We provide a historical review and critique of regional geoid and quasigeoid modelling over the Australian continent, covering the earliest models from the late 1960s through to the present day and beyond. The most recently released official model for GPS/GNSS surveyors, AUSGeoid2020, was specifically calculated to enable them to determine Australian Height Datum heights from Geocentric Datum of Australia 2020 ellipsoidal heights in a more direct manner without the need for post-surveying adjustments. We summarise the deficiencies in the Australian Height Datum and how they are now being addressed by a proposed new vertical height system that is underpinned by a gravimetric-only quasigeoid model. We also summarise the results of some experiments that we have conducted to explore potential refinements that could be made to our computational processes, and future plans to acquire gravity data in the problematic coastal zones using airborne methods.

University’s approach R. Goyal, W.E. Featherstone, S.J. Claessens, O. Dikshit, N. Balasubramanian 1) Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India; rupeshg@iitk.ac.in, onkar@iitk.ac.in, nagaraj@iitk.ac.in 2) School of Earth and Planetary Sciences, Curtin University of Technology, GPO Box U1987, Perth WA 6845, Australia; w.featherstone@curtin.edu.au, s.claessens@curtin.edu.au

<p>Spherical harmonic synthesis (SHS) can be used to compute various gravity functions (e.g., geoid undulations, height anomalies, deflections of vertical, gravity disturbances, gravity anomalies, etc.) using the 4pi fully normalised Stokes coefficients from the many freely available Global Geopotential Models (GGMs).  This requires a normal ellipsoid and its gravity field, which are defined by four parameters comprising (i) the second-degree even zonal Stokes coefficient (J2) (aka dynamic form factor), (ii) the product of the mass of the Earth and universal gravitational constant (GM) (aka geocentric gravitational constant), (iii) the Earth’s angular rate of rotation (ω), and (iv) the length of the semi-major axis (a). GGMs are also accompanied by numerical values for GM and a, which are not necessarily identical to those of the normal ellipsoid.  In addition, the value of W<sub>0,</sub> the potential of the geoid from a GGM, needs to be defined for the SHS of many gravity functions. W<sub>0</sub> may not be identical to U<sub>0</sub>, the potential on the surface of the normal ellipsoid, which follows from the four defining parameters of the normal ellipsoid.  If W<sub>0</sub> and U<sub>0</sub> are equal and if the normal ellipsoid and GGM use the same value for GM, then some terms cancel when computing the disturbing gravity potential.  However, this is not always the case, which results in a zero-degree term (bias) when the masses and potentials are different.  There is also a latitude-dependent term when the geometries of the GGM and normal ellipsoids differ.  We demonstrate these effects for some GGMs, some values of W<sub>0</sub>, and the GRS80, WGS84 and TOPEX/Poseidon ellipsoids and comment on its omission from some public domain codes and services (isGraflab.m, harmonic_synth.f and ICGEM).  In terms of geoid heights, the effect of neglecting these parameters can reach nearly one metre, which is significant when one goal of modern physical geodesy is to compute the geoid with centimetric accuracy.  It is also important to clarify these effects for all (non-specialist) users of GGMs.</p>

We employ Newton's integral in the spectral domain to solve two geodetic/geophysical tasks for the Moon. Firstly, we determine 3D bulk density distribution within the lunar crust (inverse problem). For this purpose, we develop a linear mathematical model that parameterises the laterally variable density component by surface spherical harmonics. We exploit GL1500E GRAIL gravitational field model and LOLA topography model to determine bulk density in three types of function: 1) constant, 2) laterally variable, and 3) 3D spatially variable (assuming a linear change in the radial direction). Secondly, we calculate lunar gravitational field models inferred by these three crustal compositions (forward problem) up to spherical harmonic degree 2519 corresponding to a spatial resolution of similar to 2.2 km at the lunar equator. Efficacy of these models is assessed with respect to the GRAIL Level 2 gravitational field models. Our spatially variable crustal model represents the best fit globally and also locally in highland areas. We also test the performance of GRAIL models, recent and independent forward models, and our new models against Level 1B GRAIL satellite-to-satellite tracking data focusing on evaluation beyond Level 2 data (i.e., spherical harmonic degrees greater than 650). These medium- and high-frequency signals from our models correlate with the Level 1B observations the best among all global gravitational field models tested. Our high resolution geopotential model with the optimized 3D crustal density variation should be an asset to future lunar lander navigation and geophysical exploration.

