A general dynamical cluster identification framework including both modeling and computation is developed. The earthquake declustering problem is studied to demonstrate how this framework applies.
A stochastic model is proposed for earthquake occurrences that considers the sequence of occurrences as composed of two parts: earthquake clusters and single earthquakes. We suggest that earthquake clusters contain a “mother quake” and her “offspring.” Applying the filtering techniques, we use the solution of filtering equations as criteria for declustering. A procedure for calculating maximum likelihood estimations (MLE’s) and the most likely cluster sequence is also presented.
"A cluster identification framework illustrated by a filtering model for earthquake occurrences." Bernoulli 15 (2) 357 - 379, May 2009. https://doi.org/10.3150/08-BEJ159