Earthquake Sources and Magnitude

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Earthquake Sources and Magnitude

• Annabel Kelly
• USGS Menlo Park, CA

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What is an Earthquake ?
An Earthquake Instrumentally recorded (or felt)
ground shaking
An Earthquake Source A sudden change in stress
in the Earth that generates seismic waves
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Seismic Sources

• Fault movement
• Volcanic activity (magma movement or eruptions)
• Ocean storms (microseisms)
• Cave collapse, rock fall, etc
• Manmade sources explosions, vibrators, cultural
  noise

BGS recordings of an explosion at an oil storage
depot near London Dec 16, 2005. Equivalent to
M2.4 earthquake
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Tectonic earthquakes
Elastic Rebound Theory Reid (1910)
8.5 feet offset in San Andreas fault from 1906
earthquake. Marin County
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Comparing an earthquake to the breaking of a
chopstick

• Failure
• Build-up of stress (strain energy)
• Difficult to predict time and place
• Breaks at weakest point
• Sometimes hear precursors
• Sound of breaking same as seismic waves

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Types of faults
Normal fault
Thrust (Reverse) fault
Strike-slip fault
Images courtesy of IRIS
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Strike-Slip Faults
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1979 Imperial Valley, California (M6.5)
Photo by D. Cavit, USGS
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Complicated Slip Distributions

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Rupture
Sumatra earthquake, Dec 28, 2004
Haskell, 1964
Sumatra
Ishii et al., Nature 2005
doi10.1038/nature03675
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Asperity a region of a fault with higher
strength than its surroundings
The evolution in time and space of the 1985
Michoacán, Mexico, earthquake. Note that this is
almost 2 separate earthquakes, one in the south
and one in the north, separated by 10 sec and
100 km.
Bormann 2002. New Manual of Seismological
Observatory Practice.
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Seismic Moment (Mo)
15 km
Area (A)

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Slip (S)
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Seismic Moment (Rigidity)(Area)(Slip)
0
M4 M5 M6
Courtesy of Jim Mori
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Seismic moments and fault areas of some famous
earthquakes
Courtesy of Jim Mori
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Point source approximation - Equivalent Body
Forces
Couple (Single Couple)
Double Couple
Bormann 2002, New Manual of Seismological
Observatory Practice
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Moment tensor dipoles and couples
9 components, but symmetric matrix so 6 are
independent
USGS
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Moment Tensor for an Explosion


USGS
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Moment Tensor for Fault Slip

Double Couple Fault - Slip
USGS
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Magnitude a measure of how large an Earthquake
is.
Incomplete for 2006
Average 1 M8 / year
Average 13-15 M7 / year
Average 130-150 M6
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Types of Magnitude
Name Data used Period range
Ml Local magnitude regional S and surface waves 0.1-1 sec
mb (short period) body wave magnitude teleseismic P waves 1-5 sec
Ms Surface wave magnitude teleseismic surface waves (20 sec)
Traditional magnitudes based on amplitudes of
recorded data.
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Local magnitude - Ml
Charles Richter 1900-1985
USGS, NEIC
Ml log Amax log A0 Defined using horizontal,
short period seismometer. Therefore no period
consideration. Log A0 correction taken from
published tables and related to distance (lt
600km) The 1 sec period response of the
seismometer is similar to many small buildings,
therefore still useful for engineers.
Bruce Bolt. Earthquakes. WH Freeman and Company
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Surface wave magnitude - Ms
Ms log (A/T)max sS(?) log (A/T)max 1.66
log ? 3.3

• First defined by Gutenberg 1945.
• IASPEI Standard Distances 2 degrees lt ? lt 160
  degrees.Depth h lt 50 km.Any surface wave period
  measured on horizontal and vertical components
• NEICLimit periods to 18 lt T lt 22 sec and only
  use vertical component.Distances from 20 degrees
  lt ? lt 160 degrees

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Body wave magnitude - mb
Distance correction from Gutenberg 1945
mb log (A/T)max Q(?,h)

• Calculated from P wave displacement amplitude.
  Commonly reported but very variable calculation
  methods
• Fairly standard features of measurement
  distance 20 deg lt ? lt 100 deg, period T lt 3 sec.
  

