basic seismology

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Chris Goldfinger Burt 282 7-5214 gold_at_coas.or
egonstate.edu http//activetectonics.coas.oregonst
ate.edu Reading for Thursday Miller et al., 2001
McCaffrey et al., 2000 Hawkes et al., 2005,
Natawidjaja et al., 2003 Suggested
Supplements Moores and Twiss Chapter 7
Convergent Margins Massonet et al., 1994 Landers
InSAR
OCE 661 Plate Tectonics
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GPS affords excellent global coverage 24/7/365
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A little intro to GPS measurements for crustal
motion will help in interpreting GPS results
reported in the literature For small GPS
receivers, position is calculated from
pseudoranges, the corrected distance to several
satellites and results in 3D navigation (XYZ and
time). Precision is 20-20 m, and up until
2000, was degraded by altering the clock times
enough to degrade positions by an additional 50 m
or so, resulting in a 95 position circle of
100m.
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Now this effect, known as Selective availability
(S/A) has been turned off, and small receivers
now get the native accuracy of the system. But
how do we measure crustal motion with something
that can only measure position to within 30m? We
would like 1 mm precision!!!
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Now this effect, known as Selective availability
(S/A) has been turned off, and small receivers
now get the native accuracy of the system. If
you have a DOD receiver (larger US NSF and NOAA
ships have them), you can receive and use the
P-code signal, which will get you down to 10-20
m precision. But how do we measure crustal
motion with something that can only measure
position to within 30m? We would like 1 mm
precision!!!
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One way to do it is with what is known as
differential positioning. If we have a receiver
at a well known position, we can then compare the
variations in the data from the known position,
and apply them to a nearby receiver. Why would
this work? Because by far the greatest source
of errors are what are known as common mode
errors, that is they are things like ionospheric
effects that will affect both receivers the same
way, as long as they are close to each other.
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Differential GPS (DGPS) Techniques The idea
behind all differential positioning is to correct
bias errors at one location with measured bias
errors at a known position. A reference receiver,
or base station, computes corrections for each
satellite signal. Because individual
pseudo-ranges must be corrected prior to the
formation of a navigation solution, DGPS
implementations require software in the reference
receiver that can track all SVs in view and form
individual pseudo-range corrections for each SV.
These corrections are passed to the remote, or
rover, receiver which must be capable of applying
these individual pseudo-range corrections to each
SV used in the navigation solution. Applying a
simple position correction from the reference
receiver to the remote receiver has limited
effect at useful ranges because both receivers
would have to be using the same set of SVs in
their navigation solutions and have identical
GDOP terms (not possible at different locations)
to be identically affected by bias errors.
Differential Code GPS (Navigation)
Differential corrections may be used in
real-time or later, with post-processing
techniques. Real-time corrections can be
transmitted by radio link. The U. S. Coast Guard
maintains a network of differential monitors and
transmits DGPS corrections over radiobeacons
covering much of the U. S. coastline. DGPS
corrections are often transmitted in a standard
format specified by the Radio Technical
Commission Marine (RTCM). Private DGPS services
use leased FM sub-carrier broadcasts, satellite
links, or private radio-beacons for real-time
applications. Corrections can be recorded for
post processing. Many public and private agencies
record DGPS corrections for distribution by
electronic means. To remove Selective
Availability (and other bias errors),
differential corrections should be computed at
the reference station and applied at the remote
receiver at an update rate that is less than the
correlation time of SA. Suggested DGPS update
rates are usually less than twenty seconds. DGPS
removes common-mode errors, those errors common
to both the reference and remote receivers (not
multipath or receiver noise). Errors are more
often common when receivers are close together
(less than 100 km). Differential position
accuracies of 1-10 meters are possible with DGPS
based on C/A code SPS signals.
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Ok, well this is better but were not exactly at
1mm yet. Recent improvements in differential
positioning include WAAS, or Wide Area
Augmentation System, a satellite based
differential system for the US and coastal areas
designed to eventually replace the Instrument
Landing System (ILS) for aircraft. It will
reliably give 2-3 m precision in covered areas,
and 1m with specially equipped receivers for
aircraft near an airport.
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It turns out that the navigation solution derived
from pseudoranges is not used at all for geodetic
measurements of crustal motion. The position in
the window of the 14,000 Ashtech receiver is
more or less the same as the one from GI Joes,
calculated the same way, and is there for
convenience. Its not used for anything else.
So, how is it done?
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The navigation solution used in most GPS
applications is based on pseudoranges. The
precision is too low for geodetic
measurements. Instead, phase measurements of the
carrier signal are used to compare very precise
ranges between two sites and a given satellite.
