1. Jens Havskov and Mathilde B. Sørensen
Magnitudes
Jens Havskov and Mathilde B. Sørensen

2. Earthquake strength
There are different measures for the strength of an earthquake
Some describe the rupture, other the effect on the surface of Earth
The most important are:
Magnitude
Seismic moment
Macroseismic intensity

3. Magnitude
Magnitude: Measure of the energy release during an earthquake
Magnitude is routinely determined from instrumental data
Magnitude is the most common measure of the size or strength of an earthquake

4. Macroseismic intensity
Based on observed and felt effects of the earthquake at a given location, without the use of instruments
Based on how people experience the earthquake and the damage it causes
Varies with distance to the earthquake
The intensity at the epicenter is a measure of the strength of the earthquake
Today, intensity is determined from questionnaires and field observations
For historical earthquakes, historical data is used

5. The European Macroseismic scale EMS-98

6. Macroseismic intensity
The distribution of intensity can help locating earthquakes for which no recordings are available, for example historical earthquakes.
The intensity at the epicenter is a measure of the strength of the earthquake.
The felt area can be related to magnitude.

7. Instrumental magnitude
Using seismic recordings is now the most common way to determine the magnitude
All magnitude scales are tied the the original Richter so-called local magnitude scale for California
The Richter scale gives arbitrary values not tied directly to any physical unit

8. Local Richter magnitude Ml
Procedures:
Measure the maximum amplitude on the seismogram of a Wood-Anderson seismogram
Determine the distance to the earthquake
Use the nomogram to determine magnitude
A 1 mm amplitude at 100 km distance was arbitrarely defined to be magnitude 3
Alternetively use a formula

9. Wood Anderson simulation, needed since we do not have Wood-Anderson seismographs
Modern ML formula
ML = log(A) log(r) r
A is maximum ground displacement in nm
R is hypocentral distance in km

10. Coda magnitude Mc, used when instruments are not calibrated
Mc = a log(tcoda) + br+c

11. General amplitude based magnitude
Reading the amplitude A from the base line and the period T from two peaks b) Reading the amplitude peak to peak (2A). Figure modified from NMSOP.
M = log(A/T) + Q(Δ,h)
Q is the attenuation function which corrects for distance and depth

12. Body wave magnitude mb, measured on a short period seismogram
mb = log(A/T) + Q(Δ,h)
Distance larger than 20 degrees

13. Mb attenuation curve Q
mb = log(A/T) + Q(Δ,h)

14. Surface wave magnitude, measured on a long period seismogram
MS = log(A/T)max log (Δ) +3.3
A is amplitude, T is period and Δ is distance
Distance larger than 20 degrees

15. Magnitude discrepancies
Ideally, you want the same value of magnitude for any one earthquake from each scale you develop, i.e.
MS = mb = ML
But this does not always happen:
Turkey 8/17/99:
MS = 7.8, mb = 6.3
Taiwan 9/20/99:
MS = 7.7, mb = 6.6
EASA-193 Intro to Earthquakes

16. Why Don’t Magnitude Scales Agree?
Most complicated reason:
Magnitude scales saturate
This means there is an upper limit to some magnitudes no matter how “large” the earthquake is
For instance Ms (surface wave magnitude) never gets above
Fall 2002
EASA-193 Intro to Earthquakes

17. EASA-193 Intro to Earthquakes
Saturation
EASA-193 Intro to Earthquakes

18. What causes saturation?
-The rupture process.
Small earthquakes rupture small areas and are relatively enriched in short period signals.
Large earthquakes rupture large areas and are relatively depleted in high frequencies.
EASA-193 Intro to Earthquakes

19. The solution, use seismic moment
Measures the size of an earthquake
Based on the force behind the rupture
M0=μAd
μ: shear modulus (ability to change shape)
A: rupture area
d: displacement along the fault
Fasthetsmodulen endrer seg ikke mye, så A og d kontrollerer momentet

20. Moment magnitude - Mw
The moment magnitude is based on the seismic moment M0:
The seismic moment can be determined from the determination of the moment tensor or by spectral analysis
Mw=2/3 log10(M0) – 10.7 [dyn-cm=10-7Nm]
Mw=2/3(log10(M0)-9.1) [Nm]
Mw is today seen as the ’most correct’ magnitude measure
Problem: takes longer time to determine

21. Rupture area example Sumatra earthquake (M=9.3):
Total rupture length: ca 1200 km
Total rupture width: ca 150 km
Maximum displacement: 20 m

22. Rupture area example Japan earthquake (M=9.2):
Total rupture length: ca 500 km
Total rupture width: ca 250 km
Maximum displacement: m (!)
The dimensions of structures limit the maximum earthquake magnitude
Displacement is also important
The largest earthquakes are found in subduction zones

23. Rupture area vs. magnitude

24. Determine rupture area
If the rupture is seen at the surface it might be possible to measure the lenght (L) and the displacment (D). Mostly this is not possible and the fault dimension must then be measured by the extension of the aftershocks or from other seismic observations.

25. Moment from spectra and moment tensor inversion

26. Moment from earthquake spectra
Magnitude saturation due to seismic moment not being proportial to amplitude picked due to using a too high frequency

27. Earthquake energy Earthquakes can release enormous amounts of energy
A magnitude increase of 1 represents a factor 32 increase in energy release
Hiroshima bomb ~ M=6

28. Comparison of recent and historic earthquakes by energy release

29. EASA-193 Intro to Earthquakes
The largest earthquake ever recorded by seismometers (the 1960 Chilean event with 9.5 Mw ) had a seismic moment equivalent to the energy of 9 trillion kilotons of TNT!
Fall 2002
EASA-193 Intro to Earthquakes

30. Equivalent energy in an earthquake
The energy in lightening
5 A tornado
The Hiroshima nuclear bomb
Largest known nuclear bomb

31. List of the deadliest earthquakes known in history, they are not the biggest!
The earthquake of Dec.26th 2004 was the third deadliest earthquake in the world in known history. The others were:
1976 July 27, Tangshan, China, casualties (M=7.5)
2004 Dec 26, Off NW-Sumatra (tsunami) casualties (M=9.0)
1780 Feb 28, Iran, casualties (M=?)
1920 Dec 16, China, Gansu, casualties (M=8.6)
1927 May 22, Tsinghai, China, casualties (M=7.9)
1556 Jan 23, Senshi, China, casualties (M=~8.0)
1923 Sept 1, Japan Kanto (Tokyo fire), casualties (M=7.9)
1948 Oct 5, Ashgabat, Turkmenistan, casualties (M=7.3)

32. Gutenberg-Richter magnitude recurrence relationship

33. Earthquake statistics
Log N = a-bM
N is the sum of all events larger than M
b is often 1 so the equation is
Log N =a – M
So if e.g. we have 10 events larger than M=5 in one year in an area, then we have 100 events larger than M=4
and
1 event larger than 6
The relation can therefore be used to statisitcally predict the number of events of a given size in a particular area

34. Detection threshold
When we reach the point where the curve no longer increases linearly, we no longer detect all the events.

35. b-value example

36. Conclusion
Magnitude is the most used measure of the size of an earthquake
Many magnitude scales are used but moment magnitude is now the most quoted