# Presentation: 598486

## Earthquake Sources and Magnitude

**Annabel Kelly**
**USGS Menlo Park, CA**

## What is an Earthquake ?

- Instrumentally recorded (or felt) ground shaking

**An Earthquake Source :**
- A sudden change in stress in the Earth that generates seismic waves

**Notes:**
We can think of an earthquake as two components, the source and the shaking. 

## Seismic Sources

**Fault movement**
**Volcanic activity (magma movement or eruptions)**
**Ocean storms (microseisms)**
**Cave collapse, rock fall, etc**
**Manmade sources – explosions, vibrators, cultural noise**

- BGS recordings of an explosion at an oil storage depot near London Dec 16, 2005. Equivalent to M2.4 earthquake

**Notes:**
Seismic waves can be generated by many sources, all involve changes in the stress conditions inside the earth. Most recorded earthquakes are generated by movement on a fault.

## Tectonic earthquakes 

- Elastic Rebound Theory
-   Reid (1910)

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

**Tectonic earthquakes **

**Notes:**
The first person to suggest the model that fault movement caused earthquakes, was Henry Reid in 1910 – after studying the famous 1906 San Francisco earthquake. He came up with elastic rebound theory – the idea that strain slowly builds up for many years (may be as much as ~100 or ~200 years for areas with irregular large earthquakes) and then, when the strain is greater than the fault strength it is rapidly released in a few seconds as the fault slips to remove the strain, creating the earthquake.

## Failure
Build-up of stress (strain energy)
Difficult to predict time and place
Breaks at weakest point
Sometimes hear precursors
Sound of breaking same as seismic waves

- Failure
- Build-up of stress (strain energy)
- Difficult to predict time and place
- Breaks at weakest point
- Sometimes hear precursors
- Sound of breaking same as seismic waves

**Notes:**
You can see many of the same stages of the elastic rebound model if you slowly bend and break a chopstick (or other piece of wood).

## Types of faults

- Thrust (Reverse) fault

- Normal
- fault

- Strike-slip fault

- Images courtesy of IRIS

**Types of faults**

**Notes:**
It is also useful (and common) to characterize earthquakes using the geometry of the fault and the slip direction. The illustrations show the three end member modes of faulting. 
Normal faults are associated with tectonic tension and movement on the fault results in extension, the faults are often steep (at least at the near surface), commonly dipping at ~60 degrees. 
Reverse faults and thrust faults are associated with compressional tectonics and movement on the fault results in shortening. Reverse faults are steeply dipping and thrust faults shallow dipping. The movement on normal and reverse/thrust faults is sometimes referred to as dip-slip, distinguishing them from the third type of fault.
Strike-slip fault are formed in areas with shearing forces, one side of the fault slides past the other without causing either extension or shortening.

## Strike-Slip Faults

**Strike-Slip Faults**

**Notes:**
Strike-slip faults can be described as either left-lateral, where the far side of the fault moves to the left – or right-lateral, when the far side of the fault moves to the right.

## 1979 Imperial Valley, California (M=6.5)

- Photo by D. Cavit, USGS

**Notes:**
You can see from the off-set furrows that the there was recent right-lateral movement on the fault. However, normally the fault moves deep in the crust and there is not surface expression of the rupture, so we need to look at the recorded seismic waves to try and work out what happened at the fault

## Complicated Slip Distributions

**Notes:**
This figure shows the amount of slip on each part of the fault for the M8.7 March 2005 Sumatra earthquake, it is clear that some areas of the fault slipped far more than others. This is very important when thinking about tsunami generation – tsunamis are generated by displacing a large volume of water, with variable slip the seabed deformation will be complicated and so some areas above the rupture may generate a tsunami while others do not.

## Sumatra

- Haskell, 1964

-           Ishii et al., Nature 2005 doi:10.1038/nature03675

- Rupture

- Sumatra earthquake, Dec 28, 2004

**Notes:**
For large earthquakes the rupture propagates along the fault with only a small section slipping at any one time. Models of the Sumatra earthquake calculated from the recorded seismograms show that this happened in this earthquake, the rupture propagated northward for ~500 sec, with different sections rupturing at any give time.

## Asperity = a region of a fault with higher strength than its surroundings

- Bormann 2002. New Manual of Seismological Observatory Practice.

- The evolution in time and space of the 1985 Michoacán, Mexico, earthquake. Note that this is almost 2 separate earthquakes, one in the south and one in the north, separated by ~10 sec and ~100 km.

