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 Plag Nevada 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 ( 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 networks IGS, 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 give the 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 positions e.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/ambizapftp://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~ Run Ambizap to resolve biases n 4. 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