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; 1 st 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 Rupture Rectangular rupture Circular rupture Distributed slip models ・ Earthquake Size Magnitudes Seismic Moment Energy Theoretical Seismology 1: Sources

Concepts and Terminology

San Francisco Earthquake April 18, 1906 Mw km rupture of San Andreas fault

Elastic Rebound Theory Reid (1910) (Data in , , 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 stress do to a rock?

What does a critical amount of applied stress do to a rock? s max s min s int

Types of faults Thrust (Reverse) fault Normal fault Oblique-slip fault Dip Slip Strike, dip, slip

Strike-Slip Faults Left-lateralRight-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 Auxiliary plane

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 Double Couple was equivalent to fault slip

Moment tensor: dipoles and couples (LW p.343; AR p.50) 9 components Symmetric matrix so 6 independent u(t) i = S G ij (t) m j

Moment Tensor for an Explosion

⇒ Double Couple Fault - Slip Moment Tensor for Fault Slip North

N E 34 G A 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 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 L Fault width W Rupture velocity v Permanent slip D Rise time T

Circular Crack – Sato and Hirasawa, 1973

Haskell Line Source Haskell, 1964 sumatra Sumatra earthquake Ishii et al., 2005 Dislocation Source

Complicated Slip Distributions 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 57 o (6300 km) Love Waves vertical radial transverse Rayleigh Waves Body waves P PP S SS

Earthquake Size – Magnitude M = log A – log A 0 Richter, 1958 Charles Richter log of amplitude Distance correction

M L Local magnitude (California) regional S and sec surface waves M j JMA (Japan Meteorol. Agency) regional S and 5-10 sec surface waves m b Body wave magnitude short-period P waves ~ 1 sec M s Surface wave magnitude long-period surface ~ 20 sec waves M w Moment magnitude very long-period > 145 sec surface waves M e Energy magnitude broadband P waves sec M wp P-wave moment magnitude long-period P waves sec M m Mantle magnitude very-long period > 200 sec surface waves Types of Magnitude Scales Period Range

Why are there different magnitudes? Distance range –M L (local, Wood Anderson, 0.8 s) Teleseisms (recorded at long distances) –m B (uses A max /T, but in practice T is short-period) –M S (uses A max /T, but in practice T is long-period) Depth –M S not useful –m b still works, as well as M e and M w Physical significance –More recent magnitudes (M w and M e ) are related to different aspects of earthquake size.

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 Saturation –single measurement may not represent large rupture –M L and m b ~ 6.5 M S ~ 8.5 Empirical formulas –Physical significance not certain e.g., from Gutenberg-Richter, log E S = M S

M w Moment magnitude very long-period surface waves > 145 sec M e Energy magnitude broadband P waves ~ sec M wp P-wave moment magnitude long-period P waves sec M m Mantle magnitude very-long period surface waves > 200 sec More Recent Magnitude Scales

Seismic Moment =  Rigidity)(Area)(Slip) M W is derived from - Seismic Moment M w = 2/3 log M Area (A) Slip (S)

Seismic moments and fault areas of some famous earthquakes 2004 Sumatra 400 x dyne-cm Mw 9.3

M w is derived from moment, which is sensitive to displacement M e is computed from energy, which is sensitive to velocity Different magnitudes are required to describe moment and energy because they describe different characteristics of the earthquake. M w compared to M e

These two earthquakes in Chile had the same M w but different M e

Earthquakes with the same M w can have different macroseismic effects. For the Central Chile earthquakes: Earthquake 1: 6 July S 71. W Me 6.1, Mw 6.9 Felt (III) at Coquimbo, La Serena, Ovalle and Vicuna. Earthquake 2: 15 October 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.

M m Mantle Magnitude M m = log 10 (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 M m from mantle waves ⇒ For quick magnitude (seconds to minutes), determine M wp from P waves

M wp 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 m b sec P wave 131 stations M wp 8.0 – sec P waves M e 8.5 broadband P waves M s sec surface waves 118 stations M w sec surface waves M w 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 M4 M5 M6 15 km 10 0 M4 M5 M6 5

Log E = 1.5Ms + 4,8 Log E = 1.5 Me + 4.4