These in turn are Used to calculate baseline
length changes over time between sites.
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Geodetic GPS Double Difference Processing Using
double differenced observables can eliminate
selective availability effects as well as other
biases. Double differences are primarily used for
surveying and geodetic research using carrier
phase tracking however, they are not limited to
those applications. First, single differences are
formed by subtracting observation equations from
two separate receivers to a single satellite.
Taking the difference between two single
differences for a specific receiver pair gives
the carrier phase double difference.
Baselines The result is a set of baselines
between receiver pairs. Ideally, in a Campaign
mode effort, a number of receivers are all
running at the same time to reduce common mode
errors. Occupations of 24 hours or better at
each baseline pair improve precision. These
baselines are tied to a reference frame,
hopefully on the plate the campaign sites are on,
then the data is passed through a network
adjustment which minimizes misfits. When
complete, it is possible to measure baselines
with relative motions of 1-2 mm/yr Continuous
GPS When observations at permanent sites are
made continuously (usually every 30 seconds) they
do all of the above, and in addition they record
anything else that may happen, things that
campaign GPS will miss, such as earthquakes, slow
slip events, and other transients.
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GPS Overview     The Navigation System with
Timing And Ranging (NAVSTAR) Global Positioning
System (GPS) was conceived as a ranging system
from known positions of satellites in space to
unknown positions on land, sea, in air and space.
The GPS constellation consists of 24 satellites
in 6 orbital planes with 4 satellites in each
plane. The ascending nodes of the orbital planes
are separated by 60 degrees and the planes are
inclined 55 degrees. Each GPS satellite is in an
approximately circular, semi-synchronous (20,200
km altitude) orbit. The orbits of the GPS
satellites are available by broadcast -
superimposed on the GPS pseudorandom noise codes
(PRN), or after post-processing to get precise
ephemerides, they are available from
organizations such as the Jet Propulsion Lab
(JPL) or the International Geodetic Service (IGS)
among others. The GPS receivers convert the
satellite's signals into position, velocity, and
time estimates for navigation, positioning, time
dissemination, or geodesy.
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Signals Each GPS satellite transmits data on two
frequencies, L1 (1575.42 Mhz) and L2 (1227.60
MHz). The atomic clocks aboard the satellite
produces the fundamental L-band frequency, 10.23
Mhz. The L1and L2 carrier frequencies are
generated by multiplying the fundamental
frequency by 154 and 120, respectively. Two
pseudorandom noise (PRN) codes, along with
satellite ephemerides (Broadcast Ephemerides),
ionospheric modeling coefficients, status
information, system time, and satellite clock
corrections, are superimposed onto the carrier
frequencies, L1 and L2. The measured travel times
of the signals from the satellites to the
receivers are used to compute the
pseudoranges. The Course-Acquisition (C/A) code,
sometimes called the Standard Positioning Service
(SPS), is a pseudorandom noise code that is
modulated onto the L1 carrier. Because initial
point positioning tests using the C/A code
resulted in better than expected positions, the
DoD directed "Selective Availability" (SA) in
order to deny full system accuracy to
unauthorized users. SA is the intentional
corruption of the GPS satellite clocks and the
Broadcast Ephemerides. Errors are introduced into
the fundamental frequency of the GPS clocks. This
clock "dithering" affects the satellite clock
corrections, as well as the pseudorange
observables. Errors are introduced into the
Broadcast Ephemerides by truncating the orbital
information in the navigation message. The
Precision (P) code, sometimes called the Precise
Positioning Service (PPS), is modulated onto the
L1 and L2 carriers allowing for the removal of
the first order effects of the ionosphere. The P
code is referred to as the Y code if encrypted. Y
code is actually the combination of the P code
and a W encryption code and requires a DoD
authorized receiver to use it. Originally the
encryption was intended as a means to safe-guard
the signal from being corrupted by interference,
jamming, or falsified signals with the GPS
signature. Because of the intent to protect
against "spoofing," the encryption is referred to
as "Anti-spoofing" (A-S). A-S is either "on" or
it's "off" there is no variable effect of A-S as
there is with SA.
