# Theoretical Seismology 1: Sources What is the Earthquake

Theoretical Seismology 1: Sources What is the Earthquake Source? Elastic Rebound Fault Slip Double-couple Force Seismic Moment Tensor Models of Earthquake Faults Earthquake Size Magnitudes Seismic Moment Energy What is an Earthquake ? The Source

Fault mechanisms The Shaking Wave propagation Structures Chang Heng Seismometer AD132 Giuseppe Mercalli (1850-1914) John Milne (1850-1913) Sassa Seismometer (~1935), Abuyama, Kyoto Univ.

What is the cause of Earthquakes ? Associated with faults (source or cause?) Associated with magma? (Most) Earthquakes are fault movements Breaking of Chopstick

Failure Build-up of stress (strain energy) Difficult to predict time and place Breaks at weakest point Hear precursors Sound of breaking same as seismic waves Elastic Rebound Theory Reid (1910)

8.5 feet offset in San Andreas fault from 1906 earthquake. Marin County (Data in 1851-65, 1874-92, 1906) San Francisco Earthquake April 18, 1906 Mw 7.7-7.9 470 km rupture of San Andreas fault Equivalent Body Forces Single Force

Dipole Couple (Single Couple) Double Couple Single Couple versus Double Couple Single Couple Double Couple P polarity pattern same

S polarity pattern different Controversy settled by Maruyama (1963) Showed that Double Single Couple resembles fault slip Couple was equivalent to fault slip Moment tensor: dipoles and couples M pq (t ) = q f p ( , t )dV ( )

V 9 components Symmetric matrix so 6 independent (LW p.343; AR p.50) Moment Tensor for an Explosion M 11 = M 22 = M 33 M12 = M 21 = M13 = M 31 = M 23 = M 32 =0 Moment Tensor for Fault Slip

North Double Couple Fault - Slip M 12 = M 21 M11 = M 22 = M 33 = M 23 = M 23 = M13 = M 31 =0 Types of faults Normal fault

Thrust (Reverse) fault Strike-slip fault Strike-Slip Faults Left-lateral Right-lateral 1940 Imperial Valley, California (Ms 7.1) P-wave first motions

This type more likely to produce large tsunamis Harvard/NEIC Moment Tensor Solutions Single-force earthquakes volcanic eruptions and landslides

Mount St. Helens, USA Kanamori et al. 1984 Circular Crack Sato and Hirasawa, 1973 Sato and Hirasawa, 1973 Haskell Line Source Dislocation Source Haskell, 1964 Sumatra earthquake sumatra

Ishii et al., 2005 Complicated Slip Distributions - 1999 Chi-Chi, Taiwan Earthquake Earthquake Size Sato and Hirasawa, 1973 Magnitude Charles Richter 1900-1985 log of amplitude Distance correction

M = log A Sato and Hirasawa, 1973 log A0 Richter, 1958 Types of Magnitude Scales Period Range ML Local magnitude (California) regional S and surface waves 0.1-1 sec

Mj JMA (Japan Meteorol. Agency) regional S and surface waves 5-10 sec mb Body wave magnitude teleseismic P waves 1-5 s

Ms Surface wave magnitude teleseismic surface 20 se Mw Mwp waves Moment magnitude

teleseismic surface > 200 sec 200 sec waves P-wave moment magnitude teleseismic P waves 10-60 sec Mm Mantle magnitude teleseismic surface > 200 sec 200 sec Relationship between different types of magnitudes Earthquake size - Seismic Moment

15 km Area (A) 1 0 5 Slip (S) eismic Moment = Rigidity)(Area)(Slip) M 0 (t ) = S u (t ) 0

M4 M5 M6 Seismic moments and fault areas of some famous earthquakes 2004 Sumatra ~1100 x 1027 dyne-cm Mw 9.1-9.3 Types of Magnitude Scales Period Range

ML Local magnitude (California) regional S and surface waves 0.1-1 sec Mj JMA (Japan Meteorol. Agency) regional S and surface waves 5-10 sec

mb Body wave magnitude teleseismic P waves 1-5 s Ms Surface wave magnitude teleseismic surface

20 s Mw Mwp waves Moment magnitude teleseismic surface > 200 sec 200 sec waves P-wave moment magnitude teleseismic P waves 10-60 se Mm Mantle magnitude

teleseismic surface > 200 sec 200 sec Types of Magnitude Scales Period Range ML Local magnitude (California) regional S and surface waves 0.1-1 sec

Mj JMA (Japan Meteorol. Agency) regional S and surface waves 5-10 sec mb Body wave magnitude teleseismic P waves

1-5 s Ms Surface wave magnitude teleseismic surface 20 s Mw Mwp waves

Moment magnitude teleseismic surface > 200 sec 200 sec waves P-wave moment magnitude teleseismic P waves 10-60 se Mm Mantle magnitude teleseismic surface > 200 sec 200 sec 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 Magnitude from P waves (mb) is fast but underestimates moment If have time (hours), determine Mm from mantle waves For quick magnitude (seconds to minutes), determine Mwp from P waves Mm

Mantle Magnitude Source Correction Mm = log10(X()) + Cd + Cs 3.9 Cd + Cd + Cs 3.9 Cs Sato and Hirasawa, 1973 3.9 Distance Correction Spectral Amplitude amplitude measured in frequency domain surface waves with periods > 200 sec 200 sec Mwp P-wave moment magnitude

uz(t)dt Mo Mwp P-wave moment magnitude Mo = Max |uz(t)dt| 43r/Fp Mw = (log10Mo Sato and Hirasawa, 1973 7.1)/1.5 Quick magnitude from P wave Uses relatively long-period body waves (10-60 sec) Some problems for M> 200 sec8.0

Magnitudes for the Sumatra Earthquake mb 7.0 1 sec P wave 131 stations mblg 6.7

1 sec Lg waves Mwp 8.0 Sato and Hirasawa, 1973 8.5 60 sec P waves Ms 8.5 - 8.8 20 sec surface waves

Mw 8.9 - 9.0 300 sec surface waves Mw 9.1 - 9.3 3000 sec free oscillations 6 stations

118 stations Fault Areas of Damaging Earthquakes 1995 Kobe Mw 6.9 Deaths 1944 1946 1995

1944 Tonankai Mw 8.1 1223 1330 5310 1946 Nankai Mw 8.1 Seismic Radiated Energy Radiated Energy = 1.5Mw + Cd + Cs 3.9 11.8 Kanamori, 1977

Things to Remember 1. Earthquake sources are a double couple force system which is equivalent to Fault Slip 2. The moment tensor describes the Force System for earthquakes and can be used to determine the geometry of the faulting 3. Earthquake ruptures begin from a point (hypocenter) and spread out over the fault plane 4. The size of an earthquakes can be described by magnitudes, moment, and energy. Mm and Mwp are types of magnitudes used for tsunami warning systems

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