• IASPEI Standard measure Amax from whole recorded
  P wave vertical or horizontal max.
• NEIC vertical P only, measure max amp in first
  10 cycles (10-20 sec), or manually extended to
  60 sec for large earthquakes.
• China and the CTBTO measure only first 5-6
  seconds.

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Saturation

• Ml, Ms and mb all suffer from saturation.
• Occurs for 2 reasons

Time window saturation The magnitude is
calculated for a time window that is less than
the duration of the rupture (particularly effects
mb)
Spectral saturation The wavelength of the wave
is too short to see all of the rupture (effects
mb, Ml, and Ms)
Kanamori 1983
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Types of Magnitude
Name Data used Period range
Ml Local magnitude regional S and surface waves 0.1-1 sec
mb (short period) body wave magnitude teleseismic P waves 1-5 sec
Ms Surface wave magnitude teleseismic surface waves 20 sec
Mw Moment Magnitude teleseismic surface waves gt 200 sec
Me Energy magnitude teleseismic P and S waves 0.2-100 sec
Do not saturate and physically meaningful. But
more complicated to calculate
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Moment Magnitude - Mw

• Calculated from seismic moment (Mo). Therefore
  related to fault slip not energy released as
  waves. More relevant for tsunamis, less relevant
  for damage from ground shaking.

• Harvard CMT and NEIC calculate Mw from the moment
  tensor solution.
• Fit shape and amplitude of long period surface
  waves to synthetics to model moment tensor and Mo.

Stein and Wysession, An Introduction to
seismology, earthquakes and Earth structure
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Energy Magnitude Me

• Calculates the energy released as seismic waves.
• Done by integrating radiated energy flux in
  velocity-squared seismograms over the duration of
  the rupture.

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These two earthquakes in Chile had the same Mw
but different Me
Earthquake 1 6 July 199730.0 S 71. W Me
6.1, Mw 6.9No fatalities, no houses
destroyed. Earthquake 2 15 October 199730.9 S
71.2 W Me 7.6 Mw 7.17 people killed, more than
300 people injured. 5,000 houses destroyed.
Landslides and rockslides in the epicentral
region.
Courtesy of George Choy
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Types of Magnitude
Name Data used Period range
Ml Local magnitude regional S and surface waves 0.1-1 sec
mb (short period) body wave magnitude teleseismic P waves 1-5 sec
Ms Surface wave magnitude teleseismic surface waves 20 sec
Mw Moment Magnitude teleseismic surface waves gt 200 sec
Me Energy magnitude teleseismic P and S waves 0.2-100 sec
Mwp P-wave moment magnitude teleseismic P waves 10-60 sec
mB broadband body wave magnitude teleseismic P waves 0.5-12 sec
Mm Mantle magnitude teleseismic surface waves gt 200 sec
Mj JMA magnitude regional S and surface waves 5-10 sec
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Mwp
?uz(t)dt ? Mo
Mo Max ?uz(t)dt 4pra3r/Fp Mw (logMo/1.5)
10.73
Quick magnitude from P wave Uses relatively
long-period body waves (10-60 sec) Some
problems for Mgt8.0
Courtesy Jim Mori
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Mantle Magnitude - Mm
Source Correction
Mm log10(X(w)) Cd Cs 3.9
Distance Correction
Spectral Amplitude
amplitude measured in frequency domain
surface waves with periods gt 200 sec
Courtesy of Jim Mori
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Magnitudes for tsunami warnings

• Want to know the moment (fault area and size) but
  takes a long time (hours) to collect surface wave
  or free oscillation data and calculate Mw
• Magnitude from P waves (mb) is fast but
  underestimates moment, so
• If have time (hours), determine Mm from mantle
  waves or Mw from long period surface wave.
• For quick magnitude (seconds to minutes),
  determine Mwp from P waves

Courtesy of Jim Mori
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Magnitudes for the Sumatra Earthquake
Scale Mag Data time to announce number of stations
mb 7.0 1 sec P wave 131 stations
Mwp 8.0 /8.5 60 sec P waves 11 minutes / 1 hour
Ms 8.0-8.8 20 sec surface waves 118 stations
Mw 8.9-9.0 300 sec surface waves 5 hours
Mw 9.1-9.3 3000 sec free oscillations days
Courtesy of Jim Mori