Zach Horton

UC Santa Cruz

“Dependent Sojourn Markov Renewal Processes: A More Realistic Approach to Modeling Earthquake Recurrence”

In earthquake forecasting, a Markov renewal process can be used to model the time until the next earthquake using both the amount of time that has elapsed so far and the magnitude of the previous event. This model describes the sequence of magnitude categories, or states, as a Markov chain, then conditionally models inter-event times within
each state-to-state transition case. Estimating the inter-event time distributions is often done by treating each state-to-state transition case as independent. This project aims to address the setting where transition cases are not independent, which more accurately reflects
the nature of earthquake recurrence. By modeling dependency using Bayesian nonparametrics, we enable sharing of information between cases and provide both a more realistic picture of underlying mechanics and more reliable insight into earthquake recurrence characteristics.


Large earthquake recurrences are typically modeled using both magnitudes and inter-event times. However, the most commonly used methodlogies impose assumptions about data independence that, while subtle, are critically flawed. This work aims to develop a modeling framework capable of resolving the erroneous independence issue and ultimately strives for greater reliability in studying earthquake recurrence properties.

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