Download GPS and its Application to Geodynamics in East Africa

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

History of geomagnetism wikipedia, lookup

Post-glacial rebound wikipedia, lookup

Radio navigation wikipedia, lookup

Global Energy and Water Cycle Experiment wikipedia, lookup

Large igneous province wikipedia, lookup

Interferometric synthetic-aperture radar wikipedia, lookup

Magnetotellurics wikipedia, lookup

Geophysics wikipedia, lookup

Plate tectonics wikipedia, lookup

GPS signals wikipedia, lookup

Earthscope wikipedia, lookup

Geodesy wikipedia, lookup

Transcript
GPS and its Application to
Geodynamics in East Africa
Eric Calais
Purdue University, West Lafayette, IN, USA
[email protected]
The distribution of earthquakes is not random
Ocean-ocean
subduction
 island arc
Transform
fault
 strike-slip
motion
lithosphere
viscous mantle
Oceanic spreading
center
 creation of new
oceanic crust
Ocean-continent
subduction
 volcanism
Continental rift
 break-up of a
continent
lithosphere
viscous mantle
Tectonic plates are rigid and float on a viscous mantle.
Earthquakes occur at their boundaries: divergent (rifts and oceanic
spreading centers), convergent (subductions), or strike-slip
The Earth’s rigid shell (= lithosphere) is made of ~15 major plates
Notice the lack of plate boundary through East Africa…!
In Summary…
• We know:
– Plate tectonics as a kinematic theory that
describes the motion of (rigid) plates at the surface
of the Earth
• We do not know:
– The present-day motion of all plates
– Why plates move the way they do (dynamics)
• We need:
– Accurate techniques to measure present-day
motions of the Earth’s lithosphere
– Physical models that explain the dynamics of the
system (= kinematics + rheology)
The Global
Positioning System
• Three steps:
1. Satellites broadcast a radio
signal towards the Earth
2. Receivers record the signal
and convert it into satellitereceiver distances
3. Post-processing consist of
converting these distances
into positions
• Precision:
 $100 receiver  100 m
 $10,000 receiver  1 mm
Principle of GPS positioning
• Satellites broadcast signals on 1.2 GHz
and 1.5 GHz frequencies:
– Satellite 1 sends a signal at time te1
– Ground receiver receives it signal at time tr
– The range measurement r1 to satellite 1 is:
r1 = (tr-te1) x speed of light
– We are therefore located on a sphere
centered on satellite 1, with radius r1
– 3 satellites => intersection of 3 spheres
satellite 2
rr2
2
• Or use the mathematical model:
r  ( X s X r )  (Ys  Yr )  (Z s  Z r )
s
r
2
2
– Time difference between the satellite clocks
and the receiver clock
– Additional unknown => we need 4
observations = 4 satellites visible at the
same time
r1
r3
2
• A! The receiver clocks are mediocre and
not synchronized with the satellite clocks
satellite 1
satellite 3
You are here
x
Earth
Principle of GPS positioning
• GPS data = satellite-receiver
range measurements (r)
• Range can be measured in two
ways:
te
~ 20 cm
1. Measuring the propagation time
of the GPS signal:
•
•
•
Easy, cheap
Limited post-processing required
As precise as the time
measurements ~1-10 m
tr
2. Counting the number of cycles
of the carrier frequency
•
•
•
More difficult
Requires significant postprocessing
As precise as the phase
detection ~1 mm
x
Earth
From codes:
data = (tr-te) x c
(unit = meters)
From carrier:
data = x n
(unit = cycles)
Principle of GPS positioning
 GPS phase equation (units of cycles):
ki (t)  rik (t) 
f
 h k (t)  hi (t) f  ion ik (t)  tropik (t)  N ik  
c
 Range model:


