Stable North American Reference Frame (SNARF): Version 1

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Stable North American Reference Frame (SNARF)
Version 1

• SNARF Working Group
• Presented by
• Jim Davis and Tom Herring

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Outline

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

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Purpose

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

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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)

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

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GIA Predictions Requirements

• A model for the Earths viscoelastic structure
• Theory and code to calculate the time-dependent
  Greens 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 Greens functions,
  while simultaneously solving for effects due to
  the redistribution of the surface load (ice?water)

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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)

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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

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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)

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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

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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,
  Hudsons Bay, Canada (w 9.1 0.2 mm/yr)

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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

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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)

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Prior Correlation wrt Churchill
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SNARF 1.0 GIA Field
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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
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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

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