Modelling Seismicity in California as a Spatio-Temporal Point Process Using inlabru: Insights for Earthquake Forecasting

Earthquake forecasts rely upon a solid understanding of spatial and temporal patterns of seismicity. Recent testing of earthquake forecasts has identified model elements which perform well, and therefore has demonstrated the need for a robust method for identifying the model components which are most beneficial to understanding patterns of seismicity. Borrowing from ecology, we use log-Gaussian Cox process models to describe the spatially varying intensity of earthquake locations. These models are constructed using components which may influence where earthquakes occur, including the underlying fault map and past seismicity models, and a random field to account for any excess spatial variation that cannot be explained by deterministic model components. These models can be fitted in a computationally-efficient manner using integrated nested Laplace approximations, allowing the rapid construction and comparison of many different models containing different combinations of components.

Comparing alternative models allows the assessment of the performance of different model components, and therefore identifies which components are most useful for describing the distribution of observed earthquake locations. We demonstrate the effectiveness of this approach using synthetic data and by making use of the earthquake and fault information available for California. We show the flexibility of this model approach, how it might be applied in areas where we do not have the same abundance of detailed information and how such an approach could be used to construct forecasts that make best use of available datasets.