  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.
