displacements from the injection site extends over 14 km southwards with the dispersion pattern identifying linear boundaries that sharply delineate displacements in the north-west and north-east. The extent of the region impacted by ground uplift is likely linked to the distribution of extraction bores and heterogeneities in the subsurface geology, including a persistent linear feature that has not yet been considered in hydrogeological models of the region. This article focusses on the immediate surface response to the MAR injection, and identifying the constraining physical features for the injected recharge, thus providing an additional insight into the challenging and complex Perth Basin. It also demonstrates the millimetric accuracy possible from X-band radar satellites that permits MAR volumes to be managed to avoid infrastructure damage that may undermine public confidence in the MAR program.

Earth observation (EO) satellites facilitate hazard monitoring and mapping over large-scale and remote areas. Despite Synthetic Aperture Radar (SAR) satellites being well-documented as a hazard monitoring tool, the uptake of these data is geographically variable, with the Australian continent being one example where the use of SAR data is limited. Consequently, less is known about how these data apply in the Australian context, how they could aid national hazard monitoring and assessment, and what new insights could be gleaned for the benefit of the international disaster risk reduction community. The European Space Agency Sentinel-1 satellite mission now provides the first spatially and temporally complete global SAR dataset and the first opportunity to use these data to systematically assess hazards in new locations. Using the example of Australia, where floods and uncontrolled bushfires, earthquakes, resource extraction (groundwater, mining, hydrocarbons) and geomorphological changes each pose potential risks to communities, we review past usage of EO for hazard monitoring and present a suite of new case studies that demonstrate the potential added benefits of SAR. The outcomes provide a baseline understanding of the potential role of SAR in national hazard monitoring and assessment in an Australian context. Future opportunities to improve national hazard identification will arise from: new SAR sensing capabilities, which for Australia includes a first-ever civilian EO capability, NovaSAR-1; the integration of Sentinel-1 SAR with other EO datasets; and the provision of standardised SAR products via Analysis Ready Data and Open Data Cubes to support operational applications.

This paper combines gravity data collected from airborne, shipborne and terrestrial surveys and those derived from satellite altimetry to determine a high-resolution gravimetric and hybrid geoid model (on a 30" × 30″ grid) in and around Taiwan. Some 6000 new land gravity values at a 0.03-mGal precision make a notable contribution to the geoid modeling. Shipborne gravity data in waters 20 km offshore Taiwan were collected to improve the coastal geoid precision. In a circular area of 50 km around each of the five major tide gauges in Taiwan, gravity data were measured to improve vertical datum connections between Taiwan and its four offshore islands. Height anomalies were computed first and then converted to geoid heights. At > 2000 benchmarks, we obtained measured geoid heights to assess the gravimetric-only geoid and to create a hybrid geoid. Our assessments and formal errors from least-squares collocation indicate few cm of standard deviations for both geoid models, but the gravimetric geoid has mean differences of up to 20 cm with the measured geoidal heights. The hybrid geoid is used in RTK-VBS orthometric heighting, achieving a 5-cm precision. The gravimetric geoid is used to determine the relative differences in the ocean's mean dynamic topography (MDT) between Taiwan and the four offshore islands, which are also compared with those from oceanic and altimetric methods for estimating MDT. Differences in MDT help to identify 41.7 cm and 54.1 cm offsets in the current vertical datums of Penghu and Lanyu islands. In a low-lying, flood-prone region of southern Taiwan, the hybrid geoid improves LiDAR mapping of sub-zero elevation zones by 20 cm, corresponding to 70 years of sea level rise at an assumed rate of 0.286 cm/yr.

The interferometric synthetic aperture radar (InSAR) small baseline subset (SBAS) technique can be applied to land with varying deformation magnitudes ranging from mm/yr to tens of cm/yr. SBAS defines a network of interferograms that is limited by temporal and spatial baseline thresholds that are often applied arbitrarily, or in apparently subjective ways in the literature. We use simulated SAR data to assess (1) the influence of residual noise and SBAS network configuration on InSAR-derived deformation rates, and (2) how the number of interferograms and data gaps in the time series may further impact the estimated rates. This leads us to an approach for defining a SBAS network based on geodetic reliability theory represented by the redundancy number (r-number). Simulated InSAR datasets are generated with three subsidence signals of linear rates plus sinusoidal annual amplitudes of −2 mm/yr plus 2 mm, −20 mm/yr plus 5 mm and −100 mm/yr plus 10 mm, contaminated by Gaussian residual noise bounded within [−2;+2] mm, [−5;+5] mm and [−10;+10] mm, corresponding to standard deviations of approximately 0.5 mm, 1.5 mm and 3.0 mm, respectively. The influence of data gaps is investigated through simulations with percentages of missing data ranging from 5% to 50% that are selected (1) randomly across the 4-year time series, and (2) for three-month windows to represent the northern winter season where snow cover may cause decorrelation. These simulations show that small deformation rates are most adversely affected by residual noise. In some extreme cases, the recovered trends can be contrary to the signal (i.e., indicating uplift when there is simulated subsidence). We demonstrate through simulations that the r-number can be used to pre-determine the reliability of SBAS network design, indicating the r-values between ~0.8 and ~0.9 are optimal. r-numbers less than ~0.3 can deliver erroneous rates in the presence of noise commensurate with the magnitude of deformation. Finally, the influence of data gaps is not as significant compared to other factors such as a change in the number of interferograms used, although the blocks of “winter” gaps in the SBAS network show a larger effect on the rates than gaps at random intervals across the simulated time series.

