Geoff Blewitt, Corn é Kreemer, Bill Hammond, and Hans-Peter Plag

1. 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

2. 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??

3. 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.

4. 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

5. 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

6. 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

7. 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

8. Enables routine processing of…

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

10. 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

11. 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

12. 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!!

13. 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

14. 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 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

15. 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

16. 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

17. Future concept(in collaboration with JPL) • As now, solve for orbits and clocks with full ambiguity resolution using N~60 stations • Produce PPP solutions for N~1000 • Run Ambizap to resolve biases n • 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

18. 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