5:15 PM - 6:45 PM
[SCG55-P08] Objective Judgement of Time Variation in the Stress-field Inversion Using Gaussian Processes
The stress state in the Earth's crust provides fundamental insights into seismotectonics. The spatial distribution of regional stress fields has been estimated through inversion analyses of seismological data (e.g., Terakawa and Matsu'ura, 2010; Uchide et al., 2022). By estimating temporal changes in stress fields, it may be possible to extract information on earthquake preparation processes and postseismic stress relaxation. Due to computational and other methodological limitations, temporal changes of a stress field have been evaluated by dividing the observational data into several periods, assuming a constant stress field in each period, and by comparing the estimated results (e.g., Hardebeck and Michael, 2006; Terakawa and Matsu’ura, 2023). Because the stress direction shown by each focal mechanism can have a large variety, it is important to objectively determine whether the estimated temporal changes reflect true stress changes.
Okazaki et al. (2022) developed a method to estimate spatiotemporal distribution of the stress field around Japan using Gaussian processes. By analyzing the Centroid Moment Tensor (CMT) data after the 2011 Tohoku-oki earthquake, they revealed the characteristics of stress changes around the focal region. Gaussian processes enable the objective selection of hyperparameters (e.g., amplitude and correlation distance) based on the criterion of the marginal likelihood maximization. In this study, through an analysis of real data, we show that we can objectively judge the presence of temporal changes of a stress field.
The CMT solutions were obtained from the F-net catalog in the Tohoku region during 2003–2019. Considering the significant changes in seismic activity after the Tohoku-oki earthquake, we estimated the spatiotemporal variations of the stress field for three datasets: (i) the pre-earthquake, (ii) the post-earthquake, and (iii) the entire periods. We particularly focused on optimal values of a hyperparameter regarding the characteristic time scale of stress variations (correlation time). First, in the pre-earthquake period (i), the marginal likelihood monotonically increased with the correlation time, indicating that the stress field before the Tohoku earthquake was stationary. In contrast, in the post-earthquake period (ii), the marginal likelihood reached its maximum at a correlation time of 19 years, suggesting a slight but significant temporal change occurred after the Tohoku-oki earthquake. In the entire period (iii), the correlation time was determined to be 8 years suggesting a considerable temporal change in stress fields.
Furthermore, we explored a method to detect whether the stress field underwent a stepwise change due to earthquakes or other factors. The approach is realized by modifying the values of the covariance function in the Gaussian process around a specific time within the analysis period and by optimizing the hyperparameter value that define the extent of this change based on the maximization of the marginal likelihood. When we took the specific time at the beginning of 2014, for the data set of the post-earthquake period (ii), we obtained an optimal value indicating no significant stepwise change, which demonstrates the robustness of this method against random partitioning. On the other hand, when we took the specific time at the time of the Tohoku-oki earthquake, for the data set of the entire period (iii), we obtained the optimal value suggesting a significant stepwise change had occurred. In summary, the criterion of the marginal likelihood maximization in the Gaussian process inversion works effectively in objectively determining the significance of temporal changes.
Okazaki et al. (2022) developed a method to estimate spatiotemporal distribution of the stress field around Japan using Gaussian processes. By analyzing the Centroid Moment Tensor (CMT) data after the 2011 Tohoku-oki earthquake, they revealed the characteristics of stress changes around the focal region. Gaussian processes enable the objective selection of hyperparameters (e.g., amplitude and correlation distance) based on the criterion of the marginal likelihood maximization. In this study, through an analysis of real data, we show that we can objectively judge the presence of temporal changes of a stress field.
The CMT solutions were obtained from the F-net catalog in the Tohoku region during 2003–2019. Considering the significant changes in seismic activity after the Tohoku-oki earthquake, we estimated the spatiotemporal variations of the stress field for three datasets: (i) the pre-earthquake, (ii) the post-earthquake, and (iii) the entire periods. We particularly focused on optimal values of a hyperparameter regarding the characteristic time scale of stress variations (correlation time). First, in the pre-earthquake period (i), the marginal likelihood monotonically increased with the correlation time, indicating that the stress field before the Tohoku earthquake was stationary. In contrast, in the post-earthquake period (ii), the marginal likelihood reached its maximum at a correlation time of 19 years, suggesting a slight but significant temporal change occurred after the Tohoku-oki earthquake. In the entire period (iii), the correlation time was determined to be 8 years suggesting a considerable temporal change in stress fields.
Furthermore, we explored a method to detect whether the stress field underwent a stepwise change due to earthquakes or other factors. The approach is realized by modifying the values of the covariance function in the Gaussian process around a specific time within the analysis period and by optimizing the hyperparameter value that define the extent of this change based on the maximization of the marginal likelihood. When we took the specific time at the beginning of 2014, for the data set of the post-earthquake period (ii), we obtained an optimal value indicating no significant stepwise change, which demonstrates the robustness of this method against random partitioning. On the other hand, when we took the specific time at the time of the Tohoku-oki earthquake, for the data set of the entire period (iii), we obtained the optimal value suggesting a significant stepwise change had occurred. In summary, the criterion of the marginal likelihood maximization in the Gaussian process inversion works effectively in objectively determining the significance of temporal changes.