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Observables Code Pseudorange The pseudorange is
the "distance" between the GPS satellite at some
transmit time and the receiver at some receive
time. Because the transmit time and the receive
time are different, it is impossible to measure
the true range between the satellite and the
receiver. The basic definition of the pseudorange
observable is where rho is the observed
pseudorange calculated from the light time
equation, rhotrue is the difference of the
position of the receiver at the true receive time
minus the position of the satellite at the true
transmit time and the rest of the equation
represents the biases created by the errors in
the clocks. Phase Pseudorange Another observable,
based on the carrier phase of the signal, does
not require the actual information being
transmitted. The basic definition of the phase
observable is where where the fractional
beat phase of the signal is converted into a
pseudorange by scaling with the wavelength.
rhotrue and the clock corrections remain the same
as for the code pseudorange definition. The
integer number of cycles, N, is typically not
known and varies for every receiver-satellite
combination. As long as the connection between
the receiver and the satellite is not broken, N
remains constant while the fractional beat phase
changes over time. Because of the ambiguous
nature of N, it is referred to as the ambiguity
and can either be solved for by using the code
pseudoranges, or estimated. The loss of signal
lock between a GPS satellite and the receiver is
referred to as "cycle slip." If the signal lock
is re-established, a new ambiguity will exist and
must be solved for separately from the original
ambiguity.
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Atmospheric Effects The GPS signals passing
through the atmosphere encounter refraction
effects including ray bending and propagation
delays. These include the atmospheric effects of
the troposphere and ionosphere. Troposphere The
largest effects of the troposphere can be avoided
by prescribing an elevation mask for your
receiver, thereby avoiding signals from low
elevation satellites. With a 15 degree elevation
mask, 4-8 satellites will be simultaneously
observable from a location on the Earth at any
instant of time. The troposphere is composed of
the "hydrostatic (dry)" portion and the "wet"
portion accounting for water vapor. The dry
portion constitutes 90 of the tropospheric
refraction, whereas the wet portion constitutes
10. However, the models for the dry troposphere
are more accurate than the models for the wet
troposphere. Therefore, the errors in the wet
troposphere have a larger effect on the
pseudorange bias than the errors in the dry
troposphere. Ionosphere Some models try to
account for all effects of the ionosphere, but
require much effort in modeling the highly time
dependent total electron count of the atmosphere.
A technique to remove the first order effects of
the ionosphere linearly combines the L1 and L2
observables to form a new signal that is free of
ionospheric effects. Alternatively, a correction
to one of the two signals can be solved for. The
first order contribution of the ionosphere to the
pseudorange bias is related to the inverse of the
frequency squared. To actually use this new
observable, it is necessary to compute the
wavelength of the ionosphere free signal.
Substituting values yields a wavelength of about
48.5 cm for the ionosphere free signal or a
frequency of 618.8 Mhz (60.5f.0). Because the
ratio between the L1 and L2 frequencies is not an
integer value, the ambiguity term is no longer an
integer. Alternatively, the ionospheric
correction, a, could have been solved for.
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Non-Clock Related Pseudorange Biases There are
other corrections besides the clock offsets and
atmospheric effects which would appear as
pseudorange biases. Receiver specific biases due
to antenna phase center offset should be
considered as well. The phase center of an
antenna is where the signal is essentially
received at and where the measurement refers to.
Therefore, the distance between the antenna phase
center and the point of interest needs to be
known in order to correct the results to the
point of interest. When satellite signals reflect
off of another surface and then arrive at the
receiver simultaneously with non-reflected
signals, this is known as multipath. The effect
of multipath is greater on code based
pseudoranges than phase based pseudoranges.
Mathematical models to account for the multipath
effect are impractical because the multipath
effect is so highly dependent upon the specific
geometry of the situation. Instead of accounting
for multipath, it is recommended that multipath
be avoided by placing the antenna as far from
reflective objects as possible. In instances
where multipath can not be avoided, the bias can
be estimated from the ionospheric free
combination pseudoranges or the effects can be
removed through digital filtering, wideband
antennas, or radio absorbent antenna ground
planes. Because the reference frames fixed with
the GPS satellite and the receiver are
accelerated compared to the reference frame fixed
in the Earth, special and general relativistic
effects must be considered. The gravitational
field of the Earth causes perturbations in the
satellite orbits and space-time curvature of the
satellite signal. The acceleration of the
reference frames cause perturbations in the
fundamental frequency of the satellite and
receiver clocks.
