Seismicity Pattern Dynamics & Rock Fracture

What do we know about earthquakes? Either a lot or very little, depending on the