**Notes:**
The rupture process can be very complicated in space and time. In the case of this earthquake there are two distinct times and places where a large amount of seismic energy was released. These periods of high energy release are associated with the breaking of asperities.

## Seismic Moment (Mo)

- Area (A)

- Slip (S)

- 15 km

- 10

- 0

- M4    M5     M6

- 5

**Seismic Moment (M****o****)**

- Courtesy of Jim Mori

**Notes:**
Seismic moment quantifies the size of an earthquake using the average slip of the rupture area.
On the right the colored blocks illustrate the approximate fault size for different magnitude earthquakes.  Note that the fault size does not increase by 10 for each magnitude step, but instead increases by 2-3 times.

## Seismic moments and fault areas

- of some famous earthquakes

- Courtesy of Jim Mori

**Notes:**
This slide shows the fault area (and the seismic moment) for some famous damaging earthquakes. Chile 1960 is the largest ever recorded earthquake, Alaska 1964 was also larger than Sumatra 2005, but the Sumatra event had the longest ever recorded rupture length (it was just a narrower rupture than the other two). Note however, that many of the damaging earthquakes do not have particularly large seismic moments – 5000 people died in Kobe, even though it was only a M=6.9 event.

## Point source approximation - Equivalent Body Forces

- Couple
- (Single Couple)

- Double Couple

- Bormann 2002, New Manual of Seismological Observatory Practice

**Notes:**
So after making the connection between fault movement and earthquakes, the next question is what are (and how do we represent) the force on the fault? This caused a considerable amount of discussion in the early and mid 1900s. 
Earthquakes generated by slip on a fault are generated by forces dominated by a double couple. A couple is a pair of forces separated by a small distance and offset from one another (which creates a torque). A double couple is a pair of couples. Explosions however, are dominated by approximately equal forces radiating out from the center without any offset (dipoles).

## Moment tensor: dipoles and couples

- USGS

- 9 components, but symmetric matrix so 6 are independent

**Notes:**
The most complete way to describe the forces on the fault is through the moment tensor. This is the complete series of 3 dipoles (each at 90 degrees) and 6 couples (each at 90 degrees). 

## Moment Tensor for an Explosion

- USGS

**Notes:**
This is a very versatile way of modeling the earthquake, it doesn’t even require a double couple source mechanism – for example an explosion would be represented by three positive forces on the 3 dipoles.

## Moment Tensor for Fault Slip 

- Double Couple
-    Fault - Slip

- Moment Tensor for Fault Slip

- USGS

**Notes:**
The double couple force associated with most earthquakes is represented as a force on two of the couples. 

## Magnitude – a measure of how large an Earthquake is.

- Average: ~1 M8 / year

- Average: 13-15 M7 / year

- Average: 130-150 M6

- Incomplete for 2006

**Notes:**
Magnitude is a measure of the size of an earthquake. There are several magnitude scales, discussed later, but all are logarithmic (i.e. an increase in magnitude of 1 unit (e.g. from 5.6 to 6.6) relates to an increase in seismic wave amplitude of 10 units).
There are 1 or 2 magnitude 8 earthquake each year, 13-15 M7 earthquakes, 130-150 M6 earthquakes, etc.
The increased number of recorded earthquakes is due to more and better instruments, NOT and increase in the number occurring. 

## Types of Magnitude

|  | Name | Data used | Period range |
| --- | --- | --- | --- |
| Ml | Local magnitude | regional S and surface waves | 0.1-1 sec |
| mb | (short period) body wave magnitude | teleseismic P waves | 1-5 sec |
| Ms | Surface wave magnitude | teleseismic surface waves | (20 sec) |

- Traditional magnitudes based on amplitudes of recorded data.

**Notes:**
Some of the more common magnitude scales are listed here. These are all based on amplitude of seismic waves, which is in turn related to the energy released by the earthquake. 

Which scale is the most appropriate depends on what will be done with the data, for example ML is quite popular with engineers because it calculates the magnitude using a period of wave that is similar to the resonance frequency of most buildings, so it’s quite well related to the amount of damage caused by the earthquake. 

## Local magnitude - Ml

- Charles Richter
- 1900-1985

- USGS, NEIC

- Bruce Bolt. Earthquakes.
- WH Freeman and Company

- Ml = log Amax – log A0
- Defined using horizontal, short period seismometer. Therefore no period consideration.
- Log A0 correction taken from published tables and related to distance (< 600km)
- The ~1 sec period response of the seismometer is similar to many small buildings, therefore still useful for engineers.

