The Earthquake Cycle Chapter :: n/a Image courtesy of San Francisco Public Library A German seismogram of the 1906 SF EQ
The Earthquake CycleChapter :: n/a
Image courtesy of San Francisco Public Library
A German seismogram of the 1906 SF EQ
Stages of the Earthquake Cycle• The Earthquake cycle is split into several distinct phases /
stages based on the deformation observed:– Interseismic
• The time between large earthquakes
– Preseismic• The time just before an earthquake when anomalous things happen
– Coseismic• The time during an earthquake
– Postseismic• The time after a large earthquake when anomalous deformation occurs.
• The preseismic phase has proven elusive and inconsistent– It may not even exist!
• The other three phases are commonly observed– Postseismic involves complex math !
• We will only briefly discuss this stage
The Revolution :: Elastic Rebound• After the Mw7.9 1906 SF EQ, H.F. Reid proposed that
– Earthquakes represent rapid release of strain/stress built up over a long period of time (hundreds of years)
– Called elastic rebound theory
– Confirmed by• Geodetic measurements of surface
motion (triangulation)• Geologic measurements of offset
– 450 km long rupture (360 km on land)– Average slip 4.5 m
– Reid postulated: Pacific Ocean floor must be spreading, pushing the west side of the SAF to the NW.
– He recommended a monitoring program
– Not adopted until 60 yrs later
Reid’s Evidence for Elastic Rebound
Farallon Lighthouse
Duxbury Point, Bolinas Beach
Before the 1906 Earthquake…
Farallon Lighthouse
Duxbury Point, Bolinas Beach
• Locations far from the fault were moving fast
• Locations near the fault were moving slow
• Same was true on other side of the fault, but motions were in the opposite direction
During the 1906 Earthquake…
Farallon Lighthouse
Duxbury Point, Bolinas Beach
• Locations near the fault were displaced very far
• Locations far from the fault were displaced very little
• Same was true on other side of the fault, but motions were in the opposite direction
Reid’s Hypothesis :: Elastic Rebound Theory• Although plate tectonics theory was ~50+ years from being
developed, Reid’s hypothesis is consistent with plate tectonics
+ =
Interseismic Coseismic Long-Term Block Offset
Elastic Strain is localized near fault
Elastic strain is released
After the EQ, elastic strain has been released
• Elastic rebound is also consistentwith geologic observations!
The Earthquake Cycle: Graphical Form• Reid proposed:
– Interseismic strain accumulates slowly and is eventually released in an EQ
– The coseismic strain release = total accumulated interseismic strain
• The net result:– Block offsets over geologic
timescales
• He made the prediction that the next EQ would happen when the same amount of interseismic strain had accumulated– Called a time-predictable
model– Turned out to be unreliable
Interseismic
Coseismic
Long-Term / Geologic
What is Happening During the EQ Cycle?
• Interseismic– Deep, steady, &
slow aseismic slip (i.e. creep)
• Coseismic– Rapid shallow slip
xb
y
x
Conventional Interseismic Model• Semi-infinite vertical
dislocation embedded in an elastic earth.– Semi-infinite height– Infinite length– ux = displacement of
ground around the fault– x = distance from fault– b = fault slip rate– D = locking depth
This is an analytical model based on mathematics developed by the engineering community
Displacement• Displacement = u - uo
– Final position – initial position
– Measured anywhere in a medium• Applies to the motion of a single particle
– A vector quantity (has a magnitude and direction)
– Difficult to measure in the geologic record• Don’t know initial position, only know final position
Initial position = u0
final position = u
Slip• Slip = u+ + u-
– A.k.a: Offset / Displacement Discontinuity / Burgers Vector
– Displacements are discontinuous across a fault• This is why geophysicists refer to faults as discontinuities or dislocations
– Slip is the sum of the displacements on both sides of a fault• A vector quantity (recall that the slip vector has a “rake”)
– Applies to the relative motion across a fault• So it is only measured across faults!
