12 20112 501 Essentials of Geophysics Geodetic Methods

12. 201/12. 501 Essentials of Geophysics Geodetic Methods Prof. Thomas Herring tah@mit. edu http: //www-gpsg. mit. edu/~tah 11/10 11/12/2004 12. 201/12. 501

Topics • History of geodesy • Space based methods • VLBI/SLR • GPS (Friday). 11/10 11/12/2004 12. 201/12. 501 2

History and Types • Geodesy: Science of measuring size and shape of the Earth (and temporal changes added in last 20 years) • Split into two fields: – Physical Geodesy: Study of Earth Potential fields (mainly gravity field) • Historically used surface gravity measurements: Boundary value problems (Greens Theorem etc): Given derivative of field on a surface, find the value of the field outside and on surface. • Space based methods for long wavelength (>300 km). Ground based tracking of satellites (LAGEOS), radar altimetry (TOPEX, JASON), satellite-to-satellite tracking (GRACE), gradiometers (GOCE), – Positional Geodesy: Determine of positions; land boundaries, maps and deformations. Lectures hear will cover latter topic. 11/10 11/12/2004 12. 201/12. 501 3

History and Types • Although physical and positional geodesy are often treated separately, they are dependent on each other especially with development of space base geodetic methods: – When earth orbiting objects are used as measurement targets, the gravity field is needed to integrate equations of motion of object. – To use orbit perturbations to determine gravity field, the “perturbations” are measured from ground positions which need to be known at some point. – Modern methods solve these two problems simultaneously although even today this is not always done correctly. (First and second degree harmonic terms in gravity field). 11/10 11/12/2004 12. 201/12. 501 4

Geodetic coordinate systems • Modern spaced based geodetic measurements allow determination of geometric coordinates (basically Cartesian coordinates in a global frame) – Origin of coordinates: nominally center of mass location (small movements with respect to center of figure (a few centimeters) – Orientation of axes: Z near maximum moment of inertia, X through Greenwich, Y completes systems – Mathematically compute direction of normal to ellipsoid (geodetic latitude and longitude) • However, prior to space based methods, coordinates based gravity field: – Direction of gravity vector define astronomical latitude and longitude. Height measured above an equipotential surface (geoid). 11/10 11/12/2004 12. 201/12. 501 5

Geodetic coordinates: Latitude 11/10 11/12/2004 12. 201/12. 501 6

Positional Geodesy Methods • Triangulation: Dates from 1600’s and the work of Snell. Uses angle measurements and 1 -2 short, directly measured distance (usually ~1 km). Other distances are deduced then from trigonometry. – Angles can be measured to ~1 arc sec = 5 x 10 -6 rads. – Accuracy of this geodetic method is ~10 -5 proportional error – Main geodetic method until the 1940 s • Trilateration: Direct distance measurement using electromagnetic distance measurement (EDM). – Techniques developed after WW II and followed from the RADAR development. – Most methods used phase measurements at different frequencies rather than time-of-flight measurements. 11/10 11/12/2004 12. 201/12. 501 7

Example of methods: South Africa The Meridian Arc of Abbe de Lacaille Measured in 1751 to help determine shape of Earth. 11/10 11/12/2004 12. 201/12. 501 8

Later measurements 1840 -1846 Typical sites distances are 2050 km. Points are located on tops of mountains typically The baseline measurement was in Cape Town. 11/10 11/12/2004 12. 201/12. 501 9

1920’s triangulation network 11/10 11/12/2004 12. 201/12. 501 10

Densification In tectonically active area, these old survey results can be used to get strain accumulation estimates with up to 150 year time spans. 11/10 11/12/2004 12. 201/12. 501 11

Space based measurements • The advent of the Earth orbiting satellites starting in 1955, and the development of radio astronomy (Jansky, 1932) started to bring about a revolution in geodetic accuracy. • Activity started after WWII using technology developed during the war and in response to cold war. • New methods removed the need for line-of-sight Jansky 22 Mhz steerable radio telescope (1932) Modern radio telescope 11/10 11/12/2004 12. 201/12. 501 12

Principles of new methods • Satellites allowed measurement to objects well above the surface of the earth which could be seen from locations that could not see earth other. • The electronic distance measurement methods could be used make distance measurements rather than angle measurements. (As in astronomical positioning) • Radio techniques allowed relative distance measurements using quasars • Satellite orbits perturbed by gravity field (and other non -conservative forces such as drag) and so physical and positional geodesy at the same time. 11/10 11/12/2004 12. 201/12. 501 13

