Magnitude Seismic moment Intensity Frequency-magnitude relation Earthquake magnitude

Earthquake magnitude is a measure of the size or strength of an earthquake.

It is based on amplitudes of seismograms.

In the past various magnitude scales have been developed. Local magnitude

“Richter scale” (local magnitude, ML ) was introduced by Charles Richter in 1935 for southern California earthquakes measured on a Wood-Anderson seismograph.

�� = log � + 2.76 log ∆ − 2.48 ML : local magnitude A: amplitude on Wood-Anderson seismograph in mm Δ: epicentral distance in km Various magnitude scales Body wave magnitude Correction term body wave magnitude Surface wave magnitude Earthquakes vs. nuclear explosions

Body and surface wave magnitude have been used to discriminate between nuclear explosions and earthquakes. Body and surface wave magnitude

‘Saturation’ is a problem of body and surface wave magnitudes Seismic moment, moment magnitude

ML , mb , MS are empirical.

Better: Seismic moment M0 = μ D S

μ : shear modulus [Pa = Nm-2] D : average slip along plane [m] S : surface area along which slip occurred [m2]

M0 in Nm, i.e. a measure of energy or moment/torque

Related magnitude scale: Moment magnitude

log � � = 0 − 10.73 � 1.5

-5 -2 -7 where M0 in ergs = dyne . cm = 10 N . 10 m = 10 Nm (or � = ! − 6 with M in Nm) � . 0 Seismic energy

Empirical relation between seismic energy (ES) and MW :

10 log ES = 1.5 MW + 11.8

1 unit increase in MW corresponds to a 32 time increase in ES

Note that seismic energy is only a fraction of the total energy released during an earthquake. Fracture energy and heat are (more) important. Frequency, magnitude and energy release 26-12-2004, Mw 9.1, Sumatra earthquake

Lay et al, 2005 Ammon et al, 2005 26-12-2004, Mw 9.1, Sumatra earthquake - tsunami

Lay et al, 2005 Magnitude vs. Intensity

Earthquake magnitude is measure of size of an earthquake and can be negative.

Seismic intensity is a measure of the effects of ground shaking caused by an earthquake. There are various, slightly different, intensity scales Intensity is expressed in roman numerals: I – XII, or I – X. Modified Mercalli intensity scale Intensities for the 1989, Mw 6.9, Loma Prieta earthquake

USGS 1989, Mw 6.9, Loma Prieta earthquake in San Francisco

Mariana district (artificial fill) Seismicity in the

KNMI 1992 earthquake

Intensities of Roermond earthquake of 13 April 1992 ML = 5.8, Mw = 5.3 Depth: 18 km Frequency-magnitude relation Frequency-magnitude (or Gutenberg-Richter) relation

log � = � − ��

N : number of earthquakes with magnitude greater than M within certain time span (e.g. year) for region. b : slope, relative occurrence of large compared to small earthquakes b ~ 1 (typically 0.7 – 1.3) a: 10a is number of earthquakes (in that region for time span)

Relation was found empirically and suggests self-similarity or fractal scaling (scale invariance). Frequency-magnitude relation

Deviations from log � = � − �� at high and low M.

Deviations at small M can be due to ...

Deviation at large M can be due to ... Frequency-magnitude relation log � = � − ��

N : all earthquakes with magnitude larger than 0

Alternatively,

log � = �′ − �(� − ����)

N : all earthquakes with magnitude larger than ���� Frequency-magnitude relation Seismicity for Rhenish Massif and Lower Rhine

Ahorner, 1983

Earthquakes with magnitude similar to the Roermond earthquake of 1992 happen once every ~ 200 years. The previous one was in 1756. Earthquake prediction vs earthquake hazard

In earthquake prediction, earthquakes are predicted with specified time location and magnitude.

True earthquake prediction of major earthquakes is not possible in the foreseeable future. Yet, there may be signs of an impending earthquake (foreshocks, Radon emission, changes in ground water level, strange animal behavior).

Seismic hazard analysis uses the statistics of (past) earthquakes. Seismic hazard Europe

Grünthal et al.

peak ground acceleration with 10% probability in 50 years Induced seismicity

Grigoli et al. 2017 Induced seismicity: Largest earthquakes per site

Grigoli et al. 2017 Seismic hazard USA

USGS Ground acceleration with a 2% chance of being exceeded over a period of 50 years. Note hazard caused by induced earthquakes in Oklahoma (hexagon).