A New Clustering-Function-Based Formulation of Temporal and Spatial Clustering Model Involving Area Scaling and its Application to Parameter Extraction

In this work, we develop a new clustering-function-based formulation of the temporal and spatial clustering model. This new formulation unifies the Weibull function and the clustering function into a common framework. By properly defining this clustering function, we show both the Weibull function and the clustering function have the same linear dependence on logarithmic time. More importantly, the area transformation of the clustering function is shown to be identical to that of the Weibull function. These two important properties allow us to apply the clustering function analysis methodology for the parameter extraction of experimental data, particularly with multiple areas. We demonstrate the validity of this methodology with its application to several experimental datasets with a new analysis of both T
BD
and Q
BD
data. We also discuss future improvements and limitations of the clustering model in excessive variability.