Magnitudes Jens Havskov and Mathilde B Srensen Earthquake

Magnitudes Jens Havskov and Mathilde B. Sørensen

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

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

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

The European Macroseismic scale EMS-98

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.

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

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

Wood Anderson simulation, needed since we do not have Wood-Anderson seismographs Modern ML formula ML = log(A) + 1. 11 log(r) + 0. 00189 r - 2. 09 A is maximum ground displacement in nm R is hypocentral distance in km

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

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 (2 A). Figure modified from NMSOP. M = log(A/T) + Q(Δ, h) Q is the attenuation function which corrects for distance and depth

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

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

Surface wave magnitude, measured on a long period seismogram MS = log(A/T)max + 1. 66 log (Δ) +3. 3 A is amplitude, T is period and Δ is distance Distance larger than 20 degrees

Magnitude discrepancies Ideally, you want the same value of magnitude for any one earthquake from each scale you develop, i. e. MS = m b = M L 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

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 8. 2 -8. 3 Fall 2002 EASA-193 Intro to Earthquakes Lecture-14 16

Saturation EASA-193 Intro to Earthquakes

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

The solution, use seismic moment • Measures the size of an earthquake • Based on the force behind the rupture • M 0=μAd • μ: shear modulus (ability to change shape) • A: rupture area • d: displacement along the fault

Moment magnitude - Mw • The moment magnitude is based on the seismic moment M 0: • The seismic moment can be determined from the determination of the moment tensor or by spectral analysis • Mw=2/3 log 10(M 0) – 10. 7 [dyn-cm=10 -7 Nm] • Mw=2/3(log 10(M 0)-9. 1) [Nm] • Mw is today seen as the ’most correct’ magnitude measure • Problem: takes longer time to determine

Rupture area example Sumatra earthquake (M=9. 3): Total rupture length: ca 1200 km Total rupture width: ca 150 km Maximum displacement: 20 m

Rupture area example Japan earthquake (M=9. 2): Total rupture length: ca 500 km Total rupture width: ca 250 km Maximum displacement: 40 -50 m (!) The dimensions of structures limit the maximum earthquake magnitude Displacement is also important The largest earthquakes are found in subduction zones

Rupture area vs. magnitude

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.

Moment from spectra and moment tensor inversion

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

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

Comparison of recent and historic earthquakes by energy release

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 Lecture-14 29

Equivalent energy in an earthquake 3 The energy in lightening 5 A tornado 6 The Hiroshima nuclear bomb 8 Largest known nuclear bomb

List of the deadliest earthquakes known in history, they are not the biggest! The earthquake of Dec. 26 th 2004 was the third deadliest earthquake in the world in known history. The others were: 1. 1976 July 27, Tangshan, China, 255 000 casualties (M=7. 5) 2. 2004 Dec 26, Off NW-Sumatra (tsunami) 225 000 casualties (M=9. 0) 3. 1780 Feb 28, Iran, 200 000 casualties (M=? ) 4. 1920 Dec 16, China, Gansu, 200 000 casualties (M=8. 6) 5. 1927 May 22, Tsinghai, China, 200 000 casualties (M=7. 9) 6. 1556 Jan 23, Senshi, China, 830 000 casualties (M=~8. 0) 7. 1923 Sept 1, Japan Kanto (Tokyo fire), 143 000 casualties (M=7. 9) 8. 1948 Oct 5, Ashgabat, Turkmenistan, 110 000 casualties (M=7. 3)

Gutenberg-Richter magnitude recurrence relationship

Earthquake statistics Log N = a-b. M 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