Thailand Training Program in Seismology and Tsunami Warnings, May 2006

Theoretical Seismology 1: Sources

Brief History of Global Seismology in Thailand

• 1960’s: WWSSN (World-wide Standardized Network; 100 stations)– CHG

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

• 1990’S: GDSN (Global Digital Seismograph Network)

• 2000’s: Disaster Warning Center

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

・ Describe Earth Rupture Elastic Rebound Fault Geometry

Double-couple Force Seismic Moment Tensor

・ Models of Earthquake RuptureRectangular ruptureCircular rupture Distributed slip models

・ Earthquake Size Magnitudes Seismic Moment Energy

Theoretical Seismology 1: Sources

Concepts and Terminology

San Francisco EarthquakeApril 18, 1906

Mw 7.7-7.9470 km rupture of San Andreas fault

Elastic Rebound Theory Reid (1910)

(Data in 1851-65, 1874-92, 1906)8.5 feet offset in San Andreas fault

from 1906 earthquake. Mirin County Asperity

Elastic Rebound: Loading or deformation cycle

– Four phases• Interseismic• Preseismic• Coseismic• Postseismic

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

Breaking of Brittle Rock

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

What does a critical amount of applied stressdo to a rock?

What does a critical amount of applied stressdo to a rock?

max

min

int

Types of faults

Thrust (Reverse) fault

Normalfault

Oblique-slip fault

Dip Slip

Strike, dip, slip

Strike-Slip Faults

Left-lateral Right-lateral

Equivalent Body Forces

Single Force

Dipole

Couple(Single Couple)

Double Couple

Single-force earthquakes volcanic eruptions and landslides

Mount St. Helens, USA Kanamori et al. 1984

Equivalent Body Forces

Single Force

Dipole

Couple(Single Couple)

Double Couple

1940 Imperial Valley, California (Ms 7.1)

ー＋

＋ー

P-wave first motions

This type of faulting is more likely to produce large tsunamis

Fault plane

Aux

iliar

y pl

ane

Single Couple

Double Couple

Single Couple versus Double Couple

・ P polarity pattern same

・ S polarity pattern different

・ Single Couple ‘resembles’ fault slip

Controversy settled by Maruyama (1963)

Showed that DoubleCouple was equivalentto fault slip

Moment tensor: dipoles and couples

(LW p.343; AR p.50)

9 componentsSymmetric matrix so 6 independent

u(t)i = Gij(t) mj

0322331132112 MMMMMM

　

332211 MMM

Moment Tensor for an Explosion

2112 MM

031132323332211 MMMMMMM

⇒

Double Couple Fault - Slip

Moment Tensor for Fault Slip

North

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.

NEIC fault plane and moment tensor solutions

Kinematics

Haskell Line Source

Haskell, 1964

Specifies Fault length LFault width WRupture velocity vPermanent slip DRise time T

Circular Crack – Sato and Hirasawa, 1973

Haskell Line Source

Haskell, 1964sumatra

Sumatra earthquake 　　　 Ishii et al., 2005

Dislocation Source

　　

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.

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

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

Love Waves

vertical

radial

transverse

Rayleigh Waves

Body waves

P PP S SS

Earthquake Size – Magnitude

M = log A – log A0Richter, 1958

Charles Richter1900-1985

log of amplitudeDistance correction

ML Local magnitude (California) regional S and 0.1-1 sec surface wavesMj JMA (Japan Meteorol. Agency) regional S and 5-10 sec surface wavesmb Body wave magnitude short-period P waves ~ 1 sec

Ms Surface wave magnitude long-period surface ~ 20 sec wavesMw Moment magnitude very long-period > 145 sec

surface wavesMe 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

Types of Magnitude ScalesPeriod Range

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)

• Depth– 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.

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

• Quick and simple measurements• Usually from band-limited data.

– single frequency may not all frequencies• Saturation

– 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

Mw Moment magnitude very long-period surface waves

> 145 secMe 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

More Recent Magnitude Scales

Seismic Moment = Rigidity)(Area)(Slip)

MW is derived from - Seismic MomentMw = 2/3 log M0 - 6.0

Area (A)

Slip (S) 　

)()(0 tuStM

Seismic moments and fault areasof some famous earthquakes

2004 Sumatra400 x 1027 dyne-cm

Mw 9.3

 

ogP

dtdu ut 222

0

1)(

uF

RccM osooo

2/52/1)(4

Mw is derived from moment, which is sensitive to displacement

Me is computed from energy, which is sensitive to velocity

Different magnitudes are required to describe moment and energybecause they describe different characteristics of the earthquake.

Mw compared to Me

These two earthquakes in Chile had the same Mw but different Me

 

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

Mm = log10(X()) + Cd + Cs – 3.9

Distance Correction

Source 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 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 　　　　

Mwp P-wave moment magnitude

・ Quick magnitude from P wave・ Uses relatively long-period body waves (10-60 sec)・ Some problems for M>8.0 　

∫uz(t)dt Mo∝

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.

Relationship between different types of magnitudes

Seismicity in NEIC catalog 1990 - 2005

M4

M5

M6

15 km

10

0

M4 M5 M6

5

Log E = 1.5Ms + 4,8

Log E = 1.5 Me + 4.4