Space Geodetic Techniques • Satellite Laser Ranging (SLR): Uses pulsed laser system to measure time of flight travel from ground telescope to orbiting satellite equipped with corner cube reflectors. • First deployed in late 1960 s; Lunar system deployed by Apollo and Russian programs (LLR). • Currently about 38 reporting stations (11/04). • International Laser Ranging service (ILRS): http: //ilrs. gsfc. nasa. gov/ LAGEOS I: Launched 1976, 5958 km altitude, 109 deg Inclination, 411 kg LAGEOS II: Launched 1992, 5616 -1950 km altitude, 52 deg Inclination, 400 km 60 cm diameter spheres 11/10 11/12/2004 12. 201/12. 501 14

Current SLR network (11/04) 11/10 11/12/2004 12. 201/12. 501 15

Space geodetic methods • Very long baseline interferometry (VLBI): Uses radio signals from extragalatic radio sources to measure difference in arrival times at widely separated radio telescope. • First measurements in 1969: First detection on plate motion between Europe and North America in 1986. • 38 VLBI sites currently International VLBU service (IVS) http: //ivscc. gsfc. nasa. gov/ Pietown Radio telescope (25 m diameter) (right) Effelsberg radio telescope in Germany (100 m diameter) (left) 11/10 11/12/2004 12. 201/12. 501 16

Current VLBI Network (11/04) 11/10 11/12/2004 12. 201/12. 501 17

VLBI and SLR operations • SLR sites tend to operate independently with priorities at each site as to which satellites to track. There about 30 satellites with corner cube reflectors. SLR stations need human operators and track for 8 -24 hours per day 5 -7 days per week. • VLBI measurements need to be coordinated because multiple telescopes need to look at the same radio object at the same time. Sessions are scheduled for 24 hours durations with measurements every few minutes. Regular measurements programs in EOP sessions twice per week, daily intensive sessions (1 -hr), plus other sessions. • There are mobile VLBI and SLR systems, but these are moved with trucks, and so tend to be repositioned infrequently. (In the 1980 s mobile VLBI and SLR systems made measurements in tectonically active regions, but GPS replaced these types of measurements in the 1990 s). • SLR is useful for satellite tracking, and low order gravity field changes • VLBI provides 1 -day averaged station positions and inertial reference frame 11/10 11/12/2004 12. 201/12. 501 18

Global Positioning System (GPS) 11/10 11/12/2004 12. 201/12. 501 19

GPS Original Design • Started development in the late 1960 s 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. 11/10 11/12/2004 12. 201/12. 501 20

GPS Design • Innovations: –Use multiple satellites (originally 21, now ~28) –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: • L 1 ~1. 5 GHz, L 2 ~1. 25 GHz 11/10 11/12/2004 12. 201/12. 501 21

Latest Block IIR satellite (1, 100 kg) 11/10 11/12/2004 12. 201/12. 501 22

Measurements • 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) – Doppler shift of received signal • All measurements relative to “clocks” in ground receiver and satellites (potentially poses problems). 11/10 11/12/2004 12. 201/12. 501 23

Positioning • For pseudo-range to be used for “point-positioning” we need: – Knowledge of errors in satellite clocks – Knowledge of positions of satellites • This information is transmitted by satellite in “broadcast ephemeris” • “Differential” positioning (DGPS) eliminates need for accurate satellite clock knowledge by differencing the satellite between GPS receivers (needs multiple ground receivers). 11/10 11/12/2004 12. 201/12. 501 24

Satellite constellation • Since multiple satellites need to be seen at same time (four or more): – Many satellites (original 21 but now 28) – High altitude so that large portion of Earth can be seen (20, 000 km altitude —MEO) 11/10 11/12/2004 12. 201/12. 501 25

Current constellation • Relative sizes correct (inertial space view) • “Fuzzy” lines not due to orbit perturbations, but due to satellites being in 6 -planes at 55 o inclination. 11/10 11/12/2004 12. 201/12. 501 26

Ground Track Paths followed by satellite along surface of Earth. 11/10 11/12/2004 12. 201/12. 501 27

Pseudo-range accuracy • Original intent was to position using pseudo-range: Accuracy better than planned • C/A code (open to all users) 10 cm-10 meters • P(Y) code (restricted access since 1992) 5 cm-5 meters • Value depends on quality of receiver electronics and antenna environment (little dependence on code bandwidth). 11/10 11/12/2004 12. 201/12. 501 28

GPS Antennas (for precise positioning) Nearly all antennas are patch antennas (conducting patch mounted in insulating ceramic). • Rings are called chokerings (used to suppress multi -path) 11/10 11/12/2004 12. 201/12. 501 29

Positioning accuracy • Best position accuracy with pseudo-range is about 20 cm (differential) and about 5 meters point positioning. Differential positioning requires communication with another receiver. Point positioning is “stand-alone” • Wide-area-augmentation systems (WAAS) and CDMA cell-phone modems are becoming common differential systems. • For Earth science applications we want better accuracy • For this we use “carrier phase” where “range” measurement noise is a few millimeters (strictly range change or range differences between sites) 11/10 11/12/2004 12. 201/12. 501 30

