U.S. Department of the Interior U.S. Geological Survey Earthquake Sources and Magnitude Annabel Kelly USGS Menlo Park, CA

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

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, Equivalent to M2.4 earthquake

Elastic Rebound Theory Reid (1910) 8.5 feet offset in San Andreas fault from 1906 earthquake. Marin County Tectonic earthquakes

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

Thrust (Reverse) fault Normal fault Strike-slip fault Images courtesy of IRIS Types of faults

Strike-Slip Faults

1979 Imperial Valley, California (M=6.5) Photo by D. Cavit, USGS

Complicated Slip Distributions March 28, 2005 Sumatra Earthquake

Haskell, 1964 Sumatra Ishii et al., Nature 2005 doi: /nature03675 Rupture Sumatra earthquake, Dec 28, 2004

Bormann New Manual of Seismological Observatory Practice. 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.

Seismic Moment =  Rigidity)(Area)(Slip) Area (A) Slip (S) 15 km 10 0 M4 M5 M6 5 Seismic Moment (M o ) Courtesy of Jim Mori

Seismic moments and fault areas of some famous earthquakes 2004 Sumatra 1100 x dyne-cm Mw 9.3 Courtesy of Jim Mori

d Point source approximation - Equivalent Body Forces Couple (Single Couple) Double Couple Bormann 2002, New Manual of Seismological Observatory Practice

Moment tensor: dipoles and couples USGS 9 components, but symmetric matrix so 6 are independent

Moment Tensor for an Explosion USGS

Double Couple Fault - Slip Moment Tensor for Fault Slip USGS

Magnitude – a measure of how large an Earthquake is. Average: ~1 M8 / year Average: M7 / year Average: M6 Incomplete for 2006

Types of Magnitude NameData usedPeriod range MlLocal magnituderegional S and surface waves0.1-1 sec mb(short period) body wave magnitude teleseismic P waves1-5 sec MsSurface wave magnitude teleseismic surface waves(20 sec) Traditional magnitudes based on amplitudes of recorded data. Based on velocity therefore proportional to energy Distance correction Regional correction for source directionality Optional station correction M = log(A d /T) max + σ(Δ,h) + Cr + Cs

Local magnitude - Ml Charles Richter USGS, NEIC Bruce Bolt. Earthquakes. WH Freeman and Company Ml = log A max – log A 0 Defined using horizontal, short period seismometer. Therefore no period consideration. Log A 0 correction taken from published tables and related to distance (< 600km) The ~1 sec period response of the seismometer is similar to many small buildings, therefore still useful for engineers.

Surface wave magnitude - Ms  First defined by Gutenberg  IASPEI Standard: Distances 2 degrees < Δ < 160 degrees. Depth h < 50 km. Any surface wave period measured on horizontal and vertical components  NEIC: Limit periods to 18 < T < 22 sec and only use vertical component. Distances from 20 degrees < Δ < 160 degrees Ms = log (A/T) max + σ S (Δ) = log (A/T) max log Δ + 3.3

Body wave magnitude - mb  Calculated from P wave displacement amplitude. Commonly reported but very variable calculation methods:  Fairly standard features of measurement: distance 20 deg < Δ < 100 deg, period T < 3 sec. mb = log (A/T) max + Q(Δ,h) Distance correction from Gutenberg 1945  IASPEI Standard: measure A max 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.

Saturation  Ml, Ms and mb all suffer from saturation.  Occurs for 2 reasons: Kanamori 1983 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)

Types of Magnitude NameData usedPeriod range MlLocal magnituderegional S and surface waves0.1-1 sec mb(short period) body wave magnitude teleseismic P waves1-5 sec MsSurface wave magnitude teleseismic surface waves20 sec MwMoment Magnitudeteleseismic surface waves> 200 sec MeEnergy magnitudeteleseismic P and S waves sec Do not saturate and physically meaningful. But more complicated to calculate

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. Stein and Wysession, “An Introduction to seismology, earthquakes and Earth structure”  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.

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.

These two earthquakes in Chile had the same M w but different M e Earthquake 1: 6 July S 71. W Me 6.1, Mw 6.9 No fatalities, no houses destroyed. Earthquake 2: 15 October S 71.2 W Me 7.6 Mw people killed, more than 300 people injured. 5,000 houses destroyed. Landslides and rockslides in the epicentral region. Courtesy of George Choy

Types of Magnitude NameData usedPeriod range MlLocal magnituderegional S and surface waves0.1-1 sec mb(short period) body wave magnitude teleseismic P waves1-5 sec MsSurface wave magnitude teleseismic surface waves20 sec MwMoment Magnitudeteleseismic surface waves> 200 sec MeEnergy magnitudeteleseismic P and S waves sec MwpP-wave moment magnitude teleseismic P waves10-60 sec mBbroadband body wave magnitude teleseismic P waves sec MmMantle magnitudeteleseismic surface waves> 200 sec MjJMA magnituderegional S and surface waves5-10 sec

Mwp ∫ u z (t)dt ∝ M o M o = Max | ∫ u z (t)dt| 4  3 r/F p M w = (logM o /1.5) – ・ Quick magnitude from P wave ・ Uses relatively long-period body waves (10-60 sec) ・ Some problems for M>8.0 Courtesy Jim Mori

M m = log 10 (X(  )) + Cd + Cs – 3.9 Distance Correction Source Correction Spectral Amplitude ・ amplitude measured in frequency domain ・ surface waves with periods > 200 sec Mantle Magnitude - Mm Courtesy of Jim Mori

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 ScaleMagDatatime to announce number of stations mb7.01 sec P wave131 stations Mwp8.0 / sec P waves 11 minutes / 1 hour Ms sec surface waves 118 stations Mw sec surface waves 5 hours Mw sec free oscillations days Magnitudes for the Sumatra Earthquake