Given an earthquake with a specified magnitude and distance from a site of interest, Epsilon is a measure of how ground motion deviates from the expected mean. In most cases, one is interested in a ground motion that has a probability of being exceeded over some time period. This is often quite different than the most likely (or mean) ground motion that would be experienced if the event were to occur at any time and epsilon characterizes this variability.

Please see the USGS Deaggregation site for more detailed information and references