STATISTICAL ASPECTS OF PARKFIELD EARTHQUAKE SEQUENCE AND PARKFIELD PREDICTION EXPERIMENT

This note discusses three interconnected statistical problems concerni ng the Parkfield sequence of moderate earthquakes and the Parkfield pr ediction experiment: (a) Is it possible that the quasi-periodic Parkfi eld sequence of characteristic earthquakes is no uncommon, specific ph enomenon (the research hypothesis), but can be explained by a preferen tial selection from available earthquake catalogs? To this end we form ulate the null hypothesis (earthquakes occur according to the Poisson process in time and their size follows the Gutenberg-Richter relation) . We test whether the null hypothesis can be rejected as an explanatio n for the Parkfield sequence. (b) If the null hypothesis cannot be ref uted, what is the probability of magnitude m greater than or equal to 6 earthquake occurrence in the Parkfield region? (c) The direct goal o f the Parkfield experiment is the registration of precursory phenomena prior to a m6 earthquake. However, in the absence of the characterist ic earthquake, can the experiment resolve which of the two competing h ypotheses is true in a reasonable time? Statistical analysis is hinder ed by an insufficiently rigorous definition of the research model and inadequate or ambiguous data. However, we show that the null hypothesi s cannot be decisively rejected. The quasi-periodic pattern of interme diate size earthquakes in the Parkfield area is a statistical event li kely to occur by chance if it has been preferentially selected from av ailable earthquake catalogs. The observed magnitude-frequency curves f or small and intermediate earthquakes in the Parkfield area agree with the theoretical distribution computed on the basis of a modified Gute nberg-Richter law (gamma distribution), using deformation rates for th e San Andreas fault. We show that the size distribution of the Parkfie ld characteristic earthquakes can also be attributed to selection bias . According to the null hypothesis, the yearly probability of a m grea ter than or equal to 6 earthquake originating in the Parkfield area is less than 1%, signifying that several more decades of observation may be needed before the expected event occurs. By its design, the Parkfi eld experiment cannot be expected to yield statistically significant c onclusions on the validity of the research hypothesis for many decades .