Abstract. The Thirulamai-Mountain (TM) metric was first developed to study ergodicity in fluids and glasses (Thirumalai and Mountain, 1993) using the concept of effective ergodicity, where a large but finite time interval is considered. Tiampo et al. (2007) employed the TM metric to earthquake systems to search for effective ergodic periods, which are considered to be metastable equilibrium states that are disrupted by large events. The physical meaning of the TM metric for seismicity is addressed here in terms of the clustering of earthquakes in both time and space for different sets of data. It is shown that the TM metric is highly dependent not only on spatial/temporal seismicity clustering, but on the past seismic activity of the region and the time intervals considered as well, and that saturation occurs over time, resulting in a lower sensitivity to local clustering. These results confirm that the TM metric can be used to quantify seismicity clustering from both spatial and temporal perspectives, in which the disruption of effective ergodic periods are caused by the agglomeration of events.
Caputo Fractional Differential Equations with Non-Instantaneous Random Erlang Distributed Impulses
