Resolving bias due to short- and long-term catalogue incompleteness and improving accuracy by optimal sampling in the epidemic-type aftershock sequence (ETAS) model

Abstract

Earthquake catalogues are fundamental tools for understanding seismic processes and forecasting future events. However, these catalogues are often associated with different degrees of incompleteness, including data gaps immediately after the occurrence of large earthquakes due to waveform overlaps and seismogram saturation, as well as long-term gaps arising from technological and logistical limitations in the development of seismic networks. Such incompleteness in data can lead to substantial errors and biases in earthquake models and therefore distort our understanding of seismicity behaviour in a region. Furthermore, statistical modelling is highly sensitive to how we select data samples from these catalogues, and this can also significantly impact the estimations of seismicity model parameters.

This thesis presents significant advances in the field of seismicity modelling by enhancing the Epidemic-Type Aftershock Sequence (ETAS) model. The primary goal is to address critical issues of temporal incompleteness and systematic biases that affect the estimation of ETAS parameters, which are essential for accurate earthquake forecasting and seismic hazard assessments.

In this thesis, I first address the issue of short-term incompleteness commonly observed following large mainshocks. This period of incompleteness is critical because it involves the initial aftershock sequence, which can provide valuable insight into the seismicity rates and properties of a seismic sequence. I introduce a methodological enhancement to the inversion algorithm of the ETAS model, which enables it to effectively handle incomplete data during these crucial early stages. Theoretically, this adjustment involves defining a censorship function and integrating it into the ETAS conditional intensity and likelihood functions to create a modified inversion solution. For model implementation, I use a Bayesian framework with the inlabru package, which leverages the Integrated Nested Laplace Approximation (INLA) method to provide posterior distributions of the model parameters, rather than conventional point estimates. The performance of the modified ETAS model is extensively tested through synthetic experiments designed to simulate realistic aftershock sequences with short-term incompleteness, demonstrating its ability to accurately capture ETAS parameters and actual aftershock rates even with significant data gaps.

Further, I explore optimising the selection of representative samples for the ETAS inversions, which is critical for reducing bias in parameter estimation. Various sampling strategies and their potential biases are examined, proposing a comprehensive approach to optimise survey design. This includes evaluating the sensitivity of the ETAS model to temporal binning strategies, conditioning the model on the run-in history before an earthquake sequence, the role of combination of different earthquake magnitudes, and the trade-offs between ETAS productivity parameters. I also consider the choice of incompleteness model parameters, the impact of secondary large aftershocks, and the spatial and temporal size of the modelling domain. By systematically analysing these factors, I establish guidelines that identify and minimise biases and enhance the reliability and robustness of modelling seismicity patterns when fitting the ETAS model to real earthquake data.

Finally, I expand the model’s applicability to address long-term data incompleteness, which stems from sparse network coverage and technological limitations over extended periods. This comprehensive approach significantly improves the predictive accuracy of the ETAS model, as evidenced by its application to both simulated data and real earthquake sequences. By applying the same censorship approach used for addressing short-term incompleteness, I extend the model to handle incomplete long-term data, such as century-long records from the instrumental era, that also lack distinct aftershock sequences. As a result, with this new generic framework, the ETAS model adapts to varying degrees of data completeness, ensuring robust parameter estimation even when faced with extensive temporal gaps. The enhancements to the ETAS model introduced in this thesis significantly strengthen its theoretical foundations and practical utility in delivering more reliable and flexible operational earthquake forecasts and seismic hazard assessments.