Reference Frame Theory & Practice: Implications for SNARF SNARF Workshop 1/27/04 Geoff Blewitt University of Nevada, Reno

Overview –Reference system versus reference frame –Frame realization –Choice of system –Use of frames in practice –Scientific interpretation issues –Issues for use to consider

Frame versus System Reference System –Set of conventions Reference Frame –Set of coordinates of physical points (stations, quasars…) consistent with conventions

Frame versus System Reference System –Axiomatic ideals “no-net translation wrt…”, “no-net rotation wrt….” Frame parameters: Origin, orientation, scale,… Evolution of above with time Typically includes physical concepts (center of mass of whole Earth system,…) Therefore creating the ability to tie various observation sets into one integrated system (“grand unified geodesy”) –Conventions speed of light, SI units, … –Conventional models example: station motion models (usually well known, or at least functional form is known, such as rigid plates)

“Grand Unified Geodesy” Geocenter Motion Relative Sea Level Land Load Load Potential Gravitation LLN Theory Geocentric Sea Level Surface Load Solid Earth Deformation Gravitational Potential   Deformed Ocean Bottom Momentum Frame Theory Global Positioning System (GPS) Satellite Gravimetry Earth Rotation Moment of Inertia Angular Velocity Gravity Potential Equipotential Sea Surface Mass Exchange Centrifugal Potential Satellite Altimetry VLBI Satellite Laser Ranging Remote Sensing

Frame versus System Reference Frame –A specific realization of a reference system consistent with its conventions based on physical observations –In our case Selected set of GPS stations Specified parameters of the station motion model –position coordinates at some conventional epoch –velocity coordinates –Instantaneous coordinate offsets (e.g., co-seismic,…) –or more generally – set of coordinates at many epochs –Note that the frame depends on Definition of the reference system, particularly the models Adopted set of stations Adopted set of observations leading to parameter estimates

International GPS Service Network

Frame Realization: IGS Polyhedron Assembly Global+Regional 960 km Global 1724 km

Frame Realization Steps: 1.Adopt reference system as part of GPS observation model 2.Solve for unknown parameters for station motion model (coordinates at reference epoch, velocity components, discontinuities...) 3.This is a fiducial-free (“loose”) kinematic solution –strictly not in a reference frame –but the network is tied to the center of mass of the Earth system 4.Select a subset of stations in the solution which are defined by a specific frame (e.g., ITRF00) 5.Solve for and apply a generalized Helmert transformation to minimize residuals to defined frame: –translation, orientation (and scale is optional) –translation rate, orientation rate (and scale rate is optional) 6.Note that final solution depends on –Selection of stations, and coordinate errors in ITRF00 –Conventional models (and errors!) in the IERS Reference System

Choice of System Conventional considerations –Should for the most part be consistent with IERS Reference System Interpretive considerations –Interpretation may be facilitated if frame is such that the North American plate appears stationary Question –Is it sufficient to specify “stable North America” by selecting a subset of the network that does not appear to deform? –Or can models can be implemented that make some specified portion of North America appear more like a rigid plate?

Using a Frame in Practice Fiducial method –Hold subset of stations fixed to frame coordinates Fiducial-free method –Solve for all station coordinates, then solve and apply (generalized) Helmert transformation Transformation method –Solve for stations in one frame, say ITRF00 –Apply a known transformation into the desired frame (e.g., remove rotation of North America in ITRF00) In all cases, models may also need to be applied to be consistent with the plate-fixed reference system

Frames and Interpretation From Jim Davis: Vertical velocities (mm/yr) in North America Is this “real” or is it a frame problem?

Interpretation Issues Choice of frame –Should be to facilitate interpretation –Should not introduce unnecessary errors Errors –In frame itself (specific station coordinates…) –In reference system models Coordinate system problems –“Horizontal” and “vertical” trade off if the frame has a translation rate bias (imagine a translating sphere) –Even strain inferred from velocities are not immune! A translation rate bias in the frame causes relative horizontal coordinates (latitude, longitude) between stations to vary. And can create anomalous vertical motions

A “Perfect” Example: Degree-1 Deformation Motions appear to be horizontalMotions appear to be vertical PARADOX: The deformation is actually identical !

Issues for Us to Consider Which reference system will best suit our needs? –What would be ideal? –What is actually possible? –Can ITRS conventions be adopted or improved? Which stations to select in the frame? What is the station motion model? –Part specified by the reference system itself –Part estimated by GPS data How should our “product” (system+frame) be produced and tested? How do we ensure it gets used and is useful ?