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Theoretical Seismology 1: Sources. Thailand Training Program in Seismology and Tsunami Warnings, May 2006. 1960’s: WWSSN (World-wide Standardized Network; 100 stations) CHG 1970’s: SRO (Seismic Research Observatory; 1 st global digital network) CHTO

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Theoretical Seismology 1: Sources

Thailand Training Program in Seismology and Tsunami Warnings, May 2006

brief history of global seismology in thailand
1960’s: WWSSN (World-wide Standardized Network; 100 stations)


1970’s: SRO (Seismic Research Observatory; 1st global digital network)


1990’S: GDSN (Global Digital Seismograph Network)

2000’s: Disaster Warning Center

Brief History of Global Seismology in Thailand

What is the cause of

earth movement?

  • Some earth movements are associated with magma
  • Or with mine bursts and explosions
  • Most shaking is caused by failure of rocks in the earth

Theoretical Seismology 1: Sources

  • ・ Describe Earth Rupture
  • Elastic Rebound
  • Fault Geometry
      • Double-couple Force
      • Seismic Moment Tensor
  • ・ Models of Earthquake Rupture
    • Rectangular rupture
    • Circular rupture
    • Distributed slip models
  • ・ Earthquake Size
  • Magnitudes
  • Seismic Moment
  • Energy

San Francisco Earthquake

April 18, 1906

Mw 7.7-7.9

470 km rupture of

San Andreas fault


8.5 feet offset in San Andreas fault

from 1906 earthquake. Mirin County

Elastic Rebound Theory

Reid (1910)

(Data in 1851-65, 1874-92, 1906)


elastic rebound loading or deformation cycle
Four phases





Elastic Rebound: Loading or deformation cycle

Breaking of Brittle Rock

  • Build-up of stress (strain energy)
  • Rupture at weakest point
  • Break along a plane of weakness
  • Radiation of seismic waves

(In contrast to ductile rock, which fails by creep.)

types of faults
Types of faults



Dip Slip

Thrust (Reverse) fault

Strike, dip, slip

Oblique-slip fault


Strike-Slip Faults




Equivalent Body Forces

Single Force



(Single Couple)

Double Couple

single force earthquakes volcanic eruptions and landslides
Single-force earthquakesvolcanic eruptions and landslides

Mount St. Helens, USA

Kanamori et al. 1984


Equivalent Body Forces

Single Force



(Single Couple)

Double Couple


P-wave first motions

Auxiliary plane

Fault plane

This type of faulting is more likely to produce large tsunamis


Controversy settled

by Maruyama (1963)

Showed that Double

Couple was equivalent

to fault slip

Single Couple versus Double Couple

Single Couple

Double Couple

  • ・ P polarity pattern same
  • ・ S polarity pattern different
  • ・ Single Couple ‘resembles’ fault slip
moment tensor dipoles and couples
Moment tensor: dipoles and couples

u(t)i = S Gij(t) mj

9 components

Symmetric matrix so 6 independent

(LW p.343; AR p.50)


Moment Tensor for Fault Slip


Double Couple

Fault - Slip


NEIC fault plane and moment tensor solutions

  • 05 05 18.4 0.587 N 98.459 E 34 G 6.4 6.8 A 1.0 20 695 NIAS REGION, INDONESIA. MW 6.7 (GS), 6.7 (HRV). ME 6.6 (GS). Felt (V) at Padang and Sibolga; (III) at Palembang and Pekanbaru, Sumatra. Felt (III) in Malaysia. Felt on Nias and in Singapore.
    • Broadband Source Parameters (GS): Dep 34 km; Fault plane solution: NP1: Strike=155, Dip=75, Slip=90; NP2: Strike=335, Dip=15, Slip=90; Rupture duration 7.0 sec; Radiated energy 1.6*10**14 Nm. Complex earthquake. A small event is followed by a larger event about 2 seconds later. Depth based on larger event.
    • Moment Tensor (GS): Dep 38 km; Principal axes (scale 10**19 Nm): (T) Val=1.57, Plg=65, Azm=39; (N) Val=-0.02, Plg=14, Azm=162; (P) Val=-1.55, Plg=20, Azm=257; Best double couple: Mo=1.6*10**19 Nm; NP1: Strike=10, Dip=28, Slip=121; NP2: Strike=156, Dip=66, Slip=74.
    • Centroid, Moment Tensor (HRV): Centroid origin time 05:05:24.6; Lat 0.42 N; Lon 98.24 E; Dep 39.0 km Bdy; Half-duration 5.6 sec; Principal axes (scale 10**19 Nm): (T) Val=1.49, Plg=66, Azm=61; (N) Val=0.06, Plg=1, Azm=329; (P) Val=-1.55, Plg=24, Azm=238; Best double couple: Mo=1.5*10**19 Nm; NP1: Strike=326, Dip=22, Slip=88; NP2: Strike=149, Dip=69, Slip=91. Scalar Moment (PPT): Mo=1.3*10**19 Nm.

Haskell Line Source

Haskell, 1964


Fault length L

Fault width W

Rupture velocity v

Permanent slip D

Rise time T


Haskell Line Source

Dislocation Source

Haskell, 1964


Sumatra earthquake Ishii et al., 2005


Complicated Slip Distributions


1999 Chi-Chi, Taiwan Earthquake

what is magnitude why do we need it
Magnitude is a number that represents earthquake size no matter where you are located.

