Physics Colloquium - Friday, Apr. 25th, 2008, 4:00 P.M.

E300 Math/Science Center; Refreshments at 3:30 P.M. in Room E200

Jörn Davidsen
Complexity Science Group
Department of Physics and Astronomy
University of Calgary

Scaling, universality and spatio-temporal clustering in seismicity and rock fracture phenomena

Many striking features of natural processes including seismicity can be portrayed as patterns or clusters of localized events. A generic attribute in all these cases is that one event can trigger or somehow induce another one to occur - or possibly numerous further events. Sometimes, an accounting of causal connections between clustered events is explicitly rationalized by the microscopic state and rules of the dynamical system. More often than not, though, the causal connections cannot be resolved from the data at hand and remain ambiguous. Thus, one is confronted with inferring a plausible causal structure from clusters of localized events without a detailed or "fundamental" knowledge of the true microscopic dynamics. I will present a method to search for such signs of causal structure in spatio-temporal data making minimal a priori assumptions about the underlying microscopic dynamics. To this end, the elementary concept of recurrence for a point process in time is generalized to recurrent events in space and time. For earthquakes, the method in particular allows to recover the scaling of the rupture length with magnitude. Moreover, I will present a detailed statistical analysis of acoustic emission time series from a range of rock fracture experiments. In all considered cases, the waiting time distribution can be described by a unique scaling function indicating its universality. This scaling function is even indistinguishable from that for earthquakes suggesting its general validity for fracture processes independent of time, space and magnitude scales.