Earthquake
seismology
Fence offset by the 1906 San
Francisco earthquake
The San Andreas fault in the
Carrizo plain, California
Offset drainage along the San
Andreas fault, Wallace Creek,
California
Elastic strain
accumulation
•
GPS-derived velocities in Southern California (19922000). Velocities are shown with respect to North
America. The active faults of California are shown in
orange.
•
(Most) faults are locked
between earthquakes
The area around faults
accumulates elastic strain
The seismic
cycle
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Between earthquakes:
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–
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During an earthquake:
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–
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Faults are locked
Area around faults accumulate deformation
A fault slips suddenly
The deformation accumulated around the fault is
released
After an earthquake:
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Stresses around the fault are modified
Readjustments on the fault plane = aftershocks
The seismic cycle
Click for earthquake cycle animation
Between earthquakes:
– Faults are locked
– Area around faults accumulate deformation
Anim ation: R. Stein, USGS
During an earthquake:
– A fault slips suddenly
– The deformation accumulated around the
fault is released
– Stresses around the fault are modified
Earthquake seismology
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Location of the earthquake (hypocenter)?
Frequency of similar earthquakes?
Focal mechanism?
Rupture mechanism?
Size?
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Intensity
Magnitude
Moment
Energy release
• Earthquake triggering?
Locating earthquakes
Difference in travel time
for P and S waves
increases with increasing
epicentral distance:
tS =
D
VS
tP =
D
VP
$1
1 '
" t S # t P = D& #
)
V
V
% S
P (
VP = 5.85
km / s
" D = ( t S # t P ) * 8.0
VS = 3.38
km / s
Locating earthquakes
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With at least 3 stations:
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Calculate S-P time difference
Convert to distance
Draw circles centered on stations
Location = intersection of circles
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Errors:
– Picking arrivals
– Actual travel times are slightly
different from theoretical ⇒ location
is dependent on the Earth model used
(global or local).
Earthquake focal
mechanisms
• Earthquake = release of
accumulated elastic energy by
displacement on a fault
• Problem: what type of fault motion?
• Case of a strike-slip fault: particle
motion due to fault slip:
– Blue quadrants: particles pushed
away from the focus ⇒
compressional first motion = UP
– Red quadrants: particles pulled
towards the focus ⇒ dilatational
first motion = DOWN
• As a result, we obtain 4 quadrants:
– 2 compressional quadrants: first
motion down
– 2 extensional quadrants: first
motion up
compressional
first motion
dilatational
first motion
tension
axis
compression
axis
extensional
quadrant
compressional
quadrant
compressional
quadrant
extensional
quadrant
auxiliary plane
fault plane
Earthquake focal
mechanisms
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•
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Earthquake = release of accumulated
elastic energy by displacement on a
fault
Problem: what type of fault motion?
Let’s assume an earthquake on a
reverse fault:
– Compressional / tensional quadrants
– Compressional quadrant: surface is
pulled down ⇒ first motion DOWN
– Tensional quadrant: surface is pushed
up ⇒ first motion UP
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If we map first motion, we can find:
– 2 focal planes
– P- and T-axis
Earthquake focal mechanisms
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Seismic rays travel away from the focus
Each ray “samples” a dilatational or compressional quadrant around the
focus
Seismic stations at different distances record up or down first motions
Rays along nodal planes?
in cross-section
focal mechanism
(stereonet proj.)
Earthquake focal mechanisms
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The “focal sphere”:
– Center = earthquake hypocenter
– In each quadrant: first motion identical
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Seismic stations are at the surface,
(usually) not underground
– Rays bend upward and eventually
reaches a seismic station at the surface
– The important parameter is the initial
take-off angle
– Take-off angle can be calculated
knowing the earth’s structure =>
accuracy of focal mechanisms depend
on our knowledge of the Earth structure
(local, regional, global)
The focal sphere:
Earthquake focal
mechanisms
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Strike-slip faulting:
– Vertical focal planes
– Horizontal P-axis and T-axis
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Other types of faulting:
– Focal planes will have a dip
– P-axis and T-axis will have a
dip
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For representation: focal sphere
+ stereographic projection of
focal planes and P-T-axis ⇒
“Beach balls”
In the horizontal plane:
Earthquake focal mechanisms
reverse
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Focal mechanisms define
the type of faulting that
occurred during the
earthquake.
The actual fault plane is
ambiguous
Focal mechanisms can
combine these types of
faulting.
