Esci 203, Earth Structure and Deformation Introduction to the global positioning system (GPS) John Townend EQC Fellow in Seismic Studies

Recent events Preliminary GPS displacement data (version 0.1) provided by the ARIA team at JPL and Caltech. All Original GEONET RINEX data provided to Caltech by the Geospatial Information Authority (GSI) of Japan.

Overview What is GPS –A space-based Global Positioning System How does it work? –Trilateration using very accurate timing measurements What are some of its limitations? How can earth scientists use it? –General positioning, deformation monitoring…

What is GPS? Space segment, Navstar –24 satellites orbiting at an altitude of ~20,000 km Control segment –5 ground stations User segment –Users with GPS receivers Global Positioning System

Campaign and permanent GPS Campaign (temporary) GPS station Pu`u O`o, Kilauea, Hawai`i Continuous (permanent) GPS station Gisborne, New Zealand Figures courtesy of Peter Cervelli, HVO, and Land Information New Zealand

The satellite signal Each satellite transmits low-power (20– 50 W) signals on various frequencies –Civilian receivers listen at MHz The receiver determines the signal travel time from the satellite –With four or more satellites, the receiver can determine its latitude, longitude, altitude, and internal clock error

Pseudo-random codes The signal emitted by each satellite is unique and extremely complex (“pseudo-random”) The receiver generates the same signal, and compares it with what it receives from the satellite to determine the travel time Receiver signal Satellite signal tt

Extra steps What is the time? –Each satellite carries an atomic clock but the receiver’s internal clock is much less accurate –So, the receiver uses an extra satellite signal to estimate the difference in time between it’s onboard clock and the standardised satellite time And where are the satellites exactly? –The control stations measure each satellite’s ephemeris very precisely; this data is broadcast to the satellites and included in the GPS signal

Trilateration distance = travel time  speed of light Sat 1 Sat 3 Sat 2 Sat 4 The receiver determines the distance (“pseudo-range”) to 4+ satellites, and calculates its position; it’s like locating an earthquake in reverse!

Sources of error Ionospheric/tropospheric delays Multi-pathing Receiver clock errors Ephemeris errors Constellation geometry and weather Intentional signal degradation: –“selective availability”, which limited accuracy to ~6–12 m but has now been switched off

Selective availability Figure courtesy of Peter Cervelli, HVO

Geometric dilution of precision High GDOP; low confidenceLow GDOP; high confidence

Differential GPS (“dGPS”) GPS signal dGPS correction signal Satellite Reference station Mobile receiver Reference stations broadcast corrections to the satellites’ signals; typical dGPS accuracy is ~1–5 m

A typical permanent GPS installation

Geodetic velocities We commonly make use of the east and north components of velocity, v E and v N The overall velocity vector v has a magnitude (length), v 2 = v E 2 + v N 2, and an azimuth  = atan (v E /v N ) vEvE vNvN v 

Measuring velocities The velocity in each direction (east, north, up) is just the gradient of the position time series

Measuring velocities The velocity in each direction (east, north, up) is just the gradient of the position time series e.g. v N =  n/  t tt nn

Relative motion (1) v plane-air v air-ground v plane-ground = v plane-air + v air-ground

Relative motion (2) v A-B v B-ref v A-ref = v A-B + v B-ref meaning that v A-B = v A-ref – v B-ref = v A-ref + (– v B-ref )

Relative motion (3) Site A Site B vAvA vBvB vAvA vBvB –vB–vB v A-B

Summary Points to revise –How GPS basically works –Key factors affecting position estimates –Measuring site velocities from GPS data and relative velocities between sites Extra material online –

Reading material Van der Pluijm and Marshak –Section 14.9 Fowler (2005) –Sections 2.1 and 2.2 Mussett and Khan –Section 20.5 If you need to brush up on vectors, try “Mathematics : a simple tool for geologists”, by Waltham; this is in the library