toward “broadband exploration” of tectonic-magmatic interactions: demonstration of...
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Toward “Broadband Exploration” of Tectonic-Magmatic Interactions:
Demonstration of Self-Consistent, "All-in-One" Rapid Analysis of GPS Mega-Networks using the Ambizap Algorithm
Geoff Blewitt, Corné Kreemer, Bill Hammond,
and Hans-Peter PlagNevada Geodetic Laboratory,
University of Nevada, Reno, USA
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Introduction Transients in station positions
Reflect rheological responses to history of stress change in the “solid Earth”
Over a broad spatio-temporal spectrum Spectral connections are possible:
Common forcing factors (earthquakes, magma,…) Feedback between forcing factors
“Broadband exploration” must be consistent across the spatio-temporal spectrum Can consistency be provided by GPS??
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Tectonic-Magmatic Transients
Late 2003: Few-mm transient at Slide Mountain, Sierra Nevada, USA Deep (~20 km) crustal magma intrusion in non-volcanic region!! Is this a method to accommodate tectonic extension? [Smith et al., 2004] Associated with ~1000 km extensional transients? [Davis et al., 2006] Detection by GPS requires carrier phase ambiguity resolution Problem: this is computationally prohibitive for large networks So networks are pieced together – difficult to manage – inconsistencies.
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Objectives “Broadband exploration” using GPS Develop a GPS analysis scheme that is:
Spatially consistent (1–10,000 km) Temporally consistent (0.01-10 yr)
“All-in-one” network analysis approach Requires a method for consistent
ambiguity resolution for highly densified global networks
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Remind me – What is carrier phase ambiguity resolution?
range = ( phase + n ) × wavelength
for each station, number of parameters:
NPAR = 3(xyz) + 1(clock) + 3(tropo) + 30(n) = 37
first estimate all n as real-valued Now, if we resolve n exactly as integers:
NPAR = 3(xyz) + 1(clock) + 3(tropo) + 1(n) = 8
fewer parameters improves precision of xyz
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So what is Ambizap then? Ambizap enhances PPP precision PPP = “Precise Point Positioning”
invented 1997 by Jim Zumberge, JPL 1-station carrier phase + orbits + clocks takes ~10 sec / station / day of data
Ambizap = rapid ambiguity resolution additional ~5 sec / station / day of data factor ~2 improvement in horizontal
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What’s the big deal? Ambiguity resolution since
~1989 BUT, for classical network
ambiguity resolution, processing time scales as:
T ~ N 4
takes 24 hrs to process N =100 stations
Ambizap time scales linearly: T ~ N
takes < 9 minutes for N =100
takes < 2 hrs for N =1000
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Enables routine processing of…
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Example: Western US networksIGS, PBO, NEARNET, SCIGN, PANGA, BARGEN, EBRY, BARD, …
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Why is Ambizap so fast? Classical ambiguity resolution
uses “bootstrapping” technique resolve best-determined n first improve estimates of all remaining n then resolve next-best n (and so on…)
Ambizap treat N stations as N–1 baselines only bootstrap within each baseline
so process time scales linearly with N
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What’s the catch?
Ambizap does give same answer if ambiguities are successfully resolved
But lack of full network bootstrapping limits
Ambizap to lines of L < 2000 km But but…
no problem… just use all the stations in the world, then
baselines of L < 2000 km can connect all stations
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Interesting paradox Classical ambiguity resolution
strictly limited to N << 100 for any reasonable processing time
smaller networks are easier to handle Ambizap
limited to N >> 100 for global networks larger networks are easier to handle
e.g., include badly monumented stations too!!
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Another catch Classical ambiguity resolution
can be easily used to improve satellite orbits and satellite clock parameters
(but typically N ~ 60 ) Ambizap
strictly for PPP solutions so no orbit and clock improvement (yet) covariance matrix not complete
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Why does Ambizap givethe same answer?
“Fixed point theorem” centroid of a baseline (hence entire
network) invariant to ambig. resolution network origin fixed by initial PPP solution Only relative positions are affected
N–1 baselines specify all relative positionse.g., (A-C) = (A-B) – (B-C)
so initial PPP + N–1 baselines has all the information of full network solution
take care not to count PPP data twice
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Implementation Add-on software for JPL’s GIPSY
go to ftp://gneiss.unr.edu/ambizap main script and most modules in c-shell couple of routines in FORTRAN-95
User group now doing “beta testing” Could in principle be implemented for
any software with PPP capability undifferenced phase processing
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Benefits Speed
Can rapidly reprocess data, try different models, etc.
Very large networks now possible Hence no need for sub-networks
Just one unified global network! Easy and fast to add extra station(s) to an
existing network solution No need to recompute entire solution
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Future concept(in collaboration with JPL)
1. As now, solve for orbits and clocks with full ambiguity resolution using N~60 stations
2. Produce PPP solutions for N~10003. Run Ambizap to resolve biases n4. With N~300, solve for orbits and
clocks, holding fixed the biases n Will improve PPP, LOD positioning Will improve geocenter, reference frame Will improve vertical motion interpretation
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Conclusions Ambizap will enable “broadband
exploration” of tectonic-magmatic processes
Now routinely processing ~1300 stations Approx. 4 hours PPP + 2 hours Ambizap (1 cpu)
Simplifies data management No need to process sub-networks Easy to add extra stations later
Opens possibility to future scheme to improve GPS orbits + clocks, and PPP