Statistical Modeling of Spatial-Temporal Fields of Earthquakes

Annotation For given history (X{t,x};Yt) before moment T, t ∈ [0;T], rise alarm in window [T ; T + δ1] when failure event arises in window [T + δ1; T + δ1 + δ2]. Data is failures Yt: (yt)Tt=1 ∈ {0, 1} and (X(t,x))Tt=1: for each fixed index {x}, Xt is multivariate timeseries of features: (Xt1, . . . , Xtj ) Index {x} could be both Rd and I ⊂ N. Examples of such tasks are: prediction of breakages in complex technical systems, prediction of natural disasters. In this paper we focus on the prediction of earthquakes Proposed precursor The Poisson model of earthquakes is considered. The parameter intensity is parameterized as a linear function of covariates. Using the Bayesian inference, a posteriori distributions are obtained for the parameters of the model, which will be a harbinger. Using the matrix identities, the nuclear form of precursors has also been obtained. Proposed clusterization method It is assumed that aftershocks and foreshocks follow one direction. Thus, it is possible to model earthquake sequences clustering them along directions. A model based on a mixture of regressions is proposed. Variational Bayesian inference was used. Results A new precursor of earthquakes was obtained in the work, which showed its importance in experiments. Having complicated its structure, it was possible to keep the closed form, which makes its recalculation with the arrival of new data fast. It also received its sound version. A method for decalcling the earthquake catalog based on a mixture of regressions is proposed. The algorithm is tested on the data of Japan and Italy. The result obtained surpassed the standard classification algorithms. 1