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Encyclopedia of Complexity and Systems Science pp 1–33Cite as

Earthquake Location, Direct, Global-Search Methods

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Definition of the Subject

An earthquake location specifies the place and time of occurrence of energy release from a seismic event. A location together with a measure of size forms a concise description of the most important characteristics of an earthquake. The location may refer to the earthquake’s epicenter, hypocenter, or centroid or to another observed or calculated property of the earthquake that can be spatially and temporally localized. A location is called absolute if it is determined or specified within a fixed, geographic coordinate system and a fixed time base (e.g., Coordinated Universal Time, UTC); a location is called relative if it is determined or specified with respect to another spatiotemporal object (e.g., an earthquake or explosion) which may have unknown or uncertain absolute location.

For rapid hazard assessment and emergency response, an earthquake location provides information such as the locality of potential damage or the source region of a possible tsunami,...

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Abbreviations

Arrival time:

The time of the first measurable energy of a seismic phase on a seismogram.

Centroid:

The coordinates of the spatial or temporal average of some characteristic of an earthquake such as surface shaking intensity or moment release.

Data space:

If the data are described by a vector d, then the data space D is the set of all possible values of d.

Direct search:

A search or inversion technique that does not explicitly use derivatives. Usually involves repeated application of a forward problem.

Earthquake early warning:

The goal of earthquake early warning is to estimate the shaking hazard of a large earthquake at a nearby population center or other critical site before destructive S and surface waves have reached the site. This requires that useful probabilistic constraint on the location and size of an earthquake is obtained very rapidly.

Earthquake location:

An earthquake location specifies a spatial position and time of occurrence for an earthquake. The location may refer to the earthquake hypocenter and corresponding origin time, a mean or centroid of some spatial or temporal characteristic of the earthquake, or another property of the earthquake that can be spatially and temporally localized. This term also refers to the process of locating an earthquake.

Epicenter:

The point on the Earth’s surface directly above a hypocenter.

Error:

A specified variation in the value assumed by a variable. See also uncertainty.

Forward problem:

A mathematical expression that relates the parameters defining a physical system (model space) to the data (data space) produced by a physical process acting on the system.

Global search:

A search or inversion that samples throughout the prior pdf of the unknown parameters.

Hypocenter:

The point in three-dimensional space of initial energy release of an earthquake rupture or other seismic event.

Importance sampling:

A sampling procedure that draws samples following the posterior pdf of an inverse optimization or other search problem. Since these problems involve initially unknown, posterior pdf functions, importance sampling can only be performed approximately, usually through some adaptive or learning procedure as sampling progresses.

Inverse problem, inversion:

The problem of determining the parameters of a physical system given some data. The solution of an inverse problem requires measurements of observable quantities of the physical system and knowledge of the relevant forward problem. In inverse problems, estimates of the unknown parameters in the model space and of their uncertainties are sought from the combination of the available information on the model parameters (prior pdf), the data, and the forward problem.

Likelihood function:

A non-normalized pdf.

Misfit function:

A function that quantifies the disagreement between observed and calculated values of one or more quantities. See objective function.

Model space:

If the model parameters are described by a vector m, then model space M is the set of all possible values of m.

Objective function:

A function expressing the quality of any point in the model space. Inversion and optimization procedures use an objective function to rank and select models. Usually objective functions are defined in terms of misfit functions, and for probabilistic inversion, the objective function must be a pdf or likelihood function.

Origin time:

The time of occurrence of initial energy release of an earthquake rupture or other seismic event.

Posterior pdf :

A pdf that expresses the information about the unknown parameters available after inversion. The posterior pdf for an earthquake location is often a function of the three spatial dimensions and the origin time of the hypocenter parameters; this function may be complicated. See also Inverse problem.

Prior pdf :

A pdf that expresses the information on the unknown parameters available before an inverse problem is solved. For an earthquake location, the prior pdf is often a simple function (e.g., boxcar) of three spatial dimensions and time. See also Inverse problem.

Probability density function – pdf :

A function in one or more dimensional space X that (i) when integrated over some interval Δx in X gives a probability of occurrence of any event within Δx and (ii) has unit integral over space X, where X represents a space of possible events. An earthquake location pdf is often a three-dimensional probability density function over all possible spatial locations or a four-dimensional probability density function over all possible spatial locations and times of occurrence.

Ray path:

A local, minimum-time path between a source and receiver of idealized infinite frequency wave energy of a specified wave type (e.g., P or S).

Receiver or station:

Synonyms for an observation point where ground motion is detected and a seismogram recorded.

Seismic phase:

A distinct packet of energy from a seismic source. Usually refers to a specified wave type (e.g., P or S) satisfying a particular physics of wave propagation.

Seismicity:

The distribution in space and time of seismic event locations.

Seismogram:

An analogue or digital recording of the ground motion at a point (receiver or station) in the Earth. Also called a waveform.

Source:

A general term referring to an earthquake, explosion or other release of seismic energy as a physical phenomenon localized in space and time.

Station:

See receiver.

Travel time:

The time that a signal, e.g., elastic wave energy of a seismic phase, takes to propagate along a ray path between two points in a medium.

Uncertainty:

Random variation in the values assumed by a variable. See also error.

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Authors and Affiliations

  1. ALomax Scientific, Mouans-Sartoux, France

    Anthony Lomax

  2. Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy

    Alberto Michelini

  3. ECOSSE (Edinburgh Collaborative of Subsurface Science and Engineering), Grant Institute of GeoSciences, The University of Edinburgh, Edinburgh, UK

    Andrew Curtis

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  1. Anthony Lomax
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  2. Alberto Michelini
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  3. Andrew Curtis
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Correspondence to Anthony Lomax .

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  1. Ramtech Ltd., Larkspur, California, USA

    Robert A. Meyers

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Lomax, A., Michelini, A., Curtis, A. (2014). Earthquake Location, Direct, Global-Search Methods. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-3-642-27737-5_150-2

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