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GEOLOGY 415/515:
TECTONIC GEODESY
C. Rubin, Central Washington University
Introduction
Earthquakes: fundamental concepts & focal mechanisms
Earthquakes: magnitude, earthquake cycle
Tectonic geodesy
Strike-slip faults
Normal faults
Subduction zones (Megathrust earthquakes)
Thrust/Reverse faults
Plate interiors
Earthquake recurrence & hazards
Shaded ellipses depict
typical ranges for classes
of processes.
Hachured boundaries
indicate the present
range of various
techniques for making
geodetic measurements.
EDM: electronic distance
meter
GPS: global positioning
system
OB: observation
SLR: satellite laser ranging
VLBI: very long baseline
interferometry.
Modified after Minster et
al. (1990).
Displacement at three
intervals, beginning with
t0 is illustrated.
A. Fault zone is very
weak and is creeping so
that all motion occurs
directly along fault.
B. Fault zone is relatively
strong and strain is
distributed across broad
zone on either side of
the fault.
C. Some creep occurs on
the fault, and rigid block
rotations occur on either
side of the fault, taking up
the additional motion.
D. Schematic results from
an alignment array along
a creeping fault that is
displaced about 80 mm in
20 years.
Modified after Sylvester
(1986).
GPS GEODESY
Repeated measurements that
locate of certain fixed reference
points on the Earth's surface.
Fixed points are marked by metal
disks set into concrete casings
(called bench-marks) or very stable
structures called monuments.
The Earth’s surface can move up,
down and sideways - the reference
point includes a vertical position and
horizontal position.
The horizontal position of a reference
point is described by its latitude
(north-south position) and longitude
(east-west position).
The vertical position of a reference
point is described by its height
above or below mean sea level.
GPS GEODESY
Global mean sea level is complicated
since the Earth's mass is not uniformly
distributed within
an elliptical shell.
Areas with greater mass have a
stronger gravitational attraction than
areas with less mass, and these
differences cause differences in
actual mean sea level on the Earth's
surface.
To account for these differences,
geodesists imagine a threedimensional surface so that the Earth's
gravitational attraction is the
same at every point on the surface.
This surface is called the geoid, and is
a closer approximation to global
mean sea level than the ellipsoid.
Global mean sea level
Global Sea Level
Gravity anomaly map from the
NASA GRACE (Gravity Recovery
And Climate Change).
GPS GEODESY
The original design of the GPS space
segment, with 24 GPS satellites (4 satellites
in each of 6 orbits), showing the evolution
of the number of visible satellites from a
fixed point (45ºN) on earth (considering
"visibility" as having direct line of sight).
Each GPS satellite continuously
broadcasts a Navigation Message giving:
Satellite clock and its relationship to GPS
system time
Ephemeris - giving the satellite's own
precise orbit
Each satellite transmits its
navigation message with at least
two distinct spread spectrum
codes: the Coarse / Acquisition
(C/A) code, which is freely
available to the public, and the
Precise (P) code, which is usually
encrypted.
Coarse orbit and status information for
each satellite in the constellation, an
ionospheric model, and information to
relate GPS derived time to Coordinated
Universal Time (UTC).
GPS GEODESY
A GPS receiver computes the
distance to a satellites based
onamount of time required for a
radio signal from the satelliteto reach
the receiver.
The satellites and receivers both
contain accurate clocks (the
satellites contain an atomic clock
that is much more accurate than the
receivers' clock, however),
4 unknowns: x, y, z
coordinates and time
The receiver calculates the time
difference between the two signals,
and then converts this to a distance
measurement.
Four satellites are typically used to
determine the three-dimensional
position of a location on Earth.
GPS ERRORS
Atmospheric effects
Inconsistencies of atmospheric conditions
affect the speed of the GPS signals as
they pass through the Earth's atmosphere,
especially the ionosphere
Multipath effects
GPS signals can also be affected by
multipath issues, where the radio signals
reflect off surrounding terrain; buildings,
canyon walls, hard ground, etc. These
delayed signals can cause inaccuracy.
GPS ERRORS
Ephemeris and clock errors
The ephemeris data is transmitted every 30
seconds, the information itself may be up
to two hours old.
Data up to four hours old is considered
valid for calculating positions, but may
not indicate the satellites actual position.
The satellite's atomic clocks experience
noise and clock drift errors.
