Transcript Document

Stable North American Reference
Frame (SNARF): Version 1
SNARF Working Group
Presented by
Jim Davis and Tom Herring
Outline
• Jim Davis
– Problem, approach, initial results
• Tom Herring
– 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