05/12/03 12.540 Lec 23 1 12.540 Principles of the Global Positioning System Lecture 23 05/12/03 12.540 Lec 23 2 results – region of central Asia. – Example of evolution of a network – velocity model. Prof. Thomas Herring OVERVIEW ? Run through HW 03. ? Final lecture: Application area and GPS Analysis of contemporary motions in the Tien Shan Issues faced when generating multi-year (decade) 1 Homework 03 Results from analyses: Phase -2225432.8807 -4676994.9505 3711598.8548 Rinex file -2225431.6719 -4676995.2141 3711599.9580 L1 only -2225401.05 -4677074.26 3711596.32 LC data -2225395.55 -4677062.77 3711585.48 Diff BKAP -2225432.72 -4676994.79 3711599.45 Erwan -2225468.944 -4676973.873 3711593.862 Lili -2225402.870 -4677022.626 3711614.283 05/12/03 12.540 Lec 23 3 05/12/03 12.540 Lec 23 4 Central Asia Analysis ? Network monuments ? Analysis methods ? Motion relative to Eurasia ? Vertical motions – Development of network – Transition from “pins” with tripods to IVTRAN fixed-heights – Continuous stations – Pre-continuous station analysis – Merger with global GPS analyses – Methods of used to realize a Eurasia fixed frame – Vertical motions as a function of existing topographic heights 2 Network ? Development of Network – First measurements made in July 1992; just after start of International GPS Service (IGS). Since then measurements each year and often multiple campaigns per year. – The current network has over 1000 sites, many of them being recovery marks for the main stations (typically 3 per location) – Network extends from Kyrgyzstan to the Kazakh Platform – In 1995, the first continuously operating stations installed. Currently, 9 continuous sites with 2 IGS sites (POL2, SELE) – Results available on web at: http://www-gpsg.mit.edu/~tah/cont98g/cont98.html (Pages include time-series, phase residuals, atmospheric delay estimates) 05/12/03 12.540 Lec 23 5 05/12/03 12.540 Lec 23 6 Regional view of network Zoom Eurasia Fixed Frame realized using ITRF2000 50% confidence ellipses shown 3 05/12/03 12.540 Lec 23 7 Monument evolution ? which required tripod setups ? installed. Simplified setup. Three recovery marks installed for each original monument. ? After 1995, measurements made on the recovery marks rather than original marks. ? With the original marks and fixed height marks, for many stations two independent velocity estimates (results shown later) Original monuments were mainly steel pins in bedrock Starting in 1995: IVTRAN designed fixed-heights were Analysis methods ? Prior to 1995; selected IGS from Europe, Asia and Australia included in the analysis of regional data ? After 1995 when POL2 became an IGS site and was routinely included in the IGS analysis; only local sites included in the MIT analysis ? Using GAMIT/GLOBK; regional analyses are included in the Scripps Institution of Oceanography IGS (SOPAC) analysis including orbit improvement (more important in early data). ftp://garner.ucsd.edu/pub/hfiles ? Campaigns are combined with SOPAC h-files for velocity field and repeatability analyses. 05/12/03 12.540 Lec 23 8 4 05/12/03 12.540 Lec 23 9 Analysis Method ? Multiple types ? Global: Global selection of sites along with regional sites. Eurasian frame then defined using the ITRF2000 Eurasian rotation pole. ? Eurasian: Only sites from Eurasia included. Eurasian frame defined to minimize velocities of stable Eurasian sites ? In both analyses: Option to force velocities at nearby sites (<0.5 km separation) to be the same (some exceptions) ? Each campaign is rotated/translated to best align as a function of time with positions and velocities from one of the velocity analyses. Types of analyses performed with combined files: – Velocity field analysis. – Repeatability analysis: 05/12/03 12.540 Lec 23 10 IVTRAN Monuments Monument components Installed monument (SST antennas used in Central Asia Rod length 355 mm 5 Statistical analysis ? Since the network contains both continuous sites and campaign sites, we include statistical process noise in the velocity analyses to account for temporal correlations in the time series. ? Each site has random walk