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12.221 Field Geophysics!

Instructors Brad Hager bhhager@mit.edu

Tom Herring, tah@mit.edu

Web: http://geoweb.mit.edu/~tah/12.221!

Lec GPS: Introduction to GPS!

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Introduction to GPS

•  Uses of GPS in this course!– Hand held navigation. ($200)!– Differential “kinematic” positioning for

determining heights of gravity measurements and seismic locations.!

– Precise static positioning for ~1 mm positioning ($5-10K)!

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Coordinate Systems!

•  See discussion in IEEE paper!•  We will need to deal with several coordinate systems and

methods of expressing coordinates.!•  System: !

–  Origin at center of mass of Earth!–  Z-axis along average position of rotation axis (moves by 10 m during a year

– call polar motion)!–  X-axis along Greenwich meridian (convention)!

•  Before space-based geodesy (mid-1970ʼs), realizations of this system could differ by several hundred meters.!

•  Impact of this for us will be difference between North American Datum 1927 (NAD 27) (most paper maps use this system) and NAD83/World Geodetic System 1984 (WGS84) (used by GPS but with options for other systems)!

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Systems we need!

•  Modern GPS results are given in the “International Terrestrial Reference System”. Latest realization is ITRF2005 (Use Frame to denote realization)!

•  World Geodetic System WGS84 used by GPS control center (within a few meters of ITRF2005)!

•  However: Maps made well before this system and most US maps use North American Datum (NAD) 1927 (NAD27) or NAD83 (which is very close to WGS84 and ITRF2005.!

•  NAD27 is approximately 200 m away from modern system!

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Types of coordinates!•  Within a system, coordinates can be expressed in

different ways:!–  Cartesian (XYZ – Computational easy)!–  Geocentric latitude, longitude and radius (spherical)!–  Geodetic latitude, longitude and height above ellipsoid

(ellipsoidal coordinate system).!–  Universal Transverse Mercator (UTM) coordinates. Actually

ellipsoidal map projection coordinates. These have units of distance compared to latitude and longitude which are angle measurements. !

•  Coordinates expressed as Northing and Easting.!–  Digital Elevation Models (DEM) are often in UTM

coordinates.!

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GPS Original Design

•  Started development in the late 1960s as NAVY/USAF project to replace Doppler positioning system!

•  Aim: Real-time positioning to < 10 meters, capable of being used on fast moving vehicles.!

•  Limit civilian (“non-authorized”) users to 100 meter positioning.!

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Design Characteristics of GPS!

•  Innovations:!–  Use multiple satellites (originally 21, now ~30-32)!–  All satellites transmit at same frequency!–  Signals encoded with unique “bi-phase, quadrature code”

generated by pseudo-random sequence (designated by PRN, PR number): Spread-spectrum transmission.!

–  Dual frequency band transmission:!•  L1 ~1.575 GHz, L2 ~1.227 GHz !•  Corresponding wavelengths are 190 mm and 244 mm!•  Dual frequency band transmission allows the dispersive delay

of the ionosphere to be removed (10-100 m)!

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Block IIR Satellite!

• Transmission array is made up of 12 helical antenna in two rings of 43.8 cm (8 antennas) and 16.2 cm (4 antennas) radii!

• Total diameter is 87 cm!• Solar panels lead to large solar radiation pressure effects.!

• Mass: 1,110 kg!

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Measurements

•  Time difference between signal transmission from satellite and its arrival at ground station (called “pseudo-range”, precise to 0.1–10 m)!

•  Carrier phase difference between transmitter and receiver (precise to a few millimeters) but initial values unknown (ie., measures change in range to satellites). !

•  In some case, the integer values of the initial phase ambiguities can be determined (bias fixing)!

•  All measurements relative to “clocks” in ground receiver and satellites (potentially poses problems).!

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Measurement Usage!

•  “Spread-spectrum” transmission: Multiple satellites can be measured at same time.!

•  Since measurements can be made at same time, ground receiver clock error can be determined (along with position).!

•  Signal!

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Measurement usage!

•  Since the C(t) code changes the sign of the signal, satellite can be only be detected if the code is known (PRN code)!

•  Multiple satellites can be separated by “correlating” with different codes (only the correct code will produce a signal)!

•  The time delay of the code is the pseudo-range measurement.!

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Position Determination (perfect clocks)!