Focal mechanisms in an
actively deforming area
contain information about
the strain regime
normal
strike-slip
Earthquake focal mechanisms
Earthquake focal
mechanisms
• Eastern Mediterranean
• Earthquake focal
mechanism illustrate:
– Strike-slip faulting
– Reverse faulting
– Extensional faulting
• Compare with GPS
velocities
(McClusky et al., JGR, 2000)
Earthquake rupture
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An earthquake usually breaks a segment of a fault
The rupture does not always reach the surface
The earthquake is followed by aftershocks:
– Readjustments on the rupture plane
– Help define the rupture plane
Animation http://www.scecdc.scec.org/northreq.html
Northridge earthquake, January 1994, M=7.2
Earthquake rupture
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Time and space history of a rupture, example of the Northridge earthquake
Slip on the rupture plane is not homogeneous
Asperities and barriers
Animation D. Wald, http://www.scecdc.scec.org/northrup.html
Earthquake size
-F
• Shear forces on a faults ⇒
moment
• Hooke’s law relates stress
and strain for elastic
solids: for shear,
proportionality factor is
rigidity µ
b
F
Rupture area: A = L x W
MO = 2bF
" shear = µ # $shear
with
$shear =
d
2b
and
" shear =
F
F
=
A L #W
% MO = µAd
Moment = rigidity x displacement x rupture area
!
Earthquake magnitude
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•
1935: Richter worked on ranking
earthquakes as a function of their
size
First definition:
– “Maximum amplitude recorded
at 100 km from the epicenter”:
ML=log10(Amax) + 3 log10Δ - 2.92
– For local earthquakes: S-waves
have the largest amplitude
– Correction for distance: Δ (=
angular epicentral distance in
degrees)
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Richter magnitude scale:
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Open scale
Largest magnitude recorded =
Chile, 1960, MW=9.6 (MS=8.3)
Negative magnitudes are
possible…
nomogram used to compute magnitude quickly by eye
Earthquake magnitude
• ML = local magnitudes (~ 600 km from earthquake)
• At larger distances:
– Using surface waves (they have the largest amplitude)
MS = log10(Amax/T)+1.66 log10Δ + 3.3
A=max. amplitude of vertical component in microns, T = period in
seconds, D = angular distance in degrees.
– Using body-waves (P-waves)
mb = log10(Amax/T)+0.01 Δ + 5.9
– Ms – mb relationship:
mb = 0.56 MS + 2.9
Earthquake magnitude
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Spectrum of seismogram gives spectral
amplitude at all frequencies
Static moment = amplitude at low
frequencies
Corner frequency depends on duration
of rupture time TD and and rise time TR
Above corner frequency
– there is destructive interference
– Shaking cannot get higher amplitude but
continues in time longer
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As a result:
– Ms saturates at 8.3
– mb saturates at 6.2
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Use of moment magnitude:
MW = (2/3) log10MO – 10.7
2/TR
2/TD
Earthquake magnitude
• Less than 3.5: Generally not felt, but recorded.
• 3.5-5.4: Often felt, but rarely causes damage.
• Under 6.0: At most slight damage to well-designed
buildings. Can cause major damage to poorly
constructed buildings over small regions.
• 6.1-6.9: Can be destructive in areas up to about 100
kilometers across where people live.
• 7.0-7.9: Major earthquake. Can cause serious damage
over larger areas.
• 8 or greater: Great earthquake. Can cause serious
damage in areas several hundred kilometers across.
Earthquake size
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Logarithmic relationship between magnitude and:
– Coseismic displacement: M5=1 cm, M8=10m
– Rupture length: M5=1 km, M8=400 km
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Large earthquakes have a MUCH LARGER rupture displacement and
length than smaller ones
Energy release
• Energy release:
log10 E = 4.4 + 1.5M S
• Increase of one level of
magnitude corresponds to:
!
