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Earthquake Sources and Magnitude Annabel Kelly USGS Menlo Park, CA U. S. Department of the Interior U. S. Geological Survey
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
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 M 2. 4 earthquake
Tectonic earthquakes Elastic Rebound Theory Reid (1910) 8. 5 feet offset in San Andreas fault from 1906 earthquake. Marin County
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
Types of faults Normal fault Thrust (Reverse) fault Strike-slip fault Images courtesy of IRIS
1979 Imperial Valley, California (M=6. 5) Photo by D. Cavit, USGS
Complicated Slip Distributions March 28, 2005 Sumatra Earthquake
Rupture Sumatra earthquake, Dec 28, 2004 Haskell, 1964 Sumatra Ishii et al. , Nature 2005 doi: 10. 1038/nature 03675
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.
Seismic Moment (Mo) 15 km Area (A) 10 Slip (S) 5 Seismic Moment = (Rigidity)(Area)(Slip) 0 M 4 Courtesy of Jim Mori M 5 M 6
Seismic moments and fault areas of some famous earthquakes 2004 Sumatra 1100 x 1027 dyne-cm Mw 9. 3 Courtesy of Jim Mori
Point source approximation Equivalent Body Forces d Couple (Single Couple) Double Couple Bormann 2002, New Manual of Seismological Observatory Practice
Moment tensor: dipoles and couples 9 components, but symmetric matrix so 6 are independent USGS
Moment Tensor for an Explosion USGS
Moment Tensor for Fault Slip Double Couple Fault - Slip USGS
Magnitude – a measure of how large an Incomplete for 2006 Earthquake is. Average: ~1 M 8 / year Average: 13 -15 M 7 / year Average: 130 -150 M 6
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. M = log(Ad/T)max + σ(Δ, h) + Cr + Cs Based on velocity therefore proportional to energy Distance correction Regional correction for source directionality Optional station correction
Local magnitude - Ml Charles Richter 1900 -1985 USGS, NEIC Ml = log Amax – 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 (< 600 km) Bruce Bolt. Earthquakes. WH Freeman and Company The ~1 sec period response of the seismometer is similar to many small buildings, therefore still useful for engineers.
Surface wave magnitude - Ms Ms = log (A/T)max + σS(Δ) = log (A/T)max + 1. 66 log Δ + 3. 3 § § § First defined by Gutenberg 1945. 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
Body wave magnitude - mb Distance correction from Gutenberg 1945 mb = log (A/T)max + Q(Δ, h) § § § 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. 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.
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
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 teleseismic surface waves 20 sec Mw Surface wave magnitude Moment Magnitude teleseismic surface waves > 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
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”
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 Mw but different Me Earthquake 1: 6 July 1997 30. 0 S 71. W Me 6. 1, Mw 6. 9 No fatalities, no houses destroyed. Earthquake 2: 15 October 1997 30. 9 S 71. 2 W Me 7. 6 Mw 7. 1 7 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 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 teleseismic surface waves 20 sec Mw Surface wave magnitude Moment Magnitude teleseismic surface waves > 200 sec Me Energy magnitude teleseismic P and S waves 0. 2 -100 sec teleseismic P waves 10 -60 sec m. B broadband body wave teleseismic P waves magnitude 0. 5 -12 sec Mm Mantle magnitude teleseismic surface waves > 200 sec Mj JMA magnitude regional S and surface waves 5 -10 sec Mwp P-wave moment magnitude
Mwp ∫uz(t)dt ∝ Mo Mo = Max |∫uz(t)dt| 4 pra 3 r/Fp Mw = (log. Mo/1. 5) – 10. 73 ・ Quick magnitude from P wave ・ Uses relatively long-period body waves (10 -60 sec) ・ Some problems for M>8. 0 Courtesy Jim Mori
Mantle Magnitude - Mm Source Correction Mm = log 10(X(w)) + Cd + Cs – 3. 9 Distance Correction Spectral Amplitude ・ amplitude measured in frequency domain ・ surface waves with periods > 200 sec 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
Magnitudes for the Sumatra Earthquake Scale Mag Data time to announce mb 7. 0 1 sec P wave Mwp 8. 0 / 8. 5 60 sec P waves Ms 8. 0 -8. 8 20 sec surface waves Mw 8. 9 -9. 0 300 sec 5 hours surface waves Mw 9. 1 -9. 3 3000 sec free oscillations number of stations 131 stations 11 minutes / 1 hour 118 stations days Courtesy of Jim Mori