• Three satellites are needed for 3-D position with perfect clocks. !

• Two satellites are OK if height is known)!

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Position determination: with

clock errors: 2-D case!

• Receiver clock is fast in this case, so all pseudo-ranges are short !

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Positioning!

•  For pseudo-range to be used for positioning the following quantities must known:!–  Errors in satellite clocks (use of Cesium or Rubidium clocks)!–  Positions of satellites!

•  This information is transmitted by satellite in “broadcast ephemeris”. This information saved in receiver data file. We will use for in-field processing!

•  “Differential” positioning (DGPS) eliminates need for accurate satellite clock knowledge.!

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Current constellation!

• Relative sizes correct (inertial space view)

• “Fuzzy” lines not due to orbit perturbations, but due to satellites being in 6-planes at 55o inclination.

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Types of parameters estimated in GPS analysis!

•  GPS phase measurements at L1 and L2 from a global distribution of station used. Pseudo-range can be used but 100 times less accurate than phase.!

•  Giobal Analysis typically includes:!–  All site positions estimated!–  Atmospheric delay parameters estimated!–  “Real” bias parameters for each satellite global, integer values for

regional site combinations (<500 km)!–  Orbital parameters for all satellites estimated (1-day orbits, 2-

revolutions)!•  6 Integration constants!•  3 constant radiation parameters !•  6 once-per-revolution radiation parameters!

•  Orbits need not be estimated when International GNSS Service (IGS) finals orbits are used (post-1996).!

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GPS Antennas (for precise positioning)!

• Rings are called choke-rings (used to suppress multi-path)

Nearly all antennas are patch antennas (conducting patch mounted in insulating ceramic).

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Styles of Monuments!

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IGS Network!Currently over 400 stations in network

Global site motions!

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Alice Springs Tonga and ���Vanuatu

We can use positions of sites determined each day and map the motions of these sites globally as shown below.

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Example Results from GPS analyses!

•  Examples of time series for some sites!–  Tectonic motions in the Asian region!–  Motions in California (example in more detail later)!–  Time series of motions for some sites!–  Post seismic motion after 1999 Hector Mine earthquake!

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Tectonic Deformation Results!

•  “Fixed GPS” stations operate continuously and by determining their positions each day we can monitor their motions relative to a global coordinate system!

•  Temporary GPS sites can be deployed on well defined marks in the Earth and the motions of these sites can be monitored (campaign GPS)!

•  Our field camp sites will be temporary and we will measure “relative” to continuous Southern California Plate Boundary Observatory sites.!

•  http://pboweb.unavco.org/ !

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Global site motions!

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Alice Springs Tonga and ���Vanuatu

We can use positions of sites determined each day and map the motions of these sites globally as shown below.

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Fastest separating GPS sites in the world 150 mm/yr

The seafloor topography here are spreading ridges and subduction zones. This one of the most seismically active regions in the world.

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East motions at Vanuatu and Tonga!

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Figure below show east motions are Vanuatu (blue) and Tonga (black) Bottom figure is difference with linear trend of 170 mm/yr removed. A fast earthquake on May 3, 2006, Magnitude 7.9, 150 km away from Tonga can see seen. A slow earthquake event in 2004 can also be seen.

Fast Earthquake

Slow Earthquake Another Earthquake

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Examples of Geophysical Signals!

Time series show different types of motions that are seen in GPS measurements.

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Vectors show coseismic offsets and postseismic displacements after 7-years

Postseimic estimated with two different methods.

Hector Mine Co- and Post-seismic

displacements!

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Large scale postseismic deformation!

Figure from Andy Freed and Roland Burgmann

Examine North component of motion (averaged 60-days)

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Analysis for San Simeon Earthquake!

PBO stations installed after earthquake

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Time series of North motion of sites near San

Simeon!

Grey lines show motion expected for this part of California

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Parkfield Earthquake!

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Full North/East Time series for Parkfield site!

Pre-Earthquake North 20.7±0.2 mm/yr East -14.6±0.2 mm/yr

2007-2009 Velocities North 17.5±0.2 mm/yr East -13.4±0.3 mm/yr

Daily position determinations showing effects of San Simeon and Parkfield earthquakes. It takes a long time for the earth to recover. Continued motion has a role in loading for next earthquake.

