OSVGeo
One-Step integration for Vector Geoid Determination
Introduction
OSVGeo is a software package for regional geoid determination. It computes a gravimetric geoid from gravity observations (terrestrial, airborne, scalar or vector, together with the long wavelengths from satellite gravity models) and delivers mean geoid heights on a regular grid.
What sets it apart is in the name. Conventional geoid determination in the Stokes–Helmert scheme downward-continues gravity to the geoid, then converts it to geoid heights, as two separate operations. OSVGeo solves both at once, in a single least-squares inversion. This avoids error accumulation between steps, and lets observations of different types and different quality be combined according to their actual precision rather than merged in advance.
OSVGeo is also, to our knowledge, the first operational package able to use the full airborne gravity vector (the east and north components alongside the vertical) rather than discarding two-thirds of what a modern airborne system measures.
The software was developed jointly with Dr. Mehdi Goli, in partnership with Sander Geophysics Ltd and with contributions from Dr. Spiros Pagiatakis. Its continued development and expansion is hosted by the Quantum Physical Geodesy Lab at the University of Calgary.
How it works
The package is a chain of three independent programs. Each does one job, and the output of one feeds the next.
Gravity observations must first be moved into a harmonic space where the topography above the geoid is either removed entirely (No-Topography space) or condensed onto a thin layer (Helmert space). OSVGeo supports both. The long wavelengths are then subtracted using a global gravity model, leaving a residual field. That residual is inverted to residual geoid heights, and the long wavelengths and the compensation for topography are restored at the end. This ensures a theoretically rigorous workflow to computed a gravimetric geoid model using OSVGeo.
Program: TOPO
TOPO (topographic corrections)
TOPO computes the effect of the Earth's topographic masses at location of gravity observations and on the geoid: the direct topographic effect (DTE) at the observation point, the secondary indirect effect (SITE) for gravity anomalies, and the primary indirect effect (PITE) on the geoid itself. All are available in both No-Topography and Helmert space.
Accuracy here depends on how carefully the terrain nearest the station is integrated, so TOPO divides the computation into four zones and uses a different method in each: prisms on a detailed 1–3 arc-second DEM in the innermost zone, Martinec–Vaníček tesseroid formulas at 30 arc-seconds and 5 arc-minutes, and point-mass approximation in the optional far zone.
Capabilities:
- Point-value DTE, SITE, and PITE in NT and Helmert space
- Vector DTE (east, north, down) for airborne vector gravity
- Four-zone integration with prism, tesseroid, or point-mass options
- Computation on terrain, at the geoid, or at flight level
- ASCII and binary DTM input
- User-defined topographic density, either constant value, or it accepts a lateral density variation model
Direct Topographical Effect in the NT space for Auvergne area (France) computed using TOPO program
Program: TOPO_SHS
TOPO_SHS (spherical harmonic synthesis)
TOPO_SHS supplies the reference field: the long-wavelength part of gravity and of the topographic effect, synthesized from global models. It handles ultra-high-degree Earth gravity models (up to 10,400) and evaluates ten different functionals of the field.
Capabilities:
- Height anomalies, geoid heights, gravity anomalies, and the gravity disturbance vector
- Reference topographic effects (DTE, PITE) in NT and Helmert space, using harmonics of topography to arbitrary power (H, H², H³ …)
- Synthetic topographic effects from forward models such as dV_ELL_Earth2014
- Ultra-high-degree synthesis, ICGEM-format model input
- GRS80 or WGS84 normal field; grid or scattered computation points
Reference gravity field in three East-North-Vertical directions computed using TOPO_SHS
Program: One-Step
One-step (the inversion)
One-step is the core of the package. It takes residual gravity, from any combination of sources, and returns residual geoid heights, performing the downward continuation and the conversion to geoid heights simultaneously rather than in sequence.
Downward continuation is an ill-posed inverse problem, so the solution has to be stabilized. One-step solves the combined system iteratively by weighted least squares and stops before noise begins to degrade the result, either by fitting to GNSS-levelling control points, by comparison with a pre-computed low-resolution geoid, or through five automatic stopping rules when no control data exist.
Capabilities:
- Simultaneous combination of terrestrial anomalies, terrestrial disturbances, and airborne scalar or vector gravity, weighted by observation precision
- Direct, Tikhonov, and CGLS solvers with multiple stopping criteria
- Vaníček–Kleusberg kernel modification to reduce the integration radius, with truncation error computed from a global model
- Internal accuracy estimation (geoid error model) by Monte Carlo propagation
- Sparse-matrix and block-wise computation for large regions and fine grids
- Adjustable frequency content per dataset, reflecting the band-limited nature of airborne data
Geoid model over Colorado region (USA) computed using OSVGeo
Survey design and pre-analysis
Because OSVGeo propagates observation errors through the inversion and returns an internal accuracy estimate for the geoid, it can answer a question that usually goes unanswered: what data would a country/region actually need to reach a target geoid accuracy, such as a sub-centimetre geoid?
We use this to run pre-analysis studies. Starting from existing gravity holdings, we compute a preliminary geoid with its error model, then test how that error responds to changes in the input, including the density and accuracy of gravity data, the precision of the digital elevation model, and the contribution of satellite gravity. For airborne campaigns, the same machinery optimizes flight line spacing and orientation, including for systems measuring the full gravity vector.
The result is a survey specification driven by the required accuracy rather than by convention, and usually a cheaper one. Knowing in advance where new data changes the answer, and where it does not, means fewer flying hours and fewer ground stations for the same geoid.
Optimizing flight line spacing using vertical only vs. full vector airborne gravity
Validation
OSVGeo has been validated on the international geoid test datasets used by the geodetic community, for example Auvergne in France and Colorado in the United States, and on real airborne vector gravity acquired with SGL's AIRGrav system such as Colorado Airborne Vector Gravimetery test region, and New South Wales (Australia). These regions were chosen deliberately: both are mountainous, both have independent GNSS-levelling control, and both have been used to benchmark other geoid methods, which makes independent comparison possible.
Access and Training
OSVGeo is open for research and training purposes. Geoid determination involves choices such as harmonic space, integration radii, regularization, and stopping criteria, all of which materially affect the result. A package of this kind cannot be used well from documentation alone, so training is part of how we make it available. Participants work through a complete geoid computation from raw gravity to a validated model, either on the test cases the software was validated on or on a dataset of their own choice, such as data from their own country.
Sander Geophysics Ltd. holds the commercial licence for OSVGeo. To enquire about training and licensing, contact Ismael.Foroughi@ucalgary.ca