Slip
• So, slip measures the distance along a fault surface between two points that used to be connected
Fault
Offset Feature
Slip vs. Displacement
• Can’t determine displacements unless you know the original position
– In geology, you almost never know the original position
– In geophysics, you sometimes know the original position (GPS)
u+ = 1
u- = 0
u+ = 0.5
u- = 0.5
slip = 1
slip = 1
• It is the sum of the displacements on both sides of a fault (i.e. the slip) that matters when considering earthquakes
• Coseismic ruptures commonly– Are longer than they are deep
• Can be approximated by a rectangle
• If surface ruptures…– Can be measured by geologists
• If no surface rupture…– Rupture can be mapped by
aftershocks
– Rupture can be estimated by surface deformation models
– Can also be determined by analyzing seismic wave patterns
Fault Trace
Offset road from the Mw7.1 1999 Hector Mine EQ
Coseismic Rupture Dimensions
Let’s Trench!
slip
The 1966 Parkfield EQ
brittle-ductile transition
Controls on Rupture Dimensions• Recall the two main layers of the Earth:
– Lithosphere: Brittle Rocks
– Asthenosphere: Ductile RocksBrittle-Ductile Transition
• Earthquakes only occur in the lithosphere
• Heat flow / geothermal gradient controls the level of the brittle ductile transition– Hot rocks: ductile– Cold rocks: brittle
• Subduction zones have greatest potential rupture width (depth)
• Mid ocean ridges have smallest potential rupture width
0
4
12
8
0 8006004002000
20
40
Dep
th (k
m)
Pres
sure
(Kba
r)
Temperature (oC)
Largest EQ’s: Subduction
• The 3 largest earthquakes recorded:
– MW9.2 1964 Good Friday EQ, Anchorage, Alaska
– MW9.1-9.3 2004 Great Sumatra EQ
• 20 m maximum slip!!
• 1200 km long rupture!
– MW9.5 1960 Chile EQ
Depth
Into theearth
Surface of the earth
Distance along the fault plane100 km (60 miles)
Slip on an earthquake fault
START
Slip on an earthquake faultSecond 2.0
Slip on an earthquake faultSecond 4.0
Slip on an earthquake faultSecond 6.0
Slip on an earthquake faultSecond 8.0
Slip on an earthquake faultSecond 10.0
Slip on an earthquake faultSecond 12.0
Slip on an earthquake faultSecond 14.0
Slip on an earthquake faultSecond 16.0
Slip on an earthquake faultSecond 18.0
Slip on an earthquake faultSecond 20.0
Slip on an earthquake faultSecond 22.0
Slip on an earthquake faultSecond 24.0
Total Slip in the M7.3 Landers Earthquake
Rupture on a Fault
Quantifying Earthquake Size• There are two basic ways to quantify the size of an
earthquake.
– Intensity• Measures the amount of shaking at a given location• Depends on location
– i.e. a given earthquake will have lots of different intensities
– Magnitude• Measures the amount of energy released at the source• Does not depend on location
– A given earthquake will just have one magnitude (on each scale)
Haiti Photo Courtesy: UN Photo/Logan Abassi United Nations Development Programme
Intensity• Measured on the Modified Mercalli Scale (1931)
– Twelve categories
– Denoted by Roman numerals
– Plotted as isoseismals: zones of same intensity
– Intensity in general decreases away from epicenter, but local geology can completely control intensity in some cases…
(only measured by instruments)
• Magnitude of the earthquake• Distance from hypocenter• The nature of the substrate at location
– Stiff bedrock shakes less– Soft rock shakes a lot– Sedimentary basins can amplify waves
• E.g. 1985 Mexico city MW8.0 > 350 km away
• The frequency of the seismic waves– High frequency waves do most damage but do
not travel very far (i.e. they attenuate)• Car stereo analogy (bass)
– In general…– Long ruptures generate long wavelengths (low
frequencies)– Short ruptures generate short wavelengths
(high frequencies)
Severity of Shaking Depends On:
Mexico city
Buildings - Mexico City, 1985
Before
After
[TerraShake Animations]
• Thousands of buildings destroyed• Prompted Mexico to develop building
codes
Magnitude• Magnitude = A measure of the
amount of energy released at the source of the EQ.