process noise (2 mm) 2 /yr ? Without process noise, velocities of continuous sites would have sigmas of < 0.1 mm/yr; with process noise sigmas are between 0.6 and 1.0 mm/yr e.g. Site Random Walk (mm/yr) White noise (mm/yr) E N UENU POL2 0.5±0.6 3.0±0.6 -0.5±1.1 0.2±0.1 3.3±0.1 -1.1±0.2 SELE 0.9±0.8 3.7±0.8 -2.5±1.2 1.7±0.1 3.8±.0.1 -2.1±0.2 05/12/03 12.540 Lec 23 11 05/12/03 12.540 Lec 23 12 Frame Realization ? Realization of Eurasian frame; Two methods used on many plates to rotate/translate frame onto ITRF2000. ITRF2000 Eurasia pole used to rotate to Eurasia fixed frame ? Fit to ITRF2000 (52-sites): ? Horizontal RMS 0.8 mm/yr; √c 2 /f 1.2 ? Vertical RMS 1.8 mm/yr; √c 2 /f 2.4 ? Fit to Eurasian sites only(14-sites) ? Horizontal RMS 0.5 mm/yr; √c 2 /f 0.8 ? Vertical RMS 1.8 mm/yr; √c 2 /f 2.3 ? Notice c 2 depend on size of region considered. – ITRF2000: Used global distribution of sites(52) – Eurasia only: Used 14 sites on stable Eurasia to define frame is <1 for Eurasia but >1 for global; sigmas 6 05/12/03 12.540 Lec 23 13 ITRF2000 Residuals Horizontal RMS 0.8 mm/yr 52-sites 05/12/03 12.540 Lec 23 14 Eurasia only residuals Horizontal RMS 0.5 mm/yr 14 sites Postglacial rebound model at NYAL, ONSA 7 05/12/03 12.540 Lec 23 15 Zoom RMS Difference 1.3 mm/yr systematic -1.3 mm/yr E -0.7 mm/yr N If removed 0.1 mm/yr RMS Difference between Realizations Set by 05/12/03 12.540 Lec 23 16 ? Another method for frame realization is the use of velocity solution. ? The frame is then found by rotation/translation to best match the Eurasia only realization ? In this method, effects of global scale systematic errors should be reduced. ? RMS difference of velocities is 0.4 mm/yr (√c 2 /f 0.2) and only slightly changed by estimating rotation/translation between fields. Local Frame realization local stations (1200x1800 km region) in forming 8 05/12/03 12.540 Lec 23 17 Zoom Local Frame Realization Differences Differences between co-located sites ? Of the approximately 400 sites with high- quality velocity estimates, 104 sites are collated between old and new monument styles. ? Comparison: Analysis Horizontal RMS 3D-RMS Global 1.9 mm/yr (√c 2 /f 1.0) 2.5 mm/yr (√c 2 /f 1.1) Regional 1.9 mm/yr (√c 2 /f 0.9) 2.4 mm/yr (√c 2 /f1.1) 05/12/03 12.540 Lec 23 18 9 05/12/03 12.540 Lec 23 19 Collocated velocity estimates Zoom 50% confidence intervals Differences are consistent with sigmas 05/12/03 12.540 Lec 23 20 Motion in Eurasia Frame Motion from difference analyses Best Estimates: Site East North mm/yr mm/yr POL2 3.0±0.6 SELE 0.9±0.8 3.7±0.8 AZOK 1.2±0.9 0.5±0.6 1.1±0.9 CHUM -0.3±1.0 0.4±1.0 10 11 05/12/03 12.540 Lec 23 21 Complete Velocity Field Field dominated by North- South compression Also East- West extension to East Zoom 05/12/03 12.540 Lec 23 22 Profile of North Velocities 0 5 10 15 20 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 l 76 o -77 0 l 75 o -76 0 l 74 o -75 0 North Velocity (mm/yr) Latitude (deg) 12 05/12/03 12.540 Lec 23 23 East Velocities as function of Longitude -5 0 5 10 68 70 72 74 76 78 80 82 f 42-43 o f43-44 0 East Velocity (mm/yr) Longitude (deg) 05/12/03 12.540 Lec 23 24 Height Rates versus Height -8 -6 -4 -2 0 2 4 6 8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 l76 o -77 o l75 o -76 o l74 o -75 o Vertical Velocity (mm/yr) Station Height (km) Regression of height rate versus height yields values between 1.4-1.9 (mm/yr)/km 05/12/03 12.540 Lec 23 25 Conclusions ? Eurasian appears to be less than 1 mm/yr ? ? East west extension across the range front of ~3 ? Height rate range of ~4 mm/yr ? Median RMS scatter of position estimates 1.4-1.8 mm horizontal and 4.6 mm height. ? process noise of (2 mm) 2 /yr. North of the Tienshan the motion of sites relative to Within the Kyrgz Tienshan ~13 mm/yr North converge mm/yr Consistent statistics are obtained with random walk 05/12/03 12.540 Lec 23 26 Tools http://www-gpsg.mit.edu/~tah/GGMatlab ? Most modern GPS analyses now contain hundreds of GPS sites ? For the remainder of the lecture we examine results with the GAMIT/GLOBK matlab tools available at: ? Current programs are velview and tsview. 13