Plain Language Summary
The question of whether earthquake occurrence is random in time, or
perhaps chaotic with order hidden in the chaos, is of major importance
to the determination of risk from these events. It was shown many years
ago that if aftershocks are removed from the earthquake catalogs, what
remains are apparently events that occur at random time intervals, and
therefore not predictable in time. In the present work, we enlist
machine learning methods using Receiver Operating Characteristic (ROC)
analysis. With these methods, probabilities of large events and their
associated information value can be computed. Here information value is
defined using Shannon Information Entropy, shown by Claude Shannon
(Shannon, 1948) to define the surprise value of a communication such as
a string of computer bits. Random messages can be shown to have high
entropy, surprise value, or uncertainty, whereas low entropy is
associated with reduced uncertainty and high reliability. An earthquake
nowcast probability associated with reduced uncertainty and greater
reliability is most desirable. Examples of the latter could be the
statements that there is a 90% probability of a major earthquake within
3 years, or a 5% chance of a major earthquake within 1 year. Despite
the random intervals between major earthquakes, we find that it is
possible to make low uncertainty, high reliability statements on current
hazard by the use of machine learning methods.