**Notes:**
Originally defined by Richter for southern California, this is the oldest magnitude scale. Based on the displacement magnitude of S and surface waves recorded within 600 km of the source.

Variation in crustal structure around the world mean that there is no single set of calibration functions that can be applied universally. 

## Surface wave magnitude - Ms

**First defined by Gutenberg 1945.**
**IASPEI Standard: ****Distances ****2 degrees < ****Δ**** < 160 degrees.****Depth h < 50 km.****Any surface wave period measured on horizontal and vertical components**
**NEIC:****Limit periods to 18 < T < 22 sec and only use vertical component.****Distances from 20 degrees < ****Δ**** < 160 degrees**

**Ms = log (A/T)****max**** + ****σ****S****(****Δ****) = ****log (A/T)****max**** + 1.66 log ****Δ**** + 3.3**

**Notes:**
Surface wave magnitude is calculated for more distant earthquakes. As the Earth’s structure becomes more uniform beneath the top 100km a single distance correction value can be used everywhere.

However, there are differences in the way Ms is calculated. 

## Body wave magnitude - mb

**Calculated from P wave displacement amplitude. Commonly reported but very variable calculation methods:**
**Fairly standard features of measurement: ****distance 20 deg < ****Δ**** < 100 deg, period T < 3 sec. **

**mb = log (A/T)****max**** + Q(****Δ****,h) **

- Distance correction from Gutenberg 1945

***IASPEI Standard*****: measure A****max**** from whole recorded P wave; vertical or horizontal max. **
***NEIC*****: vertical P only, measure max amp in first 10 cycles (~10-20 sec), or manually extended to 60 sec for large earthquakes.**
***China and the CTBTO*****: measure only first 5-6 seconds.**

**Notes:**
Body wave magnitude was first defined by Gutenberg in 1945. His distance correction is still used. 

However, there are large differences in the time window used to calculate mb, with more of the short windows generating saturation at low magnitudes, and therefore underestimation of the size of the earthquake.

## Saturation

**Ml, Ms and mb all suffer from saturation.**
**Occurs for 2 reasons:**

- Kanamori 1983

**Time window saturation**:
- The magnitude is calculated for a time window that is less than the duration of the rupture (particularly effects mb)

**Spectral saturation**:
- The wavelength of the wave is too short to “see” all of the rupture (effects mb, Ml, and Ms)

**Notes:**
Ml, Ms and mb all suffer from saturation – i.e. the magnitudes stop increasing after a certain value.

Spectral saturation is a problem for all magnitudes based on limited frequencies. If the wavelength of the data used is shorter than the length scale of the rupture (either from faulting or the physical process generating the wave), the amplitude of the phase is insensitive to the size of the rupture. 

## Types of Magnitude

|  | Name | Data used | Period range |
| --- | --- | --- | --- |
| Ml | Local magnitude | regional S and surface waves | 0.1-1 sec |
| mb | (short period) body wave magnitude | teleseismic P waves | 1-5 sec |
| Ms | Surface wave magnitude | teleseismic surface waves | 20 sec |

| Mw | Moment Magnitude | teleseismic surface waves | > 200 sec |
| --- | --- | --- | --- |
| Me | Energy magnitude | teleseismic P and S waves | 0.2-100 sec |

**Do not saturate and physically meaningful. But more complicated to calculate**

**Notes:**
Moment and Energy magnitudes are more complicated to calculate, but are less prone to saturation and are more physically meaningful.

## Moment Magnitude - Mw

**Calculated from seismic moment (Mo). Therefore *****related to fault slip***** not energy released as waves. More relevant for tsunamis, less relevant for damage from ground shaking.**

- Stein and Wysession, “An Introduction to seismology, earthquakes and Earth structure”

**Harvard CMT and NEIC calculate Mw from the moment tensor solution. **** **
**Fit shape and amplitude of long period surface waves to synthetics to model moment tensor and Mo.**

**Notes:**
Moment magnitude is calculated from the Seismic Moment. It is therefore related to the slip on the fault, which is the important parameter for tsunami generation, as this controls the seafloor displacement. It is also a non-saturating scale (as long as it is calculated from phases with longer wavelengths than the length of the rupture).

Seismic moment is generally calculated by modeling the long period surface waves. 

