aftershock: :
Typically refers to any earthquake that occurs near (in space and time) and after a larger earthquake, which in this instance would be called the mainshock. Recent synonym: triggered earthquake

 Akaike information criterion (AIC):
measure of a model's goodness of fit to a dataset; this measure explicitly accounts for the number of degrees of freedom. A smaller AIC value is preferable.

a mistaken perception of an observation caused by an error in analysis or interpretation rather than by some inherent property of the observation

 autocorrelation function:
Describes the similarity of observations as a function of the time (or distance, or any other measure of difference) between them

unitless measure of relative frequency of small and large earthquakes; specifically, the negative of the slope of the line on a log-linear plot of earthquake magnitude versus cumulative number of events; see also Gutenberg-Richter relation

 background earthquake: Typically refers to an earthquake that has not been triggered by another; thought to be the result of tectonic loading. Alternatively, in seismic hazard assessment, may refer to an earthquake not associated with a particular fault

Bath's relation:
describes the size of the largest expected aftershock in an earthquake sequence (generally thought to be ~1.2 magnitude units smaller than the mainshock)

 Brownian passage time:
The name used in seismic hazard assessment to denote the inverse Gaussian distribution, a continuous probability distribution used to model times between earthquakes in a given sequence

point inside the earth that represents the center of moment released during an earthquake (analogous to center of mass)

centroid time:
time at which an earthquake had released half its energy

completeness (magnitude of completeness, completeness magnitude):
the minimum magnitude above which it is thought that all earthquakes are reliably recorded

conditional intensity:
function that uniquely characterizes a point process, gives the normalized probability that one event will occur in the next instant conditional on the history of the process so far

confidence interval:
an interval about an estimate or a measurement with which one quantifies the belief in the estimate or measurement; e.g., the 95% confidence interval for a measurement is the range within which one is 95% confident the true value lies

Coulomb stress:
Linear combination of normal and shear stress, commonly used to describe/explain spatial patterns of earthquake triggeringdecluster:
To remove aftershocks or, more generally, to denote which earthquakes are mainshocks and which are aftershocks; declustering may be probabilistic, i.e., one might say that there is a 25% chance that Eqk A was an aftershock of Eqk B

decluster: To remove aftershocks or, more generally, to denote which earthquakes are mainshocks and which are aftershocks; declustering may be probabilistic, i.e., one might say that there is a 25% chance that Eqk A was an aftershock of Eqk B

degree of freedom:
commonly used as synonymous with adjustable model parameter; the number of degrees of freedom is the number of parameters that need to be known before the parameter vector is fully determined; an adjustable variable that may be used to describe a dataset

not affected by a random component; a deterministic system is exactly predictable if initial conditions and current state are known

earthquake catalog:
list of earthquakes and their properties (e.g., origin time, hypocenter, magnitude, etc.)

 earthquake predictability:
the extent to which different elements of the earthquake system are predictable

earthquake sequence:
generic term used to describe a set of earthquakes that have been grouped somehow, usually due to their proximity in time and space

elastic rebound:
theory that suggests stresses in the crust build up slowly until they exceed rock strength, at which point an earthquake occurs and releases part or all of the accumulated stress

point on the surface of the earth below which an earthquake began (usually specified by latitude and longitude); the projection of the hypocenter to the surface

epidemic type aftershock sequence (ETAS):
Well-studied statistical model, based on ideas from epidemiology, that is often used to analyze earthquake data; in this model, seismicity is considered as the sum of "background" earthquakes thought to be caused by tectonic loading and "triggered" earthquakes, thought to be caused by stress transfer. Alternatively known as epidemic type earthquake sequence (ETES) model

refers to a system that has only a limited state space and therefore at any time is in a state similar to one in which it has been before; alternatively, used to describe a system in which any sample of sufficient size is equally representative of the whole

 finite source model:
typically used to describe an earthquake rupture model that considers a gridded representation of the rupture plane or rupture volume; properties such as total slip are assigned to or estimated in each patch of the rupture plane

 focal mechanism:
construct for representing the geometry of an earthquake as an infinitesimal planar fault upon which slip has occurred; defined by its strike (angle between map-view representation of the fault plane and North), dip (angle between in-plane representation of the fault plane and the surface of the earth), and rake (the direction the hanging wall moves during rupture, measured relative to strike)

Typically refers to any earthquake that occurs near (in space and time) and before a larger earthquake, which in this instance would be called the mainshock. Recent synonym: triggering earthquake

A deterministic or stochastic mathematical object that is defined by its exact or statistical self-similarity at all scales. Informally, it often refers to a rough or fragmented geometrical shape which can be subdivided into parts which look approximately the same as the original shape. A fractal has a fractal dimension that is larger than its topological dimension but less than the dimension of the space it occupies.

 fractal dimension:
a statistical quantity that gives an indication of how completely a fractal appears to fill space, as one zooms down to finer and finer scales

Gutenberg-Richter relation:
describes the exponential distribution of earthquake magnitudes; usually written log10 N = a - bM, where N is the number of earthquakes with magnitude greater than or equal to M, a and b are the ordinate intercept and slope, respectively, of the line that relates M and log10 N

  historical catalog:
earthquake catalog that includes information about earthquakes that were not recorded by seismographs; the earthquake parameters have often been estimated from written accounts of shaking duration, observed damage, etc.

point inside the earth at which an earthquake began (usually specified by latitude, longitude, and depth)

 instrumental catalog:
earthquake catalog that only includes information about earthquakes that were recorded by seismographs

a measure at a particular location of an earthquake's effect (i.e., in terms of shaking) on objects at this location

