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[SCG44-P32] Preliminary forecasting model for tectonic tremor activity using a renewal process
Keywords:tectonic tremor, slow earthquake, renewal process
Various statistical models for probabilistic earthquake forecast have been developed. However, there are not many researches for forecasting slow earthquakes. Among slow earthquakes, tectonic tremors have been observed all over the world and summarized in various catalogs. Since episodic tremor activity occurs every a few months, they seem to be easy to forecast. However, there is no commonly accepted way to group successive tremors to quantify episodic activity, and it is not obvious what values to forecast. Therefore, in order to construct a framework for forecast the "next tremor activity", we conduct modeling and forecast experiments using the renewal process for tremor time series.
In this study, we use the catalog of deep tectonic tremor in Nankai subduction zone, southwest Japan published by Mizuno and Ide (2019, EPS). The inter-event time between successive tremors at a given location has a bimodal distribution with peaks in the long term (several months) and short term (several hours). The distribution around the long-term peaks is modeled by the Brownian Passage Time distribution, which is often used in forecast models of characteristic earthquakes, and that around the short-term peaks are modeled by the lognormal distribution. These two distributions are combined with a parameter indicating the mixing ratio of the two distributions. Then each tremor time series is approximated as a renewal process with a mixture distribution described by these five parameters: two parameters for two distributions and a mixing ratio. The parameters were estimated by the maximum likelihood method for the inter-event time distributions of about 500 regional groups. For most (~80%) groups, the time series transformed by the event rate of each interval were regarded as a stationary Poisson process. For groups that cannot be regarded as a stationary Poisson process, it is possible to objectively extract an irregular period using AIC. This is useful, for example, for quantifying an irregular period of tremor activity associated with a long-term slow slip event.
The parameters estimated for each group can be used to estimate the timing of the next tremor from the time of the previous tremor at any given time, with predictive intervals, or to calculate the probability of tremor occurrence for a given period. The spatial variation of the estimated parameters is related to regional tremor activity. This statistical model will be useful as a basis for incorporating tidal response and spatio-temporal extension in the future.
In this study, we use the catalog of deep tectonic tremor in Nankai subduction zone, southwest Japan published by Mizuno and Ide (2019, EPS). The inter-event time between successive tremors at a given location has a bimodal distribution with peaks in the long term (several months) and short term (several hours). The distribution around the long-term peaks is modeled by the Brownian Passage Time distribution, which is often used in forecast models of characteristic earthquakes, and that around the short-term peaks are modeled by the lognormal distribution. These two distributions are combined with a parameter indicating the mixing ratio of the two distributions. Then each tremor time series is approximated as a renewal process with a mixture distribution described by these five parameters: two parameters for two distributions and a mixing ratio. The parameters were estimated by the maximum likelihood method for the inter-event time distributions of about 500 regional groups. For most (~80%) groups, the time series transformed by the event rate of each interval were regarded as a stationary Poisson process. For groups that cannot be regarded as a stationary Poisson process, it is possible to objectively extract an irregular period using AIC. This is useful, for example, for quantifying an irregular period of tremor activity associated with a long-term slow slip event.
The parameters estimated for each group can be used to estimate the timing of the next tremor from the time of the previous tremor at any given time, with predictive intervals, or to calculate the probability of tremor occurrence for a given period. The spatial variation of the estimated parameters is related to regional tremor activity. This statistical model will be useful as a basis for incorporating tidal response and spatio-temporal extension in the future.