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## Maximum Entropy Modeling of Earthquake Recurrence from Paleoseismic Event Time Series

Glenn P. Biasi, & Fred Bookstein

Published August 14, 2020, SCEC Contribution #10560, 2020 SCEC Annual Meeting Poster #091

Conditional probability estimates of a ground rupturing earthquake depend heavily upon something we do not know: the shape of the recurrence model distribution. We present a new recurrence model approach based on information theory and entropy maximization that shows the additional information asserted when a lognormal (LN), Brownian Passage Time (BPT) or similar model is used. The maximum entropy (MaxEnt) approach models paleoseismic event recurrence directly from the observations. For an earthquake series with a coefficient of variation (CoV) <1.0, Bookstein (in review) finds that a truncated gaussian distribution is the only distributional shape consistent with maximizing [information] entropy, or alternatively, minimizing the assertion of data beyond what is actually in the observations themselves. The resulting truncated gaussian has intuitively satisfying qualities including precisely reproducing both the mean and the variance of the recurrence interval data.

The MaxEnt method can be compared to two alternate distribution types often used in seismic hazard estimates. The Poisson model is a one-parameter model but assumes ground ruptures are random in time at a uniform rate, and CoV=1.0. However, most paleoseismic series are at least mildly time predictable (CoV<1). The MaxEnt estimate gives a measure of the information cost (data underfit) of assuming the Poisson distribution. More often, two-parameter models with strictly positive domains are used such as the Weibull, LN, and BPT. Probabilities based on these models must be conditioned on the model shape, because their applicability to paleoseismic series is only assumed. Compared to MaxEnt, each of these models assumes more information than is actually in the data. The MaxEnt solution can appear less definite than corresponding conventional models, but what shape it does have is required by the data. This makes MaxEnt solutions appropriate for baseline calculations of time-dependent seismic hazard, including conditional probabilities, such as might be useful in an update to the UCERF3 Time Dependent model. In general, paleoseismic dating uncertainty “fuzzes” estimates, but has only a minor effect on conditional probability estimates. We illustrate this using paleoseismic time series from California.

Key Words
recurrence interval estimation, conditional probability, paleoseismic event series

Citation
Biasi, G. P., & Bookstein, F. (2020, 08). Maximum Entropy Modeling of Earthquake Recurrence from Paleoseismic Event Time Series. Poster Presentation at 2020 SCEC Annual Meeting.

Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)