# Presentation: 470911

##  Theoretical Seismology 1: Sources

** ****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

**Notes:**
Japanese legend – A giant catfish causes earthquakes and tsunamis by flicking his tail

##  Theoretical Seismology 1: Sources

-      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

**Notes:**
The most important thing to get from this lecture is the basic ideas and the terminology

## San Francisco Earthquake

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

**Notes:**
The State of California commissioned a report on the earthquake. Reid was one of the people involved in this report

## Elastic Rebound Theory

-   Reid (1910)

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

- Asperity

**Notes:**

Asperity = the locking of a fault due to its roughness

## Elastic Rebound:  Loading or deformation cycle

- Four phases
- Interseismic
- Preseismic
- Coseismic
- Postseismic

**Notes:**
Interseismic = time between an earthquake
Preseismic = short period before an earthquake where deformation is seen
Coseismic = during the slip on the fault
Postseismic = deformation for a period after the earthquake

## Slide 9

## Breaking of Brittle Rock

- Rupture at weakest point
- Break along a plane of weakness
- Radiation of seismic waves

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

## What does a critical amount of applied stress

- do to a rock?

**Notes:**
The failure plane is at an angle. With shear force along the plane.

The compression can be resolved into 2 double couple forces – hence the auxiliary plane

## max

- What does a critical amount of applied stress
- do to a rock?

- max
- min
- int

## Types of faults

- Thrust (Reverse) fault

- Normal
- fault

- Oblique-slip fault

- Dip Slip

- Strike, dip, slip

**Notes:**
Strike = direction of the fault compared to north
Dip = the angle of the fault from horizontal
Slip = the direction of movement on the fault during the earthquake

## Strike-Slip Faults  

- Strike-Slip Faults

- Left-lateral

- Right-lateral

## Equivalent Body Forces

- Single Force

- Dipole

- Couple
- (Single Couple)

- Double Couple

**Notes:**
Earthquakes are generally double couple (volcanic related EQ are not necessarily 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

**Notes:**
It tock a while for seismologist to confirm that faulting is double couple. The confirmation came from polarity of S-waves 

## 1940 Imperial Valley, California (Ms 7.1)

## P-wave first motions

- This type of faulting is more likely to produce large tsunamis

- Fault plane

- Auxiliary plane

**Notes:**
P-wave polarity gives the fault plane solution.

The top is the fault plane solution for a strike-slip earthquake. The lower a thrust with some strike-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

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

- 9 components
- Symmetric matrix so 6 independent

- u(t)i = Gij(t) mj

**Notes:**
The more general representation is the moment tensor. The diagonal element give the dipole forces, the off-diagonal elements the various possible single couples.

The moment tensor can represent any mechanism – useful for the complex reality of the earth 

## Moment Tensor for an Explosion

**Notes:**
Explosion has the same magnitude for each of the dipoles 

## ⇒

- Double Couple
-     Fault - Slip

- Moment Tensor for Fault Slip

- North

## NEIC fault plane and moment tensor solutions 

**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

**Notes:**
kinematics tries to relate the seismogram to the slip on the fault

## Haskell Line Source

- Haskell, 1964
- Specifies
- Fault length L
- Fault width W
- Rupture velocity v
- Permanent slip D
- Rise time T

**Notes:**
Rise time = time taken for the slip to occur.

## Circular Crack – Sato and Hirasawa, 1973

**Notes:**
Circular rupture – starts a point, but ends abruptly 

## Haskell Line Source

- Haskell, 1964

- sumatra

- Sumatra earthquake            Ishii et al., 2005

- Dislocation Source

## Complicated Slip Distributions

-      -

- 1999 Chi-Chi, Taiwan Earthquake

**Notes:**
Colors indicate the amount of slip

## 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.

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

- 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 A0

- Richter, 1958

- Charles Richter
- 1900-1985

- log of amplitude

- Distance correction

**Notes:**
Richer M was based on California and for the Wood-Anderson seismograph. So it isn’t truly  applicable around the world. Therefore more M scales have been developed.

## Types of Magnitude Scales

-                                                          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
-                                                             waves
- 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

- Period Range

**Notes:**
The type of Magnitude scale is related to the data used to calculate it/

## 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.

**Notes:**
T = period of the wave with the maximum amplitude.

Deep earthquakes don’t produce large surface waves to Ms isn’t always useful. 

Moment (Mw) is related to the size of the fault and Me is related to the energy released by the earthquake. 

## 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

**Notes:**
Saturation – the seismic waves will only sample the portion of the fault of the same scale as their wavelength so short wavelength waves may not record all of the fault motion. 

## More Recent Magnitude Scales

- 					    > 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 is derived from - Seismic Moment
*M**w*  = 2/3 log *M**0*  - 6.0

- Area (A)

- Slip (S)

## Seismic moments and fault areas

- of some famous earthquakes

**Notes:**
Colored blocks represent the size of the fault that sliped

## Mw compared to Me

- Different magnitudes are required to describe moment and energy
- because they describe different characteristics of the earthquake.

- Mw compared to Me

**Notes:**
Although both ES and M0 have the same units of Newton-meters they are physically different measures of the size of an earthquake.  Energy is derived from velocity-squared seismograms in which the peak value is about the corner frequency of an earthquake.  In contrast, moment is derived from the low-frequency asymptote of the displacement spectra.  In fact, the ideal value of moment is proportional to displacement at zero frequency.  Thus, Moment is related to the final static displacement, which is crucial to the long-term tectonic implications of an earthquake.  In contrast, energy is a better measure of seismic potential for damage from shaking
.  
A source parameter that is a good indicator of the relative amount of energy and moment radiated by an earthquake the apparent stress, which takes the ratio of the two quantities. 
a =  ES /M0					

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

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

**Notes:**
4months, less than 1 degree. 
An example here are the paired events that occurred in central Chile.  The first event is a large shallow thrust earthquake (jul 97, Mw 6.9) and the second one is by a large normal earthquake (4 mons later in oct 97, Mw 7.1).  Note that the epicenters are separated by only about 1o.   
A cross-section taken normal to trench axis at the hypocenter of the normal-fault event with a width of about 10o10o is shown here.  What we see is a gently dipping slab, with bends in between which is a flat portion.  We note that the normal-fault event is within the delineated Benioff zone, at a bend in the slab.  The focal mechanism does have a near vertical nodal plane 

In general cold slab is old lithosphere (>30 Ma) descending at moderate to fast rates. 

Cold slab defined by thermal parameter:  age * sinking rate (vertical component of subduction= dip of slab as well as the subduction rate;
35 ma, 27 degree dip and 80 mm/year = 1400).

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

**Earthquakes with the same **** ****M****w ****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.

**Notes:**
This table shows additional source parameters for these earthquakes including  various magnitudes.  Although the MW’s are virtually the same, note the vast discrepancy in macroseismic reports.  While the first earthquake was merely felt, the second earthquake generated massive destruction.  The Me of the intraslab event is 1.5 units larger than the Me of the interface thrust earthquake.   Strongly suggests that in this particular case MW , which is derived from low frequencies, is unable to quantify the macroseismic effects while Me, which is derived from high frequencies, is more effective.

## 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

**Notes:**
Calculated by the double integration of the P wave (integral of displacement) – it isn’t a perfect measure, but it is quick to calculate. It breaks down over M8, but at this magnitude a tsunami warning would be issued, so for tsunami warnings it doesn’t really matter!

## 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.

## Slide 47

## 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 = 1.5Ms + 4,8

- Log E = 1.5 Me + 4.4

**Notes:**
Matlab/bin/energy/plotesms2.m