Issues in Characterization of Earthquake Sequences by Aperiodicity and Long-Term Fault Memory

A common way to characterize earthquake sequences and identify supercycles uses the aperiodicity or coefficient of variation, the ratio of the standard deviation of inter-event times to their mean. Sequences are often classified as perfectly periodic (aperiodicity = 0), 'quasiperiodic' (0 < aperiodicity < 1), Poissonian (aperiodicity = 1), or 'bursty' (aperiodicity > 1). Although aperiodicity has been used to describe and distinguish different earthquake recurrence behaviors, we explore issues with this measure. The first is the definition of 'quasiperiodic', which encompasses the entire range of behaviors between perfectly periodic and perfectly Poissonian. We divide this interval into a strongly periodic/weakly aperiodic portion (aperiodicity < 0.5) and a weakly periodic/strongly aperiodic portion (aperiodicity between 0.5 and 1). We use the term 'bursty' - rather than 'clustered' for aperiodicity > 1 because sequences with 'quasiperiodic' aperiodicity can be quite clustered. Earthquake sequences that would be considered clustered can fall below the nominal burstiness criterion, illustrating that a sequence must be very strongly clustered to be considered bursty. Another issue is that sequences with the same aperiodicity can be quite different. Because the aperiodicity depends only on the mean and standard deviation of the interevent times, it does not depend on the order of events. Thus, quite different sequences can have the same aperiodicity. Furthermore, sequences with aperiodicity close to 1 need not result from a Poisson process. Although they can resemble ones generated by a Poisson process, other stochastic processes, including a Long-Term Fault Memory process in which the probability drops after an earthquake, but not necessarily to zero as in the traditional earthquake cycle model, can also generate sequences with interevent times whose mean and standard deviation are similar. Finally, aperiodicity can vary within an earthquake record. In particular, it can be underestimated by short records that are likely to contain events with recurrence times shorter than the mean of a longer record. Hence a paleoseismic or instrumental record may not reflect the long-term seismicity of a fault, which has important implications for hazard assessment.