 Kolmogorov-Smirnov test:
a statistical test used to compare a sample with a known distribution (one-sample K-S test) or to compare two samples (two sample K-S test). In the one-sample test, one wants to know if it is reasonable to believe that the sample comes from the specified distribution; in the two-sample test, one wants to know if it is reasonable that the two samples came from a common parent distribution

 local magnitude:
Generic magnitude originally based on the Richter scale in southern California, usually derived from the maximum amplitude (Amax) recorded on a seismogram (often proportional to log10Amax)

 lognormal distribution:
Continuous probability distribution used to model times between earthquakes in a given sequence

A measure of the size of an earthquake; see also local magnitude, moment magnitude


Typically refers to any large or damaging earthquake, or the largest earthquake in an earthquake sequence

 Markov model:
a stochastic model in which the probability distribution of the next system state depends only on the present system state, sometimes called a memoryless model

maximum likelihood:
Likelihood is the probability of a model parameter value given an observation, and maximum likelihood is a method for estimating model parameter vales based on maximizing the likelihood.

mean (average):
The sum of the observations in a sample divided by the number of observations. Also known as arithmetic mean.

median: a. (discrete sample) the middle observation of an ordered sample with an odd number of elements; the mean of the two middle observations of an ordered sample with an even number of elements, b. (continuous sample) the value above which 50% of the sample falls.

  moment magnitude:
Measure of the size of the earthquake derived from its seismic moment, advantageous because this scale does not saturate. On the other hand, it is difficult to measure seismic moment (and therefore moment magnitude) for small earthquakes

Monte Carlo:
Typically refers to a simulation based on drawing random numbers

Omori-Utsu relation:
describes the temporal evolution of an aftershock sequence, or the average temporal behavior of many aftershock sequences, usually characterized as a exponential reduction in occurrence rate in the wake of a large earthquake; alternatively known as the modified-Omori relation and usually written n(t) = k(t + c)-p, where n(t) is the rate of aftershocks at time t after the mainshock, k, c, and p are constants. c is sometimes considered to be a time delay before the exponential fall-off.

origin time:
time at which an earthquake began

a datum that is extremely different from a similarly collected population of data, often disregarded in analysis as it is considered not to be representative of the population

the probability that a measure at least as extreme as the observed measure would be observed under the null hypothesis. A small p-value is indicative that the null hypothesis is incorrect; in this situation, one often states that the observed measure is significant. For example, the p-value that Paul the Octopus could correctly predict the winner of seven consecutive German football matches and the World Cup final, given the null hypothesis that he was guessing randomly, is 0.58 = 0.00390625 (or 1 in 256).

study of historical earthquakes typically conducted by examining field observations of very old offsets, often performed by digging trenches and inferring information regarding pre-historic earthquakes from sediment records

 point process:
a type of stochastic model that defines probabilistic rules for the occurrence of points (i.e., earthquakes) in time and/or space. A marked point process also assigns a mark, or intensity, (i.e., magnitude) to each point.

 point source:
simplest model of an earthquake, in which the event is considered to have occurred at a particular point in the earth, usually only appropriate for very small events

 Poisson distribution:
Discrete probability distribution often used to model the number of earthquake occurring within a given time interval

unordered, without pattern

rate-and-state friction:
framework in which to understand how frictional processes work in the context of earthquakes; based on laboratory experiments in which static and dynamic friction were observed to vary with hold time and sliding velocity, respectively

 runs test:
non-parametric statistical test used to check the randomness of a sequence of data or whether the observations of a two valued data sequence are mutually independent

 seismic moment:
One measure of the size of an earthquake, based on estimated rupture area, average slip, and the average rigidity over the rupture area; in practice, usually obtained from analyzing seismograms

seismicity rate: Typically, the number of earthquakes in a specified interval of space-time-magnitude, normalized by the length of the time interval. The background seismicity rate is simply the rate of background earthquakes.

slip distribution:
amount of displacement in space and/or time for a particular earthquake, usually specified on a gridded fault representation

a piecewise polynomial function often used for interpolation or smoothing of data

standard deviation:
common measure of a data set's dispersion—i.e., how far do data points fall from the average data point?; square root of a data set's variance

unchanging; a point process is said to be stationary if its joint probability distribution doesn't change under a translation in space or time

random; a stochastic model may have a random component in addition to underlying deterministic components.

a measure of force per unit area, typically thought to control earthquake occurrence; stress is accumulated via loading by plate tectonics and released by deformation

synthetic earthquake catalog:
an earthquake catalog generated by a computer algorithm (as opposed to one based on actual earthquakes)

refers to a process that either does (time-dependent) or does not change (-independent) through time (terms time-varying and time-invariant may be preferred to reduce ambiguity)

 type I error/type II error:
errors to be avoided in statistical hypothesis testing, also known as false positive and false negative, respecticely.  A Type I error occurs when a correct null hypothesis is rejected, and a Type II error occurs when an incorrect null hypothesis is not rejected.

 triggered earthquake:
an earthquake that is thought to have been caused by a previous earthquake

measure of a data set's dispersion; average of the squared deviation of each data point from the sample mean


Gutenberg, B. & C.F. Richter,1954.  Seismicity of the Earth and Associated Phenomena, 2nd ed. (Princeton, N.J.: Princeton University Press, 1954), pp 17–19 ("Frequency and energy of earthquakes").

Utsu, T., 1961. A statistical study on the occurrence of aftershocks, Geophys. Mag. 30 (1961), pp. 521–605.