SNARF: Theory and Practice, and Implications Thomas Herring Department of Earth Atmospheric and Planetary Sciences, MIT

1/27/04SNARF: Herring2 OVERVIEW  Reference Frame definition and realization  Types of reference frames:  Dynamic: Appropriate for dynamic equations of motions such as orbit integration. Implies physical properties such as transformable into non-rotating frame and registration with gravity field.  Kinematic: Appropriate for studying deformation including definition of stable plate and height reference frame  Ideally SNARF would satisfy both types. In practice, a dynamic frame probably needs to be defined globally while an adequate kinematic frame could be defined (most cleanly defined?) with only North America sites.  In modern frames, the time derivatives of the frame also need to be considered (I.e.,relationship between frame and stable plate)

1/27/04SNARF: Herring3 Frame Definition and Realization  Reference frames are composed of two parts:  Definition: Defines the origin and orientation (and scale) of the frame  Realization: The practical method to achieve the definition.  Definitions: Concepts such as  Origin at Center of Mass: Problem already. Center of Mass is probably moving relative to center of figure. For orbit integration need origin to be registered with gravity field. (Can be done with first degree harmonic coefficients in gravity field.  Orientation: Aligned with a set of axes. Theoretical considerations such as maximum moments of inertia (again, issues related to motion of these axes with respect to “crustal axes”).  Some orientations are arbitrary (for example, Greenwich meridian)  Scale: SI unit but complicated by effects such as phase center variations.

1/27/04SNARF: Herring4 Frame realization  Realization: Implementation issues  Nominally a realization is achieved by rotation, translation and (possibly scale) between two frames. The transformation parameters can be time derivatives.  Realization of the frame becomes an iterative process when the quality of sites and/or their appropriateness to the frame is not known.  For a North American frame, high quality sites on the North American plate would be chosen  Ideally a simple linear motion model would be applicable, and a frame chosen with those sites that can be represented by a rigid body rotation  In practice, nearly all sites seem to have some components of non- secular motion.

1/27/04SNARF: Herring5 Examples  North American plate realization for the SCIGN array  Data set: Loosely constrained solutions from SOPAC (h-files). Merged into global, daily network files for up to 400 sites ( )  Initial time series analysis (rotating and translating on ITRF2000) allowed selection of sites with secular motions  Stacking of combined files with velocities estimated (and offsets for equipment changes) allows selection of sites in North America that can be rotated to have near zero velocity (RMS 0.7 mm/yr, horizontal)  Since SCIGN is at the western edge of this network, Pacific sites also included. Relative motion of NA and Pacific determined from ITRF2000 Euler poles (could also have been estimated) (RMS remains near 0.7 mm/yr)  The positions and velocities of the ”good” sites in SCIGN can then be used for daily regional time series analysis in SCIGN (best position RMS 0.5 mm)  Results available at

1/27/04SNARF: Herring6 RMS Fits Horizontal 0.7 mm/yr Exclude 2 sites 0.5 mm/yr SCIGN NA Reference Frame

1/27/04SNARF: Herring7 All “North American” Sites Note: NA plate may extend into eastern Russia

1/27/04SNARF: Herring8 Nearly stable NA (< 2mm/yr) RMS 0.6 mm/yr 64 sites

1/27/04SNARF: Herring9 N -0.7 mm/yr, East 0.9 mm/yr, Height 6.5 mm/yr Time Series in East and Up for Churchill

1/27/04SNARF: Herring10 Churchill Atmospheric loading

1/27/04SNARF: Herring11 Summary  Realization of SNARF:  Secular component of SNARF can be achieved with current methods assuming that the non-secular components (water, atmospheric loads) have no secular components.  Daily realization of the frame pose problems due to non-secular components in station motions  Components include atmospheric and water loading. Mainly vertical for long wavelength features but can have large horizontal components for nearby compaction/expansion effects  With appropriate apriori models, effects can be accounted for  Care needed in definition of station coordinates when loading effects included.  Scope of the frame: Near zero velocities, limited to south-east portion of NA. Include sites with non-zero velocity relative to plate; or include more plates (e.g. Pacific)

1/27/04SNARF: Herring12 More subtle effects  Center of Mass:  GPS center of mass position estimates very sensitive to treatment of radiation parameters, nature of global networks and estimation  Bias fixing in global networks has impact on center of mass. Correlations very high and bias fixing, multi-day orbit arcs help reduce these correlations. (Also can bias the center of mass positions)  Data quality:  Individual stations can be have problems (either instrumental or physical motion of site)  Combined dynamic and kinematic SNARF probably requires global GPS analysis (plus other geodetic systems may help).