A Statistical Model for Earthquake Recurrence Based on the Assimilation of Paleoseismicity, Historic Seismicity, and Instrumental Seismicity

Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long‐term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a “clock change” model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg‐Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.