Carrier phase positioning • To use carrier phase, need to make differential measurements between ground receivers. • Simultaneous measurements allow phase errors in clocks to be removed i. e. the clock phase error is the same for two ground receivers observing a satellite at the same time (interferometric measurement). • The precision of the phase measurements is a few millimeters. To take advantage of this precision, measurements at 2 frequencies L 1 and L 2 are needed. Access to L 2 codes in restricted (anti-spoofing or AS) but techniques have been developed to allow civilian tracking of L 2. These methods make civilian receivers more sensitive to radio frequency interference (RFI) • Next generation of GPS satellites (Block IIF) will have civilian codes on L 2. Following generation (Block III) will have another civilian frequency (L 5). 11/10 11/12/2004 12. 201/12. 501 31

Phase positioning • Use of carrier phase measurements allows positioning with millimeter level accuracy and sub-millimeter if measurements are averaged for 24 -hours. • Examples: – The International GPS Service (IGS) tracking network. Loose international collaboration that now supports several hundred, globally distributed, high accuracy GPS receivers. (http: //igscb. jpl. nasa. gov) – Applications in California: Southern California integrated GPS network (SCIGN http: //www. scign. org) 11/10 11/12/2004 12. 201/12. 501 32

IGS Network Currently over 400 stations in network 11/10 11/12/2004 12. 201/12. 501 33

IGS network • Stations in the IGS network continuously track GPS satellites and send their data to international data centers at least once per day. All data are publicly available. • A large number of stations transmit data hourly with a few minutes latency (useful in meteorological applications of GPS). • Some stations transmit high-rate data (1 -second sampling) in real-time. (One system allows ± 20 cm global positioning in real-time with CDMA modem connection). 11/10 11/12/2004 12. 201/12. 501 34

Uses of IGS data • Initial aim was to provide data to allow accurate determination of the GPS satellite orbits: Since IGS started in 1994, orbit accuracy has improved from the 30 cm to now 2 -3 cm • From these data, global plate motions can be observed in “realtime” (compared to geologic rates) • Sites in the IGS network are affected by earthquakes and the deformations that continue after earthquakes. The understanding of the physical processes that generate post-seismic deformation could lead to pre-seismic indicators: – Stress transfer after earthquakes that made rupture more/less likely on nearby faults – Material properties that in the laboratory show pre-seismic signals. • Meteorological applications that require near real-time results 11/10 11/12/2004 12. 201/12. 501 35

1993 Orbit Improvement 2004 11/10 11/12/2004 12. 201/12. 501 36

Global Plate Motions 11/10 11/12/2004 12. 201/12. 501 37

Motions in California Red vectors relative to North America; Blue vectors relative to Pacific Motion across the plate boundary is ~50 mm/yr. In 100 -years this is 5 meters of motion which is released in large earthquakes 11/10 11/12/2004 12. 201/12. 501 38

Hector Mine co-seismic Brown dots are small earthquakes Green lines are faults 11/10 11/12/2004 12. 201/12. 501 39

Post-seismic Estimates As more earthquakes are seen with GPS, deformations after earthquakes are clearer Here we show log dependence to the behavior. 11/10 11/12/2004 12. 201/12. 501 40

WIDC (74 km from epicenter) Coseismic offset removed N 51. 5± 0. 8 mm E 15. 7± 0. 6 mm U 4. 3± 1. 8 mm Log amplitude N 4. 5 ± 0. 3 mm E 0. 7 ± 0. 2 mm U 3. 3 ± 0. 7 mm 11/10 11/12/2004 12. 201/12. 501 41

Deformation in the Los Angeles Basin Measurements of this type tell us how rapidly strain is accumulating Strain will be released in earthquakes (often large) 11/10 11/12/2004 12. 201/12. 501 42

Repeating slow earthquakes in Pacific North West Example of repeating “slow” earthquakes (no rapid rupture) These events give insights into material properties and nature of time dependence of deformation 11/10 11/12/2004 12. 201/12. 501 43

GPS Measured propagating seismic waves Data from 2002 Denali earthquake 11/10 11/12/2004 12. 201/12. 501 44

CONCLUSIONS • GPS, used with millimeter precision, is revealing the complex nature and temporal spectrum of deformations in the Earth. • Programs such as Earthscope plan to exploit this technology to gain a better understanding about why earthquakes and volcanic eruptions occur. • GPS is probably the most successful dual-use (civilian and military) system developed by the US • In addition to the scientific applications, many commercial applications are also being developed. 11/10 11/12/2004 12. 201/12. 501 45