**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

**random**:

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

**spline**:

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

**stationary**:

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

**stochastic**:

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

**stress**:

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)

**time-dependent/time-independent**:

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

**variance**:

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

### References

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.