The navigation message contains
corrections for these errors and estimates
of the accuracy of the atomic clock,
however they are based on observations
and may not indicate the clock's current
state.
V is the rate of relative motion
between the two blocks
v/V is the fraction of the total motion
that is exhibited by any point.
The rigidity of the fault (u2) is
one-fifth that of the right-hand
block (u1).
Most of the displacement
occurs along the weak fault
zone.
Note how the relative rigidity of
the blocks affects the shape of
the displacement within each
block.
For the highest rigidity (line 5,
left-hand block), there is very
little deformation within the rigid
block .
Modified after Lisowski et al.
(1991).
A. Monterey geodetic
network showing
triangulation stations in the
vicinity of the San Andreas
and Calaveras faults.
B. Results of trilateration
surveys between 1973 and
1989 across the San Andreas
fault zone near Monterey
Bay.
Long-term slip rates across
the San Andreas region are
about 35 mm/yr in this area.
About 15 mm/yr of North
America-Pacific relative plate
motion is accommodated on
other faults beyond the
surveyed area.
The San Andreas and the
Calaveras faults are clearly
marked by abrupt changes in
relative velocity.
These discontinuities show
that most of the relative
motion across this 80-km-wide
zone is accommodated by
slip on these two faults.
Little deformation occurs in
the bounding blocks.
Over a span of 16 years, the
total motion across the
profile is averages about 35
mm/yr
Most of the expected plate
motion is accounted for by
the measured velocities.
Modified after Lisowski et al.
(1991).
A. Triangulation network in
the vicinity of the Transverse
Ranges of southern
California.
B. The Transverse Range
data (1973-1989) shows no
differential displacement
across the San Andreas fault,
which can be interpreted as
being locked in this region.
Instead, strain is occurring
across the entire surveyed
zone.
Less than 25 mm/yr of relative
plate motion is
accommodated by
displacements along the
profile.
This indicates that considerable
strain due to Pacific-North
American relative plate motion
occurs well beyond the San
Andreas fault zone.
Modified after Lisowski et al.
(1991).
Relative uplift rates are
calculated along a 250km-long spirit-leveling line
(B) oriented approximately
perpendicular to the
Himalayan Range in
central Nepal.
The profile is fixed at its
southern end, and errors
become cumulatively
larger to the north.
The southernmost peak
of uplift (~2 mm/yr) is
interpreted as a
response to a growing
anticline within the
foreland.
No distinct topographic
signature is associated
with this deformation,
probably due to ready
erosion of the uplifted
strata.
The leveling line through
the Lesser Himalaya
shows uplift spatially
associated with the Main
Boundary Thrust and
subsidence in the
intermontane
Kathmandu region.
Uplift within the Greater
Himalaya occurs at the
highest rates (~6 mm/yr)
and is associated with
high topography.
Finite-element modelling
of deformation of elastic
crust (bottom panel)
suggests that strain
above and south of a
crustal ramp separating
the Indian and Asian
plates could generate
the observed pattern of
uplift.
Modified after Jackson
and Bilham (1994a).
Comparison of leveling-line
data and deformed river
terraces along a growing
fold.
A. Coseismic deformation
from the 1983 Coalinga
earthquake (M = 6.5) from
leveling-line data along
the center of the anticline
(line, inset).
B. Deformed terrace profile
surveyed near the nose of
the same anticline (line 1,
inset).
Similar deformation patterns
are displayed by both data
sets
The long-term pattern of
terrace deformation could
result from the accumulation
of deformation similar to that
caused by the 1983
Coalinga earthquake.
Modified after King and Stein
(1983).
The magnitude of
warping is calculated by
subtracting the
estimated undisturbed
terrace profile from the
observed profile.
Modified after King and
Stein (1983).
BOUNDARY TYPE
CHANGES WITH
ORIENTATION
CONVERGENCE ALEUTIAN TRENCH
54 mm/yr
PACIFIC - NORTH
AMERICA
STRIKE SLIP SAN ANDREAS
PACIFIC wrt
NORTH
AMERICA
pole
EXTENSION GULF OF CALIFORNIA
1989 LOMA PRIETA, CALIFORNIA EARTHQUAKE
MAGNITUDE 7.1 ON THE SAN ANDREAS
Davidson et al
GPS & EQ Cycle
Geodetic measurements of
crustal movements in California
provide critical observations for
understanding earthquakes.