• Richter Scale: A type of magnitude measurement coined by Charles Richter in 1935.– ML = log10 (max amplitude of S-waves in
units of 10-6 m)
– Used a logarithmic scale to make the wide range of measurements easy to deal with
• A change of one in Richter magnitude = 10x the ground motion and 30x the energy.
– Also called the “local magnitude”• Based on measurements of S-wave
amplitudes at 100 km from epicenter
• Can be effectively “corrected” for seismometers at different distances Photos of Charles Richter (1900-1985) courtesy of USGS
The Richter Nomogram• How seismogram
readings are made into ML
• Can have negative magnitude
• No mathematical upper limit on magnitude
– i.e. 10 is not max
Richter’s ups and Downs• Richter scale advantages:
– First quantitative measure of energy release– Can be computed minutes after an EQ– Good for nearby, shallow, and moderate EQ’s
• The Richter scale shortcomings:– At epicentral distances > 600 km, surface waves have greater amplitude
than S-waves• ML underestimates distant events• Instead, we use MS, “surface wave magnitude”, which is based on the amplitude of
surface waves (R-waves)
– Underestimates deep earthquakes (S-waves attenuate faster than P-waves)• Instead we use mb, “body wave magnitude”, for deep events.• Uses the maximum amplitude of either body wave.
• All of these underestimate very large EQ’s– We now use “Moment Magnitude”, MW = 2/3 log10 M0 - 10.7– M0 is the “Seismic Moment”
Background: seismogram from MW9.2 1964 Alaska EQ, courtesy USGS
Seismic Moment• Seismic moment, M0, is mathematically based on the
torque exerted by the shear stress couple (i.e. the deformation on both sides of a fault)
• M0 = μAd– μ = shear modulus– A = fault rupture area– d = average slip during earthquake
• μ does not greatly vary for different rock types at depth– Typically ~ 30 GPa
• So, A, and d are what matter– But what controls A and d?
Seismic Moment and the Sizes of Ruptures• Small EQ’s have small rupture areas and
small average slip
• Slip is much smaller than rupture length
• Due to finite fault width (brittle-ductile transition), small earthquakes follow different scaling
• Where would subduction EQ’s plot below?
Bigger (longer) Faults Make Bigger Earthquakes
1
10
100
1000
5.5 6 6.5 7 7.5Magnitude
Kilo
met
ers
8
Bigger Earthquakes Last Longer
1
10
100
5.5 6 6.5 7 7.5 8
Magnitude
Seco
nds
Earthquake Prediction (?)• Currently scientists can’t make short term predictions of earthquakes
– e.g. there will be an earthquake next Tuesday at 8:07 AM.
• We can make some long term predictions– There will very likely be a large earthquake on the San Andreas fault in the next
hundred years.– In the next hundred years it is unlikely that there will be a large earthquake in
central Canada
• Seismic Hazard– Is there a seismic source?
• Seismic Risk– What sort of risk does this source pose to civilization?– E.g. no people no risk
• Seismic Hazard Assessments are based on:– Locations of faults– Slip rates of faults– Recurrence intervals (time between events)– Local geology effects (liquefaction / basin fill)– Seismic gaps
Building Codes• In response to the 1971 M6.6 Sylmar EQ, the state of California passed new
laws prohibiting the building of public buildings within ¼ mile of an active fault zone (private houses within 50 feet)– Called “Alquist-Priolo Earthquake Fault Zones ”
• Since short term earthquake predictions may be impossible, building codes are the main way to save lives in future earthquake events
• Building codes (zoning laws) are based on seismic hazard assessments• Insurance companies also are very interested in seismic hazard maps
Seismic Gaps & The North Anatolian Fault, Turkey• Seismic Gaps: Areas where the fault has not moved in a long time
– These regions may be the next to go
• Stress Triggering: When an earthquake happens, the motion changes the stress on nearby faults, possibly making them more or less likely to fail.– The North Anatolian Fault is an excellent example of both of these phenomenon
(Ross Stein animations)