# Presentation: 598484

##  Theoretical Seismology 1: Sources

-      Elastic Rebound
-      Fault Slip  Double-couple Force
- ・ Seismic Moment Tensor
- ・ Models of Earthquake Faults
- ・ Earthquake Size
-       Magnitudes
-       Seismic Moment
-       Energy

-  Theoretical Seismology 1: Sources

## What is an Earthquake ?

-     Fault mechanisms
-      The Shaking
-          Wave propagation
-           Structures

## Giuseppe Mercalli

- <date/time>

- (1850-1914)

- John Milne
- (1850-1913)

- Chang Heng ‘Seismometer’ AD132

- 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

- ・ 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)

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

- 8.5 feet offset in San Andreas fault
- from 1906 earthquake. Mirin County

## San Francisco Earthquake

- April 18, 1906
- Mw 7.7-7.9
- 470 km rupture of
- San Andreas fault

## Slide 8

## 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
- ・ Single Couple ‘resembles’ fault slip

## Moment tensor: dipoles and couples

- (LW p.343; AR p.50)

- 9 components
- Symmetric matrix so 6 independent

## Moment Tensor for an Explosion

## ⇒

- Double Couple
-     Fault - Slip

- Moment Tensor for Fault Slip

- North

## Types of faults

- Thrust (Reverse) fault

- Normal
- fault

- Strike-slip fault

## Strike-Slip Faults  

- Strike-Slip Faults

- Left-lateral

- Right-lateral

## 1940 Imperial Valley, California (Ms 7.1)

- <date/time>

## 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

## Haskell Line Source

- Dislocation Source

- Haskell, 1964

- sumatra

- Sumatra earthquake            Ishii et al., 2005

## Complicated Slip Distributions

-      -

- 1999 Chi-Chi, Taiwan Earthquake

## Earthquake Size – Magnitude

- M = log A – log A0

- Richter, 1958

- Charles Richter
- 1900-1985

- log of amplitude

- Distance correction

## Types of Magnitude Scales

-                                                          surface waves
- Mj       JMA (Japan Meteorol. Agency)    regional S and           5-10 sec
-                                                           surface waves
- mb    Body wave magnitude    	         teleseismic P waves    1-5 sec
- Ms     Surface wave magnitude 	         teleseismic surface      20 sec
-                                                             waves
- Mw       Moment magnitude                   teleseismic surface     > 200 sec
-                                                              waves
- Mwp     P-wave moment magnitude        teleseismic P waves    10-60 sec
- Mm      Mantle magnitude                      teleseismic surface     > 200 sec
-                                                                                               waves

- Period Range

## Relationship between different types of magnitudes

## Seismicity in NEIC catalog 1990 - 2005

- M4

- M5

- M6

- 15 km

- 10

- 0

- M4    M5     M6

- 5

## Fault areas of some 

- famous earthquakes

## Earthquake size - Seismic Moment

- Area (A)

- Slip (S)

## Seismic moments and fault areas

- of some famous earthquakes

## Types of Magnitude Scales

-                                                          surface waves
- Mj       JMA (Japan Meteorol. Agency)    regional S and           5-10 sec
-                                                           surface waves
- mb    Body wave magnitude    	         teleseismic P waves    1-5 sec
- Ms     Surface wave magnitude 	         teleseismic surface      20 sec
-                                                             waves
- Mw       Moment magnitude                    teleseismic surface     > 200 sec
-                                                              waves
- Mwp     P-wave moment magnitude         teleseismic P waves    10-60 sec
- Mm      Mantle magnitude                       teleseismic surface     > 200 sec
-                                                                                               waves

- Period Range

## Types of Magnitude Scales

-                                                          surface waves
- Mj       JMA (Japan Meteorol. Agency)    regional S and           5-10 sec
-                                                           surface waves
- mb    Body wave magnitude    	         teleseismic P waves    1-5 sec
- Ms     Surface wave magnitude 	         teleseismic surface      20 sec
-                                                             waves
- Mw       Moment magnitude                    teleseismic surface     > 200 sec
-                                                              waves
- Mwp     P-wave moment magnitude         teleseismic P waves    10-60 sec
- Mm      Mantle magnitude                       teleseismic surface     > 200 sec
-                                                                                               waves

- Period Range

## 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 

- Mm = log10(X()) + Cd + Cs – 3.9

- Distance Correction

- Source Correction

- Spectral Amplitude

- ・ amplitude measured in frequency domain
- ・ surface waves with periods > 200 sec

## ∫uz(t)dt  ∝ Mo

- ∫uz(t)dt  ∝ Mo

## Mo = Max |∫uz(t)dt| 43r/Fp

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

- Mo = Max |∫uz(t)dt| 43r/Fp
- Mw = (log10Mo – 9.1)/1.5

## Magnitudes for the Sumatra Earthquake

- mb	7.0               1 sec P wave                  131 stations
- mblg  	6.7               1 sec Lg waves                   6 stations
- Mwp   	8.0 – 8.5        60 sec 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

## Fault Areas of 

- 1944 Tonankai
- Mw 8.1

- 1946 Nankai
-  Mw 8.1

- 1995 Kobe
- Mw 6.9

- Fault Areas of
- Damaging Earthquakes

-        Deaths
- 1944     1223
- 1946     1330
- 1995     6310

## Seismic Radiated Energy  

- Seismic Radiated Energy

- 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