Almost a century ago, Read
(1910) analyzed geodetic
measurements acquired before
and after the 1906 San
Francisco Earthquake to
establish his “elastic rebound”
theory (Figure 1).
GPS & EQ Cycle
The theory proposes a two
stage model of crustal
deformation:
elastic behavior in between
earthquakes (interseismic)
and
fault rupture (coseismic)
during earthquakes.
The elastic rebound theory
expanded into a four stage
conceptual model, known as
the “the earthquake
deformation cycle”.
The two additional stages are
pre- and post-seismic
deformation, occurring short
time before and after the larg
earthquake, respectively.
GPS & EQ Cycle
The theory proposes a two
stage model of crustal
deformation:
elastic behavior in between
earthquakes (interseismic)
and
fault rupture (coseismic)
during earthquakes.
The elastic rebound theory
expanded into a four stage
conceptual model, known as
the “the earthquake
deformation cycle”.
The two additional stages are
pre- and post-seismic
deformation, occurring short
time before and after the larg
earthquake, respectively.
GPS Velocity field - SAF
The velocity vectors with respect to the Stable North America reference
frame
Southwestward magnitude increase.
In this reference frame, crustal movements in eastern US (east of the
Colorado Plateau) are zero and increase in tectonically active areas, such as
western US.
GPS Velocity field - SAF
GPS & EQ Cycle
A subset of the GPS
velocity field in
Central California
showing velocity
variations across the
San Andreas Fault.
The velocities are
shown in the Stable
North America
reference frame.
GPS & EQ Cycle
Map of the San Francisco Bay area in a Pacific
Plate-Sierra Nevada block projection with GPS
Velocities from 1994-2003 relative to station
LUTZ in the Bay Block (yellow square).
GPS Velocity field
SAF
The region affected by postseismic deformation following the Loma Prieta earthquake.
To avoid "contamination" of the regional deformation pattern by transient processes, data
before 1994 is not included.
The southern Bay Area exhibits mostly fault-parallel right-lateral motion, with no indication of
the fault-normal compression observed in the Foothills thrust belt immediately after the Loma
Prieta Earthquake (Bürgmann, 1997).
GPS & EQ Cycle
Creep along the Hayward
fault allows the Bay block
to slide past the East Bay
Hills block
Only minimal internal
deformation and strain
accumulation within either
block.
Deformation near the Hayward fault.
Velocities relative to LUTZ on the Bay
block.
Fixed Pacific plate
Most displacement east
of SAF are parallel to fault
West of SAF, between SB
and LA, displacement is
accommodated by other
faults (thrust and reverse)
Variability of motions =
differential rotation of
blocks
Plate boundary not just
concentrated along SAF
Given the background
noise in the observations,
it is only with continuous
GPS readings that this
trend (1.1 mm/day) is
observable.
Modified after Bock et al.
(1993).
Despite the typical day-to-day variability of 5-15 mm, very precise positions
are defined using multiple days of readings.
An abrupt coseismic offset of 44 mm occurred during the 1991 Landers
earthquake.
Post-seismic slip of 22 mm that occurred during the few weeks following the
EQ (right panel). Given the background noise in the observations, it is only
with continuous GPS readings that this trend (1.1 mm/day) is observable.
Modified after Bock et al. (1993).
Radar SAR interferogram
of ground displacement
associated with the
Landers Mw 7.3
earthquake of June, 1992.
Each fringe represents 28
mm of displacement and
at least 20 fringes are
visible near the fault
(equal to 560 mm of
displacement).
Coherence is lost as the
ground rupture is
approached, probably
because the
displacement gradient is
greater than 28 mm/pixel.
Massonnet et al. (1993).
Note the broad,
asymmetric deformation
in an east-west direction
covering >75 km and the
abrupt termination of
major deformation near
the ends of the fault.
The detailed deformation
patterns seen here can
be used to constrain
models of surface
displacement due to the
Landers rupture.
B. Modeled
interferogram pattern
based on eight fault
segments rupturing
along vertical planes in
an elastic half-space.
The excellent match
between the observed
and modeled results
indicates that a simple
half-space model
models the observed
deformation pattern.
Modified after Massonnet
et al. (1993).
Mt Etna interferogram
X-band
(SIR-C/X-SAR mission)