rik  (X k  X i )2  (Y k Yi )2  (Z k  Zi )2
 = phase measurement = DATA
rik = geometric range = CONTAINS UNKNOWNS Xi,Yi,Zi
Xk,Yk,Zk = satellite positions (GIVEN)
t = time of epoch
i = receiver, k = satellite
f = GPS frequency, c = speed of light
hk = satellite clock error, hi  receiver clock error
ionik ionospheric delay, tropik tropospheric delay
Nik = phase ambiguity,  = phase noise
 Phase equation linearized
 Form a system of n_data equations for n_unknowns (positions,
phase ambiguities, tropospheric parameters)
 Solve using weighted least squares (or other estimation
techniques)
 End product: position estimates + associated covariance
Principle of GPS positioning
Error source
Treatment
Magnitude
Phase measurement noise
None
< 1 mm
Satellite clocks errors
Double difference or direct estimation
~1 m
Receiver clock errors
Double difference or direct estimation
meters
Tropospheric refraction
External measurement or estimation of “tropospheric
parameters”
0.5-2 m
Ionospheric refraction
Dual frequency measurements
1-50 m
Satellite orbits
Get precise (2-3 cm) orbits
2 cm to 100 m
Geophysical models
Tides (polar and solid Earth), Ocean loading
centimeters
Geodetic models
Precession, Nutation, UT, Polar motion
centimeters
Antenna phase center
Use correction tables
~ 1 cm
Multipath
Choose good sites!
~ 0.5 m
Site setup
Choose good operators!
???
 Precise GPS positioning requires:
• Dual-frequency equipment
• Rigorous field procedures
• Long (several days) observation sessions
• Complex data post-processing
Campaign measurements
 Field strategy:
– Network of geodetic benchmarks perfectly attached
to bedrock -- Separation typically 10-100 km
– 2 to 3 measurement sessions of 24 hours
 Advantages:
– Large number/density of sites with few receivers
– Relatively low cost
 Problems:
– Transient deformation
– Monumentation and antenna setup
Continuous measurements
 Typical setup:
– Antenna mounted permanently on a stable geodetic
monument, measurements 24h/day, 365 days/year
– Site protected and unattended
– Data downloaded daily or more frequently if needed
(and if possible)
 Advantages:
– Better long-term precision
– Better detection of transient signals
 Problems:
– Cost and number of sites
– Power and communication
GPS time series
• Processing strategy:
– GPS data (phase and
pseudorange) processed in
daily sessions
– Use of precise orbits and
Earth Orientation Parameters
from the IGS
– Use of additional continuous
sites with well-defined position
and velocity in ITRF
• Output:
– 1 position per day (per site)
– Associated uncertainty
– Successive daily positions 
times series
– Slope = long-term site velocity
due to tectonic motions
From positions to velocities
•
Velocity can be estimated by combining several measurement epochs
with the following model:
known
position
at epoch s
(in reference
frame s)
=
unknown
(final)
position
(in final
reference
frame)
+
unknown
(final)
velocity
(in final
reference
frame)
transformation between final reference frame and reference frame at epoch s
(T = translation, D = scale factor, R = rotation)
+
position
+
velocity
 i
i
i
i
i
i
X si  X comb
 (t s  t comb ) XÝcomb
 T  DX comb
 RX comb
 (t s  t comb )TÝ DÝX comb
 RÝX comb

•
•
The model is linear  X, X, T, D, R, T, D, R can be estimated using
standard least squares and error propagation.
As such, problem is rank deficient (datum defect)  define a frame by
fixing or constraining the position and velocity of a subset of sites to known
values, for instance from International Terrestrial Reference Frame (ITRF)
REVEL GPS plate model
Sella et al., JGR 2002
• Velocities are shown with arrows
• Expressed with respect to ITRF = absolute reference frame
• Can be used to quantify plate motions
From velocities to plate motions
• The motion of “plates” (= spherical
caps) can be described by:
– A pole of rotation (lat, lon), also
called Euler pole
– An angular velocity (deg/My)
• Or by a rotation vector W:
– Origin at the Earth’s center, passes
through Euler pole
– Length = scalar angular velocity
• Relation between horizontal
velocity at a given site (position
described by unit vector Pu) and
rotation vector W :