⇒ Amplitude increase: 101 = 10
⇒ Energy increase: 101.5 ≈ 30
• Energy release increases very
rapidly with magnitude
Largest Earthquakes in the World Since 1900
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Chile - 1960 05 22 - 9.5 (Ms = 8.5)
Prince William Sound, Alaska - 1964 03 28 - 9.2 (Ms = 8.3)
Off the West Coast of Northern Sumatra - 2004 12 26 - 9.0
Kamchatka - 1952 11 04 - 9.0
Off the Coast of Ecuador - 1906 01 31 - 8.8
Northern Sumatra, Indonesia - 2005 03 28 - 8.7
Rat Islands, Alaska - 1965 02 04 - 8.7
Andreanof Islands, Alaska - 1957 03 09 - 8.6
Assam - Tibet - 1950 08 15 - 8.6
Kuril Islands - 1963 10 13 - 8.5
Banda Sea, Indonesia - 1938 02 01 - 8.5
Chile-Argentina Border - 1922 11 11 - 8.5
Visit: http://neic.usgs.gov/
Earthquake
frequency
• There are far more small earthquakes
than large ones
• Many small earthquakes are not
detected
• Gutenberg-Richter law:
– Linear relationship between
log[number of earthquakes] and
magnitude:
LogN = a – b x M
– Slope = ‘b-value’
• Worldwide average is 1.0
• May vary regionally
• Lab. experiments show:
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High stress ⇒ low b (less small eqs)
Low stress ⇒ high b (more small eqs)
• Empirical tool for seismic hazard
studies
Earthquake
frequency
The USGS estimates that several
million earthquakes occur in the
world each year. Many go
undetected because they hit
remote areas or have very small
magnitudes. The NEIC now
locates about 50 earthquakes
each day, or about 20,000 a year.
Earthquake information:
http://neic.usgs.gov/
Descriptor
Magnitude
Average Annually
Great
8 and higher
1
M ajor
7 - 7.9
18
Strong
6 - 6.9
120
M oderate
5 - 5.9
800
Light
4 - 4.9
6,200 (estimated)
M inor
3 - 3.9
49,000 (estimated)
Very M inor
< 3.0
M agnitude 2 - 3: about 1,000 per day
M agnitude 1 - 2: about 8,000 per day
Frequency of occurrence of earthquakes based on observations since 1900
Intensity
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Qualitative description of earthquake size
Based on damage assessment ⇒ Mercalli scale
Can be severely biased
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Area with local amplification of seismic waves or secondary effects such as liquefaction
Subjective reports from people
Depends on vulnerability
Often the only information available for historical earthquakes
Seismic hazard
• Earthquake damage:
– Ground acceleration, in g (up to 2 g)
– Secondary effects: liquefaction, landslides, fires, etc
• Seismic risk = seismic hazard ⊗ vulnerability
• Seismic hazard = seismic potential (When? Where? What
size?) ⊗ propagation of seismic waves
– Seismic potential = probability for an earthquake of a given size
to occur
– Propagation = attenuation of seismic waves, site response
• Seismic hazard = probability to exceed a given
acceleration for a given time period
Seismic potential
• Derived from GutembergRichter law, tailored for
the are under study
• Requires earthquake
catalog ⇒ b value
• Can be complemented by
information on active
fault: geometry, slip rate
• Can be complemented by
geodetic information:
strain rate
Attenuation
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Amplitude of seismic waves
is attenuated:
– Geometric attenuation
– Intrinsic attenuation
– Attenuation relationship:
determined empirically
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Many different attenuation
relationships are available:
– Quantity of available data
– Geological nature of the
terrain: amplification or
damping
Site response
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Ground acceleration decreases
with distance, but can vary by a
factor of 10 for 2 sites at the
same distance to an earthquake
⇒ site response
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Site response depends on
geological factors:
– Softness of soil or rocks near
the surface: ground motion
amplified by soft rocks
– Sediment thickness above
bedrock: ground motion
amplified by thick sediments
Snapshots of simulated wave propagation in the LA area for the
hypothetical SAF earthquake (K. Olsen, UCSB)
Final result: seismic hazard maps
• Peak acceleration that has a 2% probability to be exceeded in 50 years
• Compare New Madrid and California!
What have we learned?
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Active faults are (usually) locked between earthquakes, while the area
around them is accumulating elastic strain.
An earthquake is the sudden release of the elastic strain accumulated
over decades.
The earthquake results in:
– A rupture, that may sometimes reach the surface
– Seismic waves, that propagate away from the rupture area
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Using seismic wave, one can figure out:
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The location of the earthquake
The type of fault motion (focal mechanism)
The magnitude of the event (energy released)
The slip distribution on the rupture plane
Magnitude scale:
– Is not linear but power law
– Gutemberg-Richter law: N = a –b M
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Earthquake hazard depends on source, attenuation, and site response
What have we learned?
• One can use seismic waves generated artificially to image
deep structures:
– Seismic reflection:
• Receiver and source close
• Arrivals describe hyperbolas
– Seismic refraction:
• Receiver and source far apart
• Arrivals describe straight lines
• Data collection, processing (increase SNR and remove
artefacts), interpretation
• Applications: oil exploration, sequence stratigraphy, etc.