A novel, explicit, and efficient forward modelling of the spheroidal harmonic spectra of external planetary gravitational fields is developed in this article. We introduce the oblate spheroidal coordinate system and derive the mathematical apparatus for the analysis of the spheroidal harmonic spectrum from the volumetric bulk density and geometry of a gravitating body. We discretise the volume integral and formulate a new and efficient numerical algorithm for the spheroidal forward modelling. We provide complete sets of recursions for calculating the associated Legendre functions of the first kind and their integrals in the Supplementary material. We also develop a computer program that implements the numerical algorithm and we test its performance. For this purpose, we consider synthetic gravitational fields of 1 Ceres (a significantly flattened asteroid) and of the Moon (a nearly spherical body). These tests prove high numerical accuracy and applicability of the spheroidal forward modelling up to degree and order 2519. We finally apply our spheroidal forward modelling and its simpler spherical counterpart for computing global gravitational field models up to degree and order 2519 generated by realistic topographic mass distributions of 1 Ceres and of the Moon. These models are compared in the spatial and spectral domains to manifest an enhanced applicability of the spheroidal approach with respect to the spherical one. In particular, we show an extended convergence space when using the spheroidal forward modelling and the corresponding harmonic representation for the oblate 1 Ceres.

Gravimetric geoid and/or quasigeoid models are routinely evaluated using co-located GPS-levelling and/or astrogeodetic vertical deflections, globally and regionally. This short note describes these ground-truth data for Australia as of August 2017, which are provided as Electronic Supplementary Material. We provide ∼7500 GPS-derived ellipsoidal heights, normal-orthometric heights from the 1971 adjustment of the Australian Height Datum, normal heights from a readjustment of levelling constrained to a model of the ocean's mean dynamic topography, and ∼1000 historical astrogeodetic vertical deflections. Updates to these data will be posted on the Intergovernmental Committee on Surveying and Mapping GitHub repository (https://github.com/icsm-au), together with a readme.txt file describing them.

Leveling remains the most precise technique for measuring changes in heights. However, for the purposes of determining vertical land motion (VLM), a time series of repeat leveling measurements is susceptible to artifacts and aliasing that may arise due to systematic errors, seasonal surface fluctuations, motions occurring during a survey, and any inconsistencies in the observation conditions among epochs. Using measurements from 10 repeat leveling surveys conducted twice yearly along a profile spanning similar to 40 km across the Perth Basin, Western Australia, we describe the observation, processing, and analysis methods required to mitigate these potential error sources. We also demonstrate how these issues may lead to misinterpretation of the VLM derived from repeat leveling and may contribute to discrepancies between geologically inferred rates of ground motion or those derived from other geodetic measurement techniques. Finally, we employ historical (similar to 40-year-old) leveling data in order to highlight the errors that can arise when attempting to extrapolate VLM derived from a geodetic time series, particularly in cases where the long-term motion may be nonlinear.

†* Recent-past subsidence of parts of the Perth Basin has most probably been caused by increased groundwater extraction for domestic and agricultural use. However, no dedicated geodetic monitoring programs were established when the increased extraction began in around 2000, thus setting a challenge to retrospectively quantify and map the subsidence. Differential levelling is likely to be less effective as only a few repeat traverses cover the areas thought to be subsiding. Repeat gravimetry is totally ineffective because of microseismic vibrations propagating through the Perth Basin. Repeat episodic GPS (Global Positioning System) is also likely to be less effective because of the few station occupations over several days or weeks and the inherent weakness of GPS for height determination. However, from a continuously operating GPS receiver at Gnangara and nearby artesian monitoring boreholes, we show that the rate of land subsidence has slowed from about -6 mm/yr to about -2 mm/yr since the reduction of groundwater extraction from the Yarragadee Aquifer in around 2005. A promising technique is InSAR (interferometric synthetic aperture radar) because it can map large areas, but the lack of historical radar imagery over the period of increased subsidence is a hindrance.

The walk through the enchanted forest of Oz, with its lions and tigers and bears, was a pretty scary proposition for Dorothy Gale and her friends. Some GPS users find themselves in a similar predicament when they try to understand the enchanted forest of geodesy and the relationship among coordinates, datums, and maps. In this month's column, Dr. Will Featherstone, senior lecturer in geodesy at the School of Surveying and Land Information, Curtin University of Technology, Perth, Western Australia, and Professor Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick in fredericton, Canada, sketch the relationships among the coordinate systems used worldwide for GPS and the coordinate systems and map projections used in various countries. They also discuss how these differences can affect the GPS user when employed incorrectly. "Innovation" is a regular column featuring discussions about recent advances in GPS technology and its applications as well as the fundamentals ofGPS positioning. The column is coordinated by Richard Langley, who appreciates receiving your comments as well as topic suggestions for future columns. To contact him, see the "Columnists" section on page 4 of this issue.

After the annexation of Austria into the German Reich the “Berufsordnung der Offentlich bestellen Vermessungsingenieure“ (ObVI) was introduced in 1940. By analysis of documents in the German Federal Archives (Berlin) statements about the political orientation of the profession and the licensing procedure are possible. Within the group of ObVI the former “Ingenieurkonsulenten fur Vermessungswesen“ were the third largest group. The surveyors had to take the licensing procedure or they had to close their offices. The number of finally approved ObVI's is significantly lower than the number of independent surveyors in Austria in 1938. The result of the approval process was like in German Empire since 1938 a market adjustment. As part of the process, the political reliability and the ancestry of the candidates has been verified. In some cases, the authorization was denied for political reasons. In most cases, the rejection was based on age or lack of skills.

The Leeuwin Current (LC) is an eastern boundary current flowing strongly southwards along the Western Australian coastline. The current varies seasonally, with weaker southwards flow occurring during the austral summer (November to March), when southerly winds are strongest. Nearly 9.5 years of TOPEX/Poseidon-derived sea-surface heights, in conjunction with the AUSGeoid98 gravimetric geoid model, have been used to investigate the temporal characteristics of the LC over the area bounded by 20 to 45°S and 108 to 130°E. The ocean dynamic height associated with the LC is used to compute the geostrophic parameters of volume transport, axis velocity, height jump, width, and axis locations of the current. These parameter estimates are then used to analyse the seasonal and interannual variability of the LC, as well as effects related to the El Niño Southern Oscillation (ENSO). Our results show that the LC is highly variable in terms of seasonal volume transport and is closely linked to ENSO events at interannual time-scales. Seasonally, when assuming an averaged isobath of 80 m, the LC has maximum volume transport of up to -7.2 Sv (106 m3 s-1, a negative sign means southwards transport) in April - June and -8.4 Sv in May - August in regions west and south of Western Australia, respectively. Inter-annually, the LC has higher volume transports than the average transport during 1993 - 2003 in most La Niña years, and the opposite in most El Niño years, which is linked to inter-basin exchange between the Pacific and Indian Oceans.

AUSGeoid98 is the national standard quasigeoid model of Australia, which is accompanied by a grid of vertical deviations (angular differences between the Earth’s gravity vector and the surfacenormal to the reference ellipsoid). Conventionally, co-located Global Positioning System (GPS) and spirit-levelling data have been used to assess the precision of quasigeoid models. Here, we instead use a totally independent set of 435 vertical deviations, observed at astrogeodetic stations across Western Australia before 1966, to assess the AUSGeoid98 gravimetrically modelled vertical deviations. This point-wise comparison shows that (after three-sigma rejection of 15 outliers) AUSGeoid98 can deliver vertical deviations with a precision (standard deviation) of around one arc-second, which is generally adequate for the reduction of current terrestrial-geodetic survey data in this State.

The south-west seismic zone (SWSZ) is a northwest-southeast trending belt of intraplate earthquake activity that occurs in the south-western corner of Western Australia, and is one of the most seismically active areas in Australia. Since the SWSZ lies as close as ~150 km from the ~1.4 million population of the Perth region, it poses a distinct seismic hazard. Earthquake activity recorded by Geoscience Australia over the past three decades suggests that the SWSZ could be deforming by 0.5-5 mmy-1. However, little is currently known about the magnitude and orientation of this deformation, and whether there is any associated surface expression. Previous geodetic studies of the SWSZ that used both terrestrial and Global Positioning System (GPS) techniques are inconclusive, due mainly to the imprecision of the technologies used in relation to the likely small amount of any surface deformation. Therefore, a new 48-point GPS-geodetic monitoring network has been established across the SWSZ to attempt to detect surface deformation, for which epochone episodic GPS-geodetic measurements were made in May 2002. This paper briefly reviews previous attempts to geodetically measure surface deformation across the SWSZ, summarises the scientific rationale for the new project, describes the network design and observations used, results of the May 2002 campaign (epoch-one) and discusses future work, including issues pertaining to the likely amount of surface deformation that can be detected.