[S-SS10] Statistical seismology and underlying physical processes

[SSS10-10] Diverse characteristics of seismic activity in comparison with spatio-temporal ETAS forecasts

*Yosihiko Ogata¹ (1.Research Organization of Information and Systems, The Institute of Statistical Mathematics)

Keywords:Delaunay triangle partition network, Hierarchical spatiotemporal ETAS model, Software HIST-PPM, Long-term prediction, Quasi-real-time correction estimation

In order to represent and elaborate the various regionalisms of seismic activity, the regionalism of various seismic activity models requires appropriate parameter values for each earthquake location. The parameter values at the location of future earthquakes are interpolated by the values at the vertices of the triangle consisting of the locations of past earthquakes. For this purpose, a Delaunay triangle partition network is constructed from the past earthquake locations, and the local linear interpolation of the parameter values is called the Delaunay function. To estimate the model, an optimal solution for the coefficients of the parameter function can be obtained by maximizing the penalized log-likelihood under appropriate smoothing constraints on the Delaunay function¹⁾ . This allows for high-resolution images in areas with dense seismic sites and precise spatio-temporal predictions during periods of seismic activity.

For example, the hierarchical spatiotemporal (HIST) ETAS model²⁾ uses the Delaunay function as a key parameter of the spatiotemporal ETAS model, in addition to modeling the anisotropy of the earthquake concentration cluster geometry. In particular, the spatial intensity (occurrence rate) of background seismic activity varies over a range of several orders of magnitude within the seismogenic region, and the inversion solution, together with the magnitude-frequency function, has been found to be effective in predicting the location of large earthquakes over time. Nevertheless, they highlight the characteristics of diverse seismic activity.

Other HIST-ETAS parameters can also represent macroscopic regional characteristics of past seismic activity, but they may not always be able to predominantly predict various characteristics of specific future seismic activity anywhere and at any time. This suggests that the physical attributes of each seismogenic environment are highly heterogeneous and therefore unpredictable. The intensity of aftershocks, for example, is useful for providing standard short-term forecasts, but accurate individualized forecasts require quasi-real-time estimation.

In this presentation, the HIST-ETAS model and others. We will demonstrate the software HIST-PPM, which handles statistical models parameterized by Delaunay functions, and show various aspects of seismic activity.

Reference

1) Ogata, Y et al. (2021) Hierarchical Space-Time Point process models (HIST-PPM), Computer Science Monographs, No 35, The Institute of Statistical Mathematics, https://www.ism.ac.jp/editsec/csm/index_j.html
https://star-e.ism.ac.jp/information/software.html

2) Ogata Yosihiko YouTube avspredict5pa https://www.youtube.com/watch?v=l9r8pLVrYkE