U.S. Department of the InteriorU.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, 2005. 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

Normalfault

Strike-slip faultImages 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, 1964Sumatra

　　 Ishii et al., Nature 2005 doi:10.1038/nature03675

Rupture

Sumatra earthquake, Dec 28, 2004 　

Bormann 2002. 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) 　

)()(0 tuStM

15 km

10

0

M4 M5 M6

5

Seismic Moment (Mo)

Courtesy of Jim Mori

Seismic moments and fault areasof some famous earthquakes

2004 Sumatra1100 x 1027 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

( ) ( , ) ( )pq q p

V

M t f t dV η η

USGS

9 components, but symmetric matrix so 6 are independent

0322331132112 MMMMMM

　

332211 MMM

Moment Tensor for an Explosion

USGS

2112 MM

031132323332211 MMMMMMM

Double Couple Fault - Slip

Moment Tensor for Fault Slip

USGS

Magnitude – a measure of how large an Earthquake is.

Average: ~1 M8 / yearAverage: 13-15 M7 / yearAverage: 130-150 M6

Incomplete for 2006

Types of MagnitudeName 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.

Based on velocity therefore proportional to energy

Distance correction

Regional correction for source directionality

Optional station correction

M = log(Ad/T)max + σ(Δ,h) + Cr + Cs

Local magnitude - MlCharles Richter

1900-1985

USGS, NEIC

Bruce Bolt. Earthquakes. WH Freeman and Company

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 (< 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 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

Ms = log (A/T)max + σS(Δ) = log (A/T)max + 1.66 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 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:

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 MagnitudeName 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 > 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.

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 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

Types of MagnitudeName 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 > 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 > 200 sec

Mj JMA magnitude regional S and surface waves 5-10 sec

Mwp

∫uz(t)dt ∝ Mo

Mo = Max |∫uz(t)dt| 43r/Fp

Mw = (logMo/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

Mm = log10(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

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 wave

s or Mw from long period surface wave. 　　 For quick magnitude (seconds to minutes), determine

Mwp from P waves 　　　

Courtesy of Jim Mori

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

Magnitudes for the Sumatra Earthquake