## Energy Magnitude Me

**Calculates the energy released as seismic waves.**
**Done by integrating radiated energy flux in velocity-squared seismograms over the duration of the rupture.**

**Notes:**
Energy magnitude is related to the total energy released as seismic waves. This is important for seismic hazard from ground shaking and landsliding.

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

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

**Earthquake 1**:   6 July 199730.0 S  71. W  *Me *6.1, *Mw *6.9No fatalities, no houses destroyed.
**Earthquake 2**: 15 October 199730.9 S  71.2 W *Me *7.6  *Mw *7.17 people killed, more than 300 people injured. 5,000 houses destroyed. Landslides and rockslides in the  epicentral region.

- Courtesy of George Choy

**Notes:**
These two earthquakes that occurred in central Chile are separated by only 4months and less than 1 degree. The first event is a large shallow thrust earthquake (July 97, Mw 6.9) and the second one is by a large normal earthquake (4 months later in oct 97, Mw 7.1). Note that the epicenters are separated by only about 1o.   
A cross-section taken normal to the trench axis at the hypocenter of the normal-fault event with a width of about 10ox10o 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 a cold slab is old lithosphere (>30 Ma) descending at moderate to fast rates. Cold slab is 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).

## Types of Magnitude

|  | Name | Data used | Period range |
| --- | --- | --- | --- |
| Ml | Local magnitude | regional S and surface waves | 0.1-1 sec |
| mb | (short period) body wave magnitude | teleseismic P waves | 1-5 sec |
| Ms | Surface wave magnitude | teleseismic surface waves | 20 sec |

| Mw | Moment Magnitude | teleseismic surface waves | > 200 sec |
| --- | --- | --- | --- |
| Me | Energy magnitude | teleseismic P and S waves | 0.2-100 sec |

| Mwp | P-wave moment magnitude | teleseismic P waves | 10-60 sec |
| --- | --- | --- | --- |
| mB | broadband body wave magnitude | teleseismic P waves | 0.5-12 sec
 |
| Mm | Mantle magnitude | teleseismic surface waves | > 200 sec |
| Mj | JMA magnitude | regional S and surface waves | 5-10 sec |

**Notes:**
These last magnitude scales are other commonly reported scales.

## Mwp

- ∫uz(t)dt  ∝ Mo

- Mo = Max |∫uz(t)dt| 43r/Fp
- Mw = (logMo/1.5) – 10.73

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

- Courtesy Jim Mori

**Notes:**
Mwp is a method of rapidly estimating the Moment Magnitude form the P wave data (which saves time as the surface waves take a long time to arrive and model). Mwp is based on the integration of the displacement (the double integration of the velocity trace), which gives the maximum displacement. This is then proportional to the seismic moment.
The slide shows the equation used to derive seismic moment from the twice integrated P, note the inclusion of a distance correction (r). The moment is converted to moment magnitude (Mw) using the lower equation. 

## Mantle Magnitude - Mm

- Distance Correction

- Source Correction

- Spectral Amplitude

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

**Mantle Magnitude - Mm**

- Courtesy of Jim Mori

**Notes:**
The equation for the mantle magnitude scale is similar to the Richter scale, but a little more complicated as it specifies a specific amplitude and corrections.

## Magnitudes for tsunami warnings

**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 and calculate Mw
- Magnitude from P waves (mb) is fast but underestimates moment, so:
- If have time (hours), determine Mm from mantle waves or Mw from long period surface wave.
- For quick magnitude (seconds to minutes), determine Mwp from P waves

## Magnitudes for the Sumatra Earthquake

| Scale | Mag | Data | time to announce | number of stations |
| --- | --- | --- | --- | --- |
| mb | 7.0 | 1 sec P wave |  | 131 stations |
| Mwp | 8.0 /8.5 | 60 sec P waves | 11 minutes /
1 hour |  |
| Ms | 8.0-8.8 | 20 sec surface waves |  | 118 stations |
| Mw | 8.9-9.0 | 300 sec surface waves | 5 hours |  |
| Mw | 9.1-9.3 | 3000 sec free oscillations | days  |  |

**Magnitudes for the Sumatra Earthquake**

**Notes:**
The first PTWC bulletin for the Dec 26, 2004 tsunami (11 mins after the earthquake) announced an Mwp=8.0, after approximately one hour this was increased to Mw=8.5 after including surface wave data. Harvard CMT made a special calculation of the Mw using longer than usual surface waves (300 sec compared to the normal 135 sec period) and published Mw=9.0 within 5 hours of the event. Days later the Mw was increased to 9.1-9.3 using very long period normal mode data.