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Differential Techniques Differential GPS As the
saying goes, necessity is the mother of
invention. The DoD envisioned the civilian
community using the GPS network and thus
constrained them to the C/A code. The combination
of the less accurate code and selective
availability degraded the possible accuracy the
civilian community could obtain. Civilian
engineers and scientists had to find a way to
improve the obtainable accuracy from GPS. The
solution came in the form of differential GPS
(DGPS). The basic concept of DGPS is the use of 2
receivers, one at a known location and one at an
unknown position, that see GPS satellites in
common. By fixing the location of one of the
receivers, the other location may be found either
by computing corrections to the position of the
unknown receiver or by computing corrections to
the pseudoranges. By using DGPS, effects of
selective availability can be removed. For short
baseline distances between receivers, some of the
biases from the atmosphere can be removed as
well. This cancellation effect is the result of
both receivers seeing the same things. If one
receiver location is known, then the bias in the
pseudorange to the known receiver can be
calculated and used to correct the solution of
the unknown receiver location. The DGPS system
designed by the US Coast Guard calculates the
biases at a known receiver location, and then
broadcasts them on a radio frequency. Double
Difference Processing Using double differenced
observables can eliminate selective availability
effects as well as other biases. Double
differences are primarily used for surveying and
geodetic research using phases however, they are
not limited to those applications. First, single
differences are formed by subtracting observation
equations from two separate receivers to a single
satellite. Taking the difference between two
single differences for a specific receiver pair
gives the carrier phase double difference For
coordinated receive and transmit times, all clock
corrections have been removed for both of the GPS
satellites and both of the receivers. Double
difference methods using phases are used
exclusively in geodetic work to achieve baseline
measurements length changes on the order of a few
mm.
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Time Series data for stations CORV and NEWP,
1999-2003. Each station shows changes in
latitude, longitude, and vertical. Note the poor
precision in the vertical component. Real GPS
data contain seasonal cycles, noise, breaks due
to antenna changes, and perhaps real signals that
are related to episodic earth motion. Compare
both stations at January 2002. Both stations
record an anomalous event at this time,
eliminating station problems. This could be a
slow earthquake.
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Pacific Northwest Geodetic Array velocity field.
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GPS and VLBI observations across a portion of the
North America-Pacific boundary zone. Extension
occurs in the Basin and Range north of about 36
degrees North, and changes smoothly into the
strike-slip motion across a well defined
transition zone. South of 36 degrees North, the
San Andreas system accommodates most of the plate
motion, and little deformation occurs in the
Basin and Range. Net motion across the boundary
zone is essentially that predicted by global
plate motion model NUVEL-1A
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Comparison of station positions for a number of
sites across the northern Cascadia subduction
zone. What are the sawtooth patterns evident
in these records?
Survey sez These are slow earthquakes, or more
recently they have been termed episodic tremor
and slip (ETS) events. They are accompanies by
seismic tremors, and last 7-14 days. If the slip
had been faster, these events would be Mw7
earthquakes. But they occur downdip of the
locked zone and are not seismic, except for the
tremors.
Miller et al., 2001
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Whats this?
InSAR Interferometric Synthetic Aperture Radar
Miller et al., 2001
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This image, possibly the most famous geodetic
image ever, represents the displacment of the
ground surface following the Landers earthquake
in Southern California, 1992.
The interference fringes come from radar images
that are used to map elevation very precisely
before and after the earthquake. Successive
Satellite passes are used, with very precisely
known orbits. Each fringe cycle represents
28 mm of vertical displacement. The offset of
the fringes can be used to measure the slip of
the fault during the earthquake.
Massonet et al., 1994
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Figure 1 Imaging geometry for a repeat-pass
interferometer. One interferogram is formed with
images acquired from positions A1 and A2. If a
ground resolution element scatters identically
for each observation, then the difference of the
two phases depends only on the path length
difference, dr (delta-ro). If a second
interferogram is formed with the image A1 and an
image A2' acquired over the same region, but in
this case an earthquake has displaced each
resolution element between observations, there is
now an additional phase change due to the radar
line-of-sight component of the displacement, Dr
(DELTA-ro). Note that the baseline length has
been greatly exaggerated for figure clarity.
Typical (usable) baselines for a C-band
(wavelength 5.6 cm) spaceborne system orbiting
at an elevation h700 km range from 0 to 200 m.
Using image pairs with longer baselines leads to
geometrical decorrelation due to the difference
of lines of sight between the two images (Zebker
and Villasenor, 1992). This baseline length
requirement scales linearly with the wavelength
of the system. (JPL)
Massonet et al., 1994
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Where does a system like this work best? The
desert!! Why? Radar backscatter works best with
exposed rocks, hard surfaces. Would this work
in Oregon? Mmmmm yes, in the cascades,
eastern Oregon, the Gorge, and oddly, Portland
where buildings make good permanent scatterers.
More info? Try http//www-radar.jpl.nasa.gov/sec
t323/InSar4crust/SarInterferometry.html
Massonet et al., 1994