It should be related to released seismic energy.

It should handle the smallest earthquake to the largest earthquake.

What is magnitude? Why do we need it?

January 26, 2001 Gujarat, India Earthquake (Mw7.7)

Body waves


Rayleigh Waves




Love Waves

Recorded in Japan at a distance of 57o (6300 km)


Earthquake Size – Magnitude

Charles Richter


log of amplitude

Distance correction

M = log A – log A0

Richter, 1958


Types of Magnitude Scales

Period Range

ML Local magnitude (California) regional S and 0.1-1 sec

surface waves

Mj JMA (Japan Meteorol. Agency) regional S and 5-10 sec

surface waves

mb Body wave magnitude short-period P waves ~ 1 sec

Ms Surface wave magnitude long-period surface ~ 20 sec


Mw Moment magnitude very long-period > 145 sec

surface waves

Me Energy magnitude broadband P waves 0.5-20 sec

Mwp P-wave moment magnitude long-period P waves 10-60 sec

Mm Mantle magnitude very-long period > 200 sec

surface waves

why are there different magnitudes
Distance range

ML(local, Wood Anderson, 0.8 s)

Teleseisms (recorded at long distances)

mB (uses Amax /T, but in practice T is short-period)

MS (uses Amax /T, but in practice T is long-period)


MS not useful

mb still works, as well as Me and Mw

Physical significance

More recent magnitudes (Mw and Me) are related to different aspects of earthquake size.

Why are there different magnitudes?
what are the limits of historic magnitudes m l m b and m s
Quick and simple measurements

Usually from band-limited data.

single frequency may not all frequencies


single measurement may not represent large rupture

ML and mb ~ 6.5 MS ~ 8.5

Empirical formulas

Physical significance not certain

e.g., from Gutenberg-Richter,

log ES = 11.8 + 1.5 MS

What are the limits of historic magnitudes(ML ,mb, and Ms)?

More Recent Magnitude Scales

Mw Moment magnitude very long-period surface waves

> 145 sec

Me Energy magnitude broadband P waves ~ 0.5-20 sec

Mwp P-wave moment magnitude long-period P waves 10-60 sec

Mm Mantle magnitude very-long period surface waves

> 200 sec


MW is derived from - Seismic Moment

Mw = 2/3 log M0 - 6.0

Area (A)

Slip (S)

Seismic Moment = (Rigidity)(Area)(Slip)


2004 Sumatra

400 x 1027 dyne-cm

Mw 9.3

Seismic moments and fault areas

of some famous earthquakes


Mw is derived from moment, which is sensitive to displacement

Me is computed from energy, which is sensitive to velocity

Mw compared to Me

Different magnitudes are required to describe moment and energy

because they describe different characteristics of the earthquake.


Earthquakes with the same Mw can have different macroseismic effects.

For the Central Chile earthquakes:

Earthquake 1: 6 July 1997 30.0 S 71. W Me 6.1, Mw 6.9

Felt (III) at Coquimbo, La Serena, Ovalle and Vicuna.

Earthquake 2: 15 October 1997 30.9 S 71.2 W Me 7.6 Mw 7.1

Five people killed at Pueblo Nuevo, one person killed at Coquimbo, one person killed at La Chimba and another died of a heart attack at Punitaqui. More than 300 people injured, 5,000 houses destroyed, 5,700 houses severely damaged, another 10,000 houses slightly damaged, numerous power and telephone outages, landslides and rockslides in the epicentral region. Some damage (VII) at La Serena and (VI) at Ovalle. Felt (VI) at Alto del Carmen and Illapel; (V) at Copiapo, Huasco, San Antonio, Santiago and Vallenar; (IV) at Caldera, Chanaral, Rancagua and Tierra Amarilla; (III) at Talca; (II) at Concepcion and Taltal. Felt as far south as Valdivia. Felt (V) in Mendoza and San Juan Provinces, Argentina. Felt in Buenos Aires, Catamarca, Cordoba, Distrito Federal and La Rioja Provinces, Argentina. Also felt in parts of Bolivia and Peru.


Mm Mantle Magnitude

Source Correction

Mm = log10(X(w)) + Cd + Cs – 3.9

Distance Correction

Spectral Amplitude

・ amplitude measured in frequency domain

・ surface waves with periods > 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 fromP 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


Mwp P-wave moment magnitude

∫uz(t)dt ∝ Mo

・ Quick magnitude from P wave

・ Uses relatively long-period body waves (10-60 sec)

・ Some problems for M>8.0


Magnitudes for the Sumatra Earthquake

mb 7.0 1 sec P wave 131 stations

Mwp 8.0 – 8.5 60 sec P waves

Me 8.5 broadband P waves

Ms 8.5 - 8.8 20 sec surface waves 118 stations

Mw 8.9 - 9.0 300 sec surface waves

Mw 9.1 - 9.3 3000 sec free oscillations


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 earthquake can be described by

different magnitudes, by moment, and by energy.

5. Quick determination of magnitude is needed for

tsunami warning systems.


15 km







M4 M5 M6

Seismicity in NEIC catalog 1990 - 2005


Log E = 1.5Ms + 4,8

Log E = 1.5 Me + 4.4