V  R W Pu

(R = mean Earth’s radius)
Plate motions, inverse problem
•
•
For a given site, linear equation:
 X  X  Z y  Y z 

    
V  RY  Y  RX z  Z x 
    

 Z  Z  Y x  X y 
W
•
If at least 2 sites with velocities, the
problem is over-determined and can
be solved using least squares (L =
data vector, W = data weight matrix):
W  (AT CV1 A)1 AT CV1L
P
Or in matrix form:
vx  0
Z Y  x 
  
 
vy

R
Z
0
X
  
 y 
  
 
vz Y X 0  z 
or
V  AW

•
The model covariance matrix is:
CW  (AT CV1 A)1

Plate kinematics and deep mantle structures
Color arrows: motion of adjacent plates with respect to Nubia (Sella
et al., 2002). Black arrows: Nubian plate motion in a hot spot frame
(Gripp and Gordon, 2002)
Behn et al., 2004: Arrows = mantle flow field, colors =
seismic velocity anomalies. Top = map view at the
base of the lithosphere (300 km), bottom: crosssection of S20RTS (Ritsema et al.)
Regional tectonics and upper mantle structures
Nyblade et al. (2000): Top = cross-section of
tomographic model (Ritsema et al., 1998) with
stacked receiver function superimposed. Bottom:
schematic interpretation.
Nubia/Somalia
kinematics
• Very few continuous GPS sites
on Nubian and Somalian plates
 Nubia-Somalia relative motion
still poorly constrained
• Two plates:
– Nubia = MAS1, NKLG, SUTH,
SUTM, GOUG (ZAMB, HRAO,
HARB)
– Somalia = MALI, HIMO, SEY1,
REUN
• Euler pole between South Africa
and SW Indian Ridge  NubiaSomalia extension rate increases
from S to N
• Discrepancy at MBAR
(Work by Saria Elifuraha)
EAR
kinematics
• Seismicity + active faults  2
possible microplates within
the EAR
• Data:
– GPS, MBAR on Victoria +
SNG1 on Rovuma
– Earthquake slip vectors
• Invert GPS + slip vectors for
block motions
• Results:
– Somalia: consistent with
previous estimates
– Victoria: CCW rotation
– Rovuma: CW rotation
(Work by Sarah Stamps)
Summary
•
•
2 major plates, divergence rate
increases from 3 to 6 mm/yr
from S to N.
GPS + slip vector data
consistent with:
–
–
•
WARNINGS:
–
–
–
•
Strain focused along narrow rift
valleys
2 undeformed domains: Victoria
and Rovuma microplates
Model
Constrained by very few GPS
data
Needs to be tested/improved
Dynamics of Victoria pl.?
Conclusions
• Kinematics:
– Combination of (limited) GPS data set + earthquake slip vectors 
preliminary kinematic model for Nubia/Somalia + 2 microplates (Victoria
and Rovuma)
– Model will be refined using new GPS data in Tanzania.
– Next GPS campaigns = August 2008 and 2010.
• Dynamics:
– Combine kinematic model with other tectonic indicators, seismic
anisotropy data, mantle and lithospheric structures (tomography, xenoliths,
etc.)
– Geodynamic modeling: driving forces, mantle-lithosphere interactions.
• Broader impacts:
–
–
–
–
Establishment of new national geodetic network
Establishment of new IGS site
Training and collaborative research
Other research projects: geoid, datum transformations, vertical motions,
etc…
Acknowledgments
• Partners:
– University College for Lands and
Architectural Studies
– Survey and Mapping Division, Ministry of
Lands and Human Settlement
– Department of Geology, University of Dar
Es Salaam
– Department of Earth and Atmospheric
Sciences, Purdue University
– Department of Geology, Rochester
University
– Hartebeesthoek Radio Astronomy
Observatory, South Africa
– Royal Museum for Central Africa,
Belgium
– Universite de Bretagne Occidentale,
IUEM, France
• Technical Support from UNAVCO
(www.unavco.org)
• A project funded by the National Science
Foundation (www.nsf.org)