Stable North American Reference Frame (SNARF): Version 1 SNARF Working Group Presented by Jim Davis and Tom Herring

Outline Jim Davis Tom Herring Problem, approach, initial results Products, use, future work

Purpose To define a geodetic reference frame for “stable” North America SNARF will form a common geodetic reference frame for PBO/EarthScope studies

Definitions and Assumptions Large parts of North American continental crust are currently not deforming (“stable”) from plate tectonic forces. These parts are mostly east of the Rocky Mountains The entire North American continent is deforming significantly due to glacial isostatic adjustment (GIA)

Ice-1 LT = 120 km nUM = 0.8  1021 Pa s nLM = 10  1021 Pa s

Definitions and Assumptions Given a geodetic solution with site velocities VGPS at locations (l,f), we can describe the solution using The velocity rotation and translation parameters are unknown and must be estimated as part of the SNARF definition

GIA Predictions: Requirements A model for the Earth’s viscoelastic structure Theory and code to calculate the time-dependent Green’s functions for deformation from surface loads A history of the time-dependent ice load, starting preferably prior to the most recent glacial maximum ~20 kYr ago Theory and code to convolve the time-dependent load with the viscoelastic Green’s functions, while simultaneously solving for effects due to the redistribution of the surface load (icewater)

GIA Predictions: Practical Issues No consensus concerning viscosity structure No consensus concerning ice history Ice & Earth models are generally not independent (inversions nonunique) Current Earth models for GIA are spherically symmetric, but lateral variations are important (Latychev et al., 2004)

SNARF Approach Rather than adopt an unrealistic ice/Earth model pair that we know will introduce systematic errors, SNARF is investigating a novel approach GPS velocities will be assimilated into an a priori GIA model based on a suite of predictions to yield an observation-driven model

Assimilation of GPS Data into GIA Models Bayesian approach We use a Kalman-filter to assimilate the GPS velocities into a prior GIA model The GIA model is the “average model” based on a suite of GIA models spanning a range of Earth models The variability of the GIA models is used to calculate a statistical distribution (and covariance matrix) for the starting GIA field We estimate GIA deformations on a grid (2°2°)

GPS Data Assimilation We simultaneously estimate six rotation and translation para-meters, and GIA velocities at n grid locations and at m GPS sites At right, the parameter vector (u = east velocity, v = north, w = radial) The observations consist of (u,v,w) for GPS sites The GIA values at the grid locations are adjusted through the covariances calculated from the suite of model predictions SNARF 1.0 solution: n = 1537, m = 99, # parameters = 4617

Assimilation Tests For proofs-of-concept tests, we focus on radial motions These tests will use no “real” GIA information (“no physics” The starting GIA model is the null field w(l,f) = 0 We adopt a Gaussian covariance model: Lij = w(li,fi) w(lj,fj) = s2 exp(-dij2/D2) Where dij is the angular distance between the locations, D = 10°, and s = 1 mm/yr In the first test, we assimilate a single GPS observation at the location of site Churchill, Hudson’s Bay, Canada (w = 9.1 ± 0.2 mm/yr)

Assimilation Tests In the second test, we assimilate a subset of NA radial site velocities The assimilated field (still “no physics”) has many features of a realistic GIA field

Assimilation Ice model: Ice-1 [Peltier & Andrews, 1976]; gives slightly better results than Ice-3G [Tushingham & Peltier, 1991] Earth models: Spherically symmetric three-layer, range of elastic lithospheric thicknesses, upper and lower mantle viscosities (see Milne et al., 2001) Elastic parameters: PREM GPS data set: Velocities from “good” GPS sites, recent NAREF solution from Mike Craymer Placed in approximate NA frame by Tom Herring (unnecessary step but simpler)

Prior Correlation wrt Churchill

SNARF 1.0 GIA Field

Solution Statistics Prefit statistics: WRMS (hor): 1.22 mm/yr WRMS (rad): 3.81 mm/yr WRMS (all): 1.74 mm/yr Postfit statistics: WRMS (hor): 0.71 mm/yr WRMS (rad): 1.30 mm/yr WRMS (all): 0.80 mm/yr

Conclusions (Part 1) Current “accuracy” of SNARF 1.0 is ~1 mm (+30% radial/-30% horizontal) Estimated rotations/translations (from “nominal” no-GIA NA-fixed)  1.5 mm/yr GPS assimilation technique seems to work, may be useful for GIA work Straightforward to assimilate other data types