This article proposes an alternative filtering technique to improve interferometric synthetic aperture radar (InSAR) time series by reducing residual noise while retaining the ground deformation signal. To this end, for the first time, a data-driven approach is introduced, which is based on Takens’s method within the sequential Monte Carlo framework, allowing for a model-free approach to filter noisy data. Both a Kalman-based filter and a particle filter (PF) are applied within this framework to investigate their impact on retrieving the signals. More specifically, PF and particle smoother [PaSm; to avoid confusion with persistent scatterers (PSs)] are tested for their ability to deal with non-Gaussian noise. A synthetic test based on simulated InSAR time series, as well as a real test, is designed to investigate the capability of the proposed approach compared with the spatiotemporal filtering of InSAR time series. Results indicate that PFs and more specifically PaSm perform better than other applied methods, as indicated by reduced errors in both tests. Two other variants of PF and adaptive unscented Kalman filter (AUKF) are presented and are found to be able to perform similar to PaSm but with reduced computation time. This article suggests that PFs tested here could be applied in InSAR processing chains.

SUMMARY Computation of gravimetric terrain corrections (TCs) is a numerical challenge, especially when using very high-resolution (say, ∼30 m or less) digital elevation models (DEMs). TC computations can use spatial or/and spectral techniques: Spatial domain methods are more exact but can be very time-consuming; the discrete/fast Fourier transform (D/FFT) implementation of a binomial expansion is efficient, but fails to achieve a convergent solution for terrain slopes >45°. We show that this condition must be satisfied for each and every computation-roving point pair in the whole integration domain, not just at or near the computation points. A combination of spatial and spectral methods has been advocated by some through dividing the integration domain into inner and outer zones, where the TC is computed from the superposition of analytical mass-prism integration and the D/FFT. However, there remain two unresolved issues with this combined approach: (1) deciding upon a radius that best separates the inner and outer zones and (2) analytical mass-prism integration in the inner zone remains time-consuming, particularly for high-resolution DEMs. This paper provides a solution by proposing: (1) three methods to define the radius separating the inner and outer zones and (2) a numerical solution for near-zone TC computations based on the trapezoidal and Simpson's rules that is sufficiently accurate w.r.t. the exact analytical solution, but which can reduce the computation time by almost 50 per cent.

J. Badekas reinterpreted M. S. Molodensky's three-dimensional similarity transformation as a vector solution using a centroid. The solution has since been (mis)interpreted by some others with inconsistent reference to the methods of both Molodensky and Badekas, principally relating to the translation vector and the stochastic model. This appears to have led to incorrect claims that the Molodensky-Badekas method is superior to the Helmert similarity and Bursa-Wolf methods. This paper reviews the development and description of the original Badekas method, reconfirming its equivalence to the Bursa-Wolf method in the forward direction, and provides an alternative solution that suits the same-formula reversal common in commercial surveying software. It is also demonstrated that the Molodensky-Badekas method has no inherent superiority over the Bursa-Wolf method, has an ambiguous functional model, and nominally underestimates its parameter statistics when these are compared directly with those from the Bursa-Wolf method.

The nature and linearity of vertical land motion (VLM) impacting the global sea level record from tide gauges is not well known, but remains of importance to understand long-term changes to sea level. Local surveys are required to directly measure VLM at tide gauges relative to a global reference frame, but this is limited by the lack of differential VLM measurements between tide gauges and continuously operating GPS (cGPS) stations that are not co-located, i.e., fixed to the tide gauge structure. We present results from an experiment using satellite radar interferometry (InSAR) scenes acquired from the TerraSAR-X satellite mission to test whether InSAR could replace repeat geodetic levelling as a 'geodetic tie' between cGPS stations and tide gauges. Comparisons are made among TerraSAR-X (TSX), cGPS and tide gauge minus altimetry VLM estimates for the Hillarys and Fremantle tide gauges (Perth, Western Australia), which are used as test sites for this method. The results suggest agreement between differential TSX and altimetry minus tide gauge VLM rates, but systematic offsets among the absolute/geocentric rates where the TSX is referenced to IGS08 at the PERT cGPS. The TerraSAR-X VLM at the Fremantle tide gauge for the period 7 October 2012 to 7 October 2017 is + 0.45 +/- 0.40 mm/yr (referenced to IGS08 at PERT cGPS), although this should be treated cautiously over this short period, and because VLM at Fremantle and Hillarys appears to be non-linear over time. We infer from this that the uncertainties in TerraSARX differential VLM rates are comparable to those from the highest quality repeat levelling, although the uncertainty approaches 1 mm/yr if the reference point uncertainty of the TSX and cGPS is considered when transformed to a terrestrial reference frame.

We present an integral-based approach for high-resolution regional recovery of the gravitational field in this article. We derive rigorous remove-compute-restore integral estimators relating the line-of-sight gravitational acceleration to an arbitrary order radial derivative of the gravitational potential. The integral estimators are composed of three terms, i.e., the truncated integration, the low-frequency line-of-sight gravitational acceleration, and the high-frequency truncation error (effect of the distant zones). We test the accuracy of the integral transformations and of the integral estimators in a closed-loop simulation over the Montes Jura region on the nearside of the Moon. In this way, we determine optimal sizes of integration radii and grid discretisation. In addition, we investigate the performance of the regional integral inversion with synthetic and realistic GRAIL observations. We demonstrate that the regional inversion results of the disturbing gravitational potential and its first order radial derivative in the Montes Jura mountain range are less contaminated by high-frequency noise than the global spherical harmonic models. (C) 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.

We present summarised formulas and worked examples for the propagation of geoid and vertical deflection errors through some common geodetic surveying computations, as well as a demonstration of their effects on least squares adjustments of small simulated geodetic networks. We also present location-specific uncertainties for the vertical deflections derived from the horizontal gradients of the AGQG2017 gravimetric-only quasigeoid model, upon which AUSGeoid2020 is based.

Gravity field modelling in coastal region faces challenges due to the degradation of the quality of altimeter data and poor coverage of gravimetric measurements. Airborne gravimetry can provide seamless measurements both onshore and offshore with uniform accuracies, which may alleviate the coastal zone problem. We study the role of airborne data for gravity field recovery in a coastal region and the possibility to validate coastal gravity field model against recent altimetry data (CryoSat-2, Jason-1, and SARAL/Altika). Moreover, we combine airborne and ground-based gravity data for regional refinement and quantify and validate the contribution introduced by airborne data. Numerical experiments in the Gippsland Basin over the south-eastern coast of Australia show that the effects introduced by airborne gravity data appear as small-scale patterns on the centimetre scale in terms of quasi-geoid heights. Numerical results demonstrate that the combination of airborne data improves the coastal gravity field, and the recent altimetry data can be potentially used to validate the high-frequency signals introduced by airborne data. The validation against recent altimetry data demonstrates that the combination of airborne measurements improves the coastal quasi-geoid, by ~ 5 mm, compared with a model computed from terrestrial and altimetry-derived gravity anomalies alone. These results show that the recently released altimetry data with relatively denser spatial resolutions and higher accuracies than older altimeter data may be beneficial for gravity field model assessment in coastal areas.

SUMMARY Quasigeoid models can be determined from surface gravity anomalies, so are sensitive to changes in the shape of the topography as well as changes in gravity. Here we present results of forward modelling gravity/quasigeoid changes from synthetic aperture radar data following the 2016 Mw 7.8 Kaikōura earthquake with land uplift of up to 10 m. We assess the impact of the topographic deformation on the reference surface of the New Zealand vertical datum in lieu of costly field gravity field measurements. The most significant modelled gravity and quasigeoid changes are—2.9 mGal and 5–7 mm, respectively. We compare our forward modelled gravity signal to terrestrial gravity observation data and show that differences between the data sets have a standard deviation of ±0.1 mGal. The largest modelled change in the quasigeoid is an order of magnitude smaller than the 57.7 mm estimated precision of the most recently computed NZGeoid model over the Kaikōura region. Modelled quasigeoid changes implied by this particular deformation event are not statistically significant with respect to estimated precision of the New Zealand quasigeoid model.

The expansion of globally consistent satellite-radar imagery presents new opportunities to measure Earth-surface displacements on intercontinental scales. Yet global applications, including a complete assessment of the land contribution to relative sea-level rise, first demand new solutions to unify relative satellite-radar observations in a geocentric reference frame. The international network of Very Long Baseline Interferometry telescopes provides an existing, yet unexploited, link to unify satellite-radar measurements on a global scale. Proof-of-concept experiments reveal the suitability of these instruments as high-amplitude reflectors for satellite radar and thus provide direct connections to a globally consistent reference frame. Automated tracking of radar satellites is easily integrated into telescope operations alongside ongoing schedules for geodesy and astrometry. Utilizing existing telescopes in this way completely avoids the need for additional geodetic infrastructure or ground surveys and is ready to implement immediately across the telescope network as a first step toward using satellite radar on a global scale.

Gravimetric geoid or quasigeoid models are often evaluated using Global Positioning System (GPS) and leveling, but the veracity of these control data is not always considered. Using a precisely surveyed 40-km-long traverse of 62 points in Perth, Western Australia, we exemplify that vertical land motion and the choice of GPS processing software may lead to spurious conclusions as to which is the best model, particularly with regard to the assessment in the presence of tilts among these data sets. We recommend that the effect of vertical land motion (if present) be factored into such evaluations, GPS data be processed using the same software and in the same reference frame, and tilts among the data sets be considered during the evaluations.