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Earthquake Magnitude

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Extreme Environmental Events

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Article Outline

Glossary

Definition of the Subject

Introduction to Common Magnitude Scales: Potential and Limitations

Common Magnitude Estimates for the Sumatra 2004 M w 9.3 Earthquake

Magnitude Saturation and Biases Due to Earthquake Complexity

Proposals for Faster Magnitude Estimates of Strong Earthquakes

Future Requirements and Developments

Bibliography

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Abbreviations

 :

Technical terms that are written in the text in italics are explained in the Glossary.

Corner frequency :

The frequency \({f_\mathrm{c}}\) at which the curve that represents the Fourier amplitude spectrum of a recorded seismic signal abruptly changes its slope (see Fig. 5). For earthquakes, this frequency is related to the fault size, rupture velocity, rupture duration and stress drop at the source. Also the frequency at which the magnification curve of a recording system (e. g., Fig. 3) changes its slope.

Dispersion :

Frequency‐dependence of the wave propagation velocity. Whereas seismic body‐waves show virtually no dispersion, it is pronounced for seismic surface waves. It causes a significant stretching of the length of the surface‐wave record and the rather late arrival of its largest amplitudes (Airy phases) from which the surface‐wave magnitude \({M_\mathrm{S}}\) and the mantle magnitude \({M_\mathrm{m}}\), respectively, are determined.

Earthquake size :

A frequently used, but not uniquely defined term. It may be related – more or less directly – to either the geometric‐kinematic size of an earthquake in terms of area and slip of the fault or to the seismic energy radiated from a seismic source and its potential to cause damage and casualty (moment or energy magnitude).

Earthquake source :

In general terms, the whole area or volume of an earthquake rupture where seismic body waves are generated and radiated outwards. More specifically, one speaks either of the source mechanism or the source location. The latter is commonly given as earthquake hypocenter (i. e. the location at the source depth h from where the seismic rupture, collapse or explosion begins) or as the point on the Earth's surface vertically above the hypocenter, called the epicenter . Earthquakes at \({h < 70\,\mathrm{km}}\) are shallow, those at larger depth either intermediate (up to \({h = 300\,\mathrm{km}}\)) or deep earthquakes (\({h = 300}\)–700 km). The determination of the geographical coordinates latitude φ, longitude λ, and focal depth h, is the prime task of seismic source location. However, for extended seismic sources, fault ruptures of great earthquakes in particular, the hypocenter is generally not the location of largest fault slip and/or seismic moment/energy release and the epicenter is then also not the location where the strongest ground shaking is felt. The locations of largest effects may be dozens of kilometers in space and many seconds to minutes in time away from the hypocenter or epicenter, respectively.

Fundamental modes :

The longest period oscillations of the whole Earth with periods of about 20 min (spheroidal mode), 44 min. (toroidal mode) and some 54 min (“rugby” mode), excited by great earthquakes.

Magnitude :

A number that characterizes the relative earthquake size. It is usually based on measurement of the maximum motion recorded by a seismograph (sometimes for waves of a particular type and frequency) and corrected for the decay of amplitudes with epicenter distance and source depth due to geometric spreading and attenuation during wave propagation. Several magnitude scales have been defined. Some of them show saturation. In contrast, the moment magnitude (\({M_\mathrm{w}}\)), based on the concept of seismic moment, is uniformly applicable to all earthquake sizes but is more difficult to compute than the other types, similarly the energy magnitude, M e, which is based on direct calculation of the seismic energy \({E_\mathrm{s}}\) from broadband seismic records.

Saturation :

(of magnitudes) Underestimation of magnitude when the duration of the earthquake rupture significantly exceeds the seismic wave period at which the magnitude is measured. The shorter this period, the earlier respective magnitudes will saturate (see relation (13) and Figs. 4 and 5).

Seismic energy :

Elastic energy \({E_\mathrm{s}}\) (in joule) generated by, and radiated from, a seismic source in the form of seismic waves. The amount of \({E_\mathrm{s}}\) is generally much smaller than the energy associated with the non‐elastic deformation in the seismic source (see seismic moment \({M_\mathrm{o})}\). The ratio \({E_\mathrm{s}/M_\mathrm{o} = (\Delta \sigma /2\mu) = \tau_\mathrm{a}/\mu}\), i. e., the seismic energy released per unit of \({M_\mathrm{o}}\), varies for earthquakes in a very wide range between some 10−6 and 10−3, depending on the geologic‐tectonic environment, type of source mechanism and related stress drop \({\Delta \sigma}\) or apparent stress \({\tau_\mathrm{a}}\).

Seismic moment M o :

A special measure of earthquake size. The moment tensor of a shear rupture (see earthquake source) has two non‐zero eigenvalues of the amount \({M_\mathrm{o}=\mu \bar{D} F_\mathrm{a}}\) with μ‑shear modulus of the ruptured medium, \({\bar{D}}\)‑average source dislocation and \({F_\mathrm{a}}\)‑area of the ruptured fault plane. \({M_\mathrm{o}}\) is called the scalar seismic moment. It has the dimension of Newton meter (Nm) and describes the total non‐elastic (i. e., ruptural and plastic) deformation in the seismic source volume. Knowing \({M_\mathrm{o}}\), the moment magnitude \({M_\mathrm{w}}\) can be determined via Eq. (11).

Source mechanism :

Depending on the orientation of the earthquake fault plane and slip direction in space, one discerns different source mechanisms. Strike‐slip faults are vertical (or nearly vertical) fractures along which rock masses have mostly shifted horizontally. Dip‐slip faults are inclined fractures. If the rock mass above an inclined fault moves down (due to lateral extension) the fault is termed normal, whereas, if the rock above the fault moves up (due to lateral compression), the fault is termed reverse (or thrust). Oblique‐slip faults have significant components of both slip styles (i. e., strike‐slip and dip‐slip). The greatest earthquakes with the largest release of seismic moment and the greatest potential for generating tsunamis are thrust faults in subduction zones where two of Earth's lithosphere plates (e. g., ocean–continent or continent–continent) collide and one of the two plates is subducted underneath the overriding plate down into the Earth's mantle. Different source mechanisms are characterized by different radiation patterns of seismic wave energy.

Transfer function :

The transfer function of a seismic sensor‐recorder system (or of the Earth medium through which seismic waves propagate) describes the frequency‐dependent amplification, damping and phase distortion of seismic signals by a specific sensor‐recorder (or medium). The modulus (absolute value) of the transfer function is termed the amplitude‐frequency response or, in the case of seismographs, also magnification curve (see Fig. 3).

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    Peter Bormann & Joachim Saul

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Bormann, P., Saul, J. (2011). Earthquake Magnitude. In: Meyers, R. (eds) Extreme Environmental Events. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7695-6_17

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