Abstract
Long recurrence intervals of large earthquakes relative to the historical record mean that geological data are often utilized to inform forecasts of future events. Geological data from any particular fault may constrain the timing of past earthquakes (paleoearthquake data), or simply the time period over which a certain amount of fault displacement has occurred due to one or more earthquakes. These data are typically subject to large uncertainties, and available records often only constrain the timing of a few events. Variability in earthquake inter‐event times (aperiodicity) has been observed for many faults, particularly in low seismicity regions, further hampering the utilisation of small data sets for developing forecasts. A challenge for earthquake forecasting therefore concerns how best to utilize all of the limited available data while fully considering uncertainties. Here we present a concise Bayesian model for developing time‐dependent earthquake forecasts from geological data. Using the additive property of the Brownian passage time distribution, we make inference on the model parameters jointly from paleoearthquake and fault displacement data. Monte Carlo Markov Chain methods are used to sample the posterior distribution of model parameters, which is subsequently used to forecast future earthquake probabilities. The method incorporates data uncertainties and does not rely on a priori assumptions of quasiperiodic earthquake recurrence, allowing application in a wide range of tectonic settings. We demonstrate the method using data from two reverse faults in Otago, southern Aotearoa New Zealand, a region in which aperiodic earthquake recurrence has previously been observed.