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El Mayor-Cucapah Baja Earthquake!•  On April 4, 2010 a Mw 7.2 earthquake struck in Baja

California, Mexico at 22:40 41.0 UTC (22:40 56.0 GPS time). The epicenter of the earthquake was at latitude 32.128 longitude -115.303 deg. The rupture plane extended almost to the US Border.!

•  General overview of event from http://www.unavco.org/research_science/science_highlights/2010/M7.2-Baja.html !

•  Analysis:!–  Secular motions on the US side of border before event!–  Coseismic offsets during the event!–  High-rate GPS solutions: 5 Hz analyses!

•  Slow ramp features!•  Surface wave properties!•  Reference station motions!

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Shake map !

•  Early estimate of the intensity of shaking form the event. !

•  Intensity was not as intense as predicted from this early (results generated by the USGS)!

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Surface Ruptures!

•  Photos of surface ruptures!

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Geodetic Results!•  Southern California is heavily instrumented with

continuously operating GPS receivers as part of the Southern Californian Integrated Geodetic Network (SCIGN) and the NSF/NASA Plate Boundary Observatory (PBO)!

•  Inter-site spacing is about 10 km on the US side of the border.!

•  Examine:!–  Inter-seismic velocities: Accumulation of strain in the region!–  Co-seismic offsets !–  High Rate (5 Hz) GPS results (data downloaded after event)!–  Initial post-seismic deformation (insights into continued loading

of San Andreas)!

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Secular motions!

•  Velocities of sites in this region relative to North America.!

•  Star is Baja Epicenter!

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Lander’s (1992) post seismic

Field Camp

Pacific Plate reference

frame!

• Motions relative to Pacific plate based on the ITRF2005 Euler rotation vectors.!

• Region is “mid-way” between the two plates!

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Velocities with offset removed

• North America fixed velocity with -16.6 E, 19.6 N mm/yr removed!

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Profile along border!

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Profile center

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Coseismic offsets!

•  Offsets based on 2-days before and after earthquake.!

•  Two days used is reduce leakage of postseismic motions.!

•  Red Star is epicenter; blue circle is 60 km (15-20 seconds surface wave speed)!

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Zoom around border!

•  Sites near the epicenter. !

•  Blue circle is 60 km radius!

• DisplacementsP494 200 mmP496 182 mmP497 97 mm…P491 9 mm!

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Coseismicresults from April 4, 2010 Baja 7.2 Earthquake (El Mayor Cucapah earthquake)

242 243 244 245 246 31

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242 243 244 245 246 31

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0 20 40 60

km

100 100 mm

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AGMT

AVRY

BBRY

BEMT

BILL

BMHL

CDMT

CNPP

CRRS

CTMS

DSSC

ECFS

EWPP

GLRS

GMPK

GMRC

GNPS

HCMN

HNPS

I40A

IID2

IMPS

LDES

LDSW

LORS

MAT2MLFP

MONP

NDAP

OAES

OPBLOPCLOPCP

OPCX

OPRD

P003

P066

P470

P471

P472

P473

P474

P475

P476

P477

P478

P479

P480

P481

P482

P483

P484

P485P486

P487 P488

P489

P490P491

P492

P493

P494

P495

P496

P497

P498

P499

P500

P501

P502P503

P504

P505

P506

P507P508

P509

P510

P511

P575

P577

P584

P585

P586

P589

P598P599

P600

P601

P603

P606

P607

P608

P610

P612P613

P614

P623

P625

P740P741

P742

P744

P795

PIN1

PPBF

RDMT

SBCC

SDHL

SIO3

SLMS

SPMS

USGC

242 243 244 245 246 31

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242 243 244 245 246 31

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Fri Apr 9 07:50:00 EDT 2010

Confidence interval : 95 ChiSquare / dof : 0.00 Formal Errors Scaled by 1.00

Velocities relative to NONE Input file : bajapbo_100406.cos

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P494 Zoom!

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P500!

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GPS Sites Around Field Camp!

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Regional view!

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12.221 Uses of GPS!

•  In the course we will use different GPS analysis packages:!–  Hand-held receivers: These have the software built in and

you just need to select correct options.!–  TRACK: Kinematic GPS processing in the field (time series

of station positions)!–  GAMIT: Full static GPS positioning (run on campus)!–  GLOBK: Used to tie our GPS results into the rest of

California.!