an:01202964
Zbl 0947.62061
Ogata, Yosihiko
Space-time point-process models for earthquake occurrences
EN
Ann. Inst. Stat. Math. 50, No. 2, 379-402 (1998).
00048828
1998
j
62M30 86A15 62P12
centroid of aftershock epicenters; ETAS model; inverse power laws; maximum likelihood estimates; magnitude based clustering algorithm; modified Omori formula; thinning simulation; MBC; epidemic type aftershock-sequence
Summary: Several space-time statistical models are constructed based on both classical empirical studies of clustering and some more speculative hypotheses. Then we discuss the discrimination between models incorporating contrasting assumptions concerning the form of the space-time clusters. We also examine further practical extensions of the model to situations where the background seismicity is spatially non-homogeneous, and the clusters are nonisotropic. The goodness-of-fit of the models, as measured by AIC values, is discussed for two high quality data sets, in different tectonic regions. AIC also allows the details of the clustering structure in space to be clarified.
A simulation algorithm for the models is provided, and used to confirm the numerical accuracy of the likelihood calculations. The simulated data sets show the similar spatial distributions to the real ones, but differ from them in some features of space-time clustering. These differences may provide useful indicators of directions for further study.