Estimating Inhomogeneous Spatio-Temporal Background Intensity Functions using Graphical Dirichlet Processes

Abstract

An enhancement in seismic measuring instrumentation has been proven to have implications in the quantity of observed earthquakes, since denser networks usually allow recording more events. However, phenomena such as strong earthquakes or even aseismic transients, as slow slip earthquakes, may alter the occurrence of earthquakes. In the field of seismology, it is a standard practice to model background seismicity as a Poisson process. Based on this idea, this work proposes a model that can incorporate the evolving spatial intensity of Poisson processes over time (i.e., we include temporal changes in the background seismicity when modeling). In recent years, novel methodologies have been developed for quantifying the uncertainty in the estimation of the background seismicity in homogeneous cases using Bayesian non-parametric techniques. This work proposes a novel methodology based on graphical Dirichlet processes for incorporating spatial and temporal inhomogeneities in background seismicity. The proposed model in this work is applied to study the seismicity in the southern Mexico, using recorded data from 2000 to 2015.

Figures (10)

• Figure 1: Graphical Dirichlet Process denoting time dependency
• Figure 2: $\lambda$ evaluated at different times
• Figure 3: Posterior mean of $\lambda$
• Figure 4: Posterior mean of $\lambda$ with transparency based on the coefficient of variation using simulated data
• Figure 5: Histogram of the posterior $\gamma_p$, $p=1,2,...,P$ using simulated data, blue dashed lines are the real $\gamma_p$ for each interval