Pseudo-prospective testing of 5-year earthquake forecasts for California using inlabru

Abstract. Probabilistic earthquake forecasts estimate the likelihood of future earthquakes within a specified time-space-magnitude window and are important because they inform planning of hazard mitigation activities on different time scales. The spatial component of such forecasts, expressed as seismicity models, generally relies upon some combination of past event locations and underlying factors which might affect spatial intensity, such as strain rate, fault location and slip rate or past seismicity. For the first time, we extend previously reported spatial seismicity models, generated using the open source inlabru package, to time-independent earthquake forecasts using California as a case study. The inlabru approach allows the rapid evaluation of point process models which integrate different spatial datasets. We explore how well various candidate forecasts perform compared to observed activity over three contiguous 5-year time periods using the same training window for the input seismicity data. In each case we compare models constructed from both full and declustered earthquake catalogues. In doing this, we compare the use of synthetic catalogue forecasts to the more widely used grid-based approach of previous forecast testing experiments. The simulated catalogue approach uses the full model posteriors to create Bayesian earthquake forecasts, not just the mean. We show that simulated catalogue based forecasts perform better than the grid-based equivalents due to (a) their ability to capture more uncertainty in the model components and (b) the associated relaxation of the Poisson assumption in testing. We demonstrate that the inlabru models perform well overall over various time periods: The full catalogue models perform favourably in the first testing period (2006–2011) while the declustered catalogue models perform better in the 2011–2016 testing period, with both sets of models performing less well in the most recent (2016–2021) testing period. Together, these findings demonstrate a significant improvement in earthquake forecasting is possible although this has yet to be tested and proven in true prospective mode.