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Earthquake: Magnitudes, Energy, and Moment

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Peter Bormann: deceased

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Abbreviations

Corner frequency:

The frequency fc at which the curve that represents the Fourier amplitude spectrum of a signal abruptly changes its slope (see Fig. 4). For earthquakes, this frequency is related to the seismic source properties such as fault size, stress drop in the source volume, rupture velocity, and related rupture duration. Also the frequency at which the magnification curve of a recording system changes its slope (cf. Fig. 1).

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 S and the mantle magnitude M 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 or seismic moment of an earthquake in terms of area and average slip of the fault or to the seismic energy radiated as seismic waves from a seismic source and thus its potential to cause damage and casualty even at larger distance from the source (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 outward. 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 km are commonly termed shallow and those at larger depth either intermediate (up to h = 300 km) or deep (h = 300–700 km). The determination of the origin time, geographical coordinates (latitude φ and longitude λ), and focal depth is the prime task of seismic source location. However, for extended seismic sources, fault ruptures of very large earthquakes in particular, the hypocenter is often not the location of the 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. These locations of the largest effects may be for great earthquakes dozens of km in space and many seconds to minutes in time away from the hypocenter or epicenter, respectively.

Fundamental modes:

Long period of 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.

Green’s function:

In seismology, the vector displacement field generated by an impulsive force applied at a point in the Earth. When combined with the source time function describing the discontinuities in displacement and traction across an internal surface, a Green’s function can represent the seismic displacements caused by earthquake faults and explosions.

Macroseismic intensity:

A cumulative measure of the effects of an earthquake at a particular place at the Earth’s surface on humans and/or structures and thus a measure of the strength of earthquake shaking. Different from magnitude, the intensity at a point depends not only on the earthquake strength (released seismic energy) or earthquake size (released seismic moment) but also on the epicenter distance, the hypocenter depth, the position of the observation point with respect to the type of source mechanism and its directivity, and the local site response. Intensity values are usually given as integer Roman numerals ranging from 0 to 12. Although coarse, they are a valuable complementary analogue for physical ground motion parameters and correlate best with ground velocity.

Magnitude:

A logarithmic 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 (e.g., local or Richter, surface wave, short-period and broadband body wave magnitudes). Some of them show saturation. In contrast, the moment magnitude (M w), based on the physical concept of seismic moment, is in principle applicable to all earthquake sizes but is more difficult to compute than other types; also the energy magnitude (M e), which is based on direct calculation of the seismic energy E s from broadband seismic records, is in principle not affected by the saturation problem. Both magnitudes, however, can be calculated only via certain empirical and theoretical model assumptions.

Radiation efficiency:

Ratio between radiated seismic energy and the potential energy available for strain release. In contrast to seismic efficiency, the radiation efficiency accounts only for strain energy loss due to fracturing but not due to the additional conversion into frictional heat and sound energy. For most earthquakes the radiation efficiency ranges between 0.25 and 1 although it may drop even below 0.1 for very slow rupturing tsunami earthquakes.

Saturation:

(of magnitudes) means the 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 measurement period, the earlier respective magnitudes will saturate (see relation (14) and Figs. 3 and 5).

Seismic efficiency:

Ratio of the energy radiated as seismic waves to the total energy released due to fault slip. It is for earthquakes in the order of a few percent and generally less than the radiation efficiency.

Seismic energy:

Elastic energy E s (in joules) generated by and radiated from a seismic source as seismic waves. The amount of E s is generally much smaller than the energy associated with the nonelastic deformation in the seismic source (see seismic moment M 0). The ratio \( {E}_{\mathrm{S}}/{M}_0=\left(\Delta \upsigma /2\upmu \right)={\uptau}_{\mathrm{a}}/\upmu \), i.e., the seismic energy released per unit of M 0, varies for earthquakes in a very wide range between some 10−7 and 10−3, depending on the geologic-tectonic environment, type of source mechanism, and related stress drop Δσ or apparent stress τa.

Seismic moment M 0 :

A special measure of earthquake size. The moment tensor of a shear rupture (see earthquake source) has two nonzero eigenvalues of the amount \( {M}_0=\upmu \overline{\mathrm{D}} \) Fa with μ, shear modulus of the ruptured medium; \( \overline{\mathrm{D}} \), average source dislocation; and Fa, area of the ruptured fault plane. M 0 is called the scalar seismic moment. It has the dimension of Newton meter (N · m) (or dyn · cm in non-SI units) and describes the total nonelastic deformation in the seismic source volume. Knowing M 0, the moment magnitude M w can be determined via Eq. 6.

Seismic scaling laws:

Relationships of magnitude, seismic moment, or seismic energy with wave frequency or related earthquake fault parameters. They are used in two ways: (a) to get a rough estimate of relevant fault parameters when magnitude M, seismic moment M 0, or seismic energy E S of the event is known from the evaluation of instrumental recordings and (b) in order to get magnitude, moment, and/or energy estimates for historic or even prehistoric events for which no recordings are available but for which some fault parameters such as the length of surface rupture and/or amount of surface displacement can still be determined from field evidence.

Seismic waves:

General term for waves generated by earthquakes, explosions, or other types of seismic sources. There are many types of seismic waves. The principal ones are (1) body waves, which travel through the whole Earth; (2) surface waves, which are bound to the Earth surface and have amplitudes that decay with depth, the faster the shorter their wavelength; and (3) coda waves, which are due to scattering and multipathing. Different magnitude scales are obtained from measurements of body waves (P-wave trains for teleseismic body wave magnitudes or S waves for the local/Richter scale) and surface waves or both, as in the case of moment tensor inversions for M w determination.

Site response:

The modification of earthquake ground motion amplitude, phase, and shape in the time or frequency domain caused by the specific conditions at the local seismic recording sites due to geological and topographic anomalies. They are not accounted for in the usually assumed one-dimensional velocity and structural models of the Earth medium in which the seismic waves propagate. Such site anomalies may cause, e.g., deviation of the actually measured wave amplitudes up to a factor of about ten times as compared to average conditions. In the case of magnitude measurements, this may be corrected by empirically determined station correction terms.

Source directivity:

The effect of the earthquake source on the amplitude, frequency content, and duration of the seismic waves propagating in different directions, depending on the direction of wave propagation with respect to fault orientation, slip direction(s), and rupture velocity. Directivity effects are comparable to but not exactly the same as the Doppler effect for a moving oscillator and different for P and S waves.

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 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 source radiation patterns of seismic wave energy.

Source radiation pattern:

Dependence of the amplitudes of seismic P and S waves on the azimuth and takeoff angle under which their seismic rays have left the seismic source. It is controlled by the type of source mechanism.

Source time function:

The ground motion generated at the fault during rupture, usually as predicted by a theoretical model and represented by a time history; more strictly a compact space-time history of the earthquake source process that will give the observed displacement waveforms as its convolution with the Green’s function for the wave propagation in the Earth and the response of the recording instrument.

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 absolute value of the transfer function is termed the amplitude-frequency response or, in the case of seismographs, also magnification curve (see Fig. 1).

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Authors and Affiliations

  1. Formerly Helmholtz Center Potsdam, German Research Center for Geosciences (GFZ), Telegrafenberg, 14473, Potsdam, Germany

    Peter Bormann

  2. International Seismological Centre (ISC), Pipers Lane, Thatcham, Berkshire, RG19 4NS, UK

    Domenico Di Giacomo

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    Robert A. Meyers

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Bormann, P., Di Giacomo, D. (2015). Earthquake: Magnitudes, Energy, and Moment. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_627-1

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