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

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??

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.

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

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

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

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

Enables routine processing of…

Example: Western US networksIGS, PBO, NEARNET, SCIGN, PANGA, BARGEN, EBRY, BARD, …

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

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

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!!

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

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

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

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

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

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