Defining a Local Reference Frame Using a Plate Motion Model and Deformation Model

Abstract

As GNSS point-positioning becomes more precise and accessible to a wider spectrum of users, the issue of misalignment between GNSS positioning reference frames and spatial data reference frames used in GIS will become more apparent. Positions of plate-fixed features within GNSS reference frames are kinematic in nature due to global plate motions and other geophysical phenomena including seismic deformation and post-glacial rebound. Coordinates within GIS and applications such as Google Earth on the other hand, are typically fixed to the Earth’s surface and tectonic plate and may be misaligned with global reference frames unless a kinematic model is applied to the data.

The problem becomes more apparent when data acquired at different epochs are combined in the absence of a kinematic model. Should a GNSS point-position or baseline vector solution be transformed to the epoch of existing spatial data, or should the spatial data be transformed to the epoch of the point-position? In either case, data acquired at different epochs within a GNSS frame will need to be transformed to a common epoch for the purpose of combination, interpretation and analysis. Furthermore, localised deformation analysis studies using remote sensing techniques such as InSAR and Lidar require removal of any secular plate motion signal prior to meaningful analysis. Presently, it is more computationally efficient to transform GNSS observations to a formalised reference epoch for spatial data.

A logical approach to the problem is to develop a Local Reference Frame (LRF) which is fixed to the crust within a defined polygon, and which is also directly traceable to GNSS reference frames such as the International Terrestrial Reference Frame (ITRF) by means of a Plate-Motion Model (PMM) and residual Deformation Model (DM). In plate boundary zones where crustal deformation is significant such as New Zealand, a PMM is of limited application and an “Absolute” Deformation Model (ADM) can be used to describe the full transformation between reference frames. PMMs are specified by an Euler Pole which can also be defined by the rotation rates of the three Cartesian axes. The Euler Pole is estimated by inversion of a selection of station ITRF site velocities. A residual DM can be estimated by kriging or least-squares collocation of site-velocity residuals within the PMM and application of a fault locking model where elastic strain or seismic deformation is evident.

Use of a PMM and associated DM enables ITRF positions and vectors (e.g. from GNSS observations) to be transformed to a local frame to support GIS data integration and combination of data acquired using terrestrial positioning techniques such as Terrestrial Laser Scanning and conventional Total Station surveys. A case-study for the development of a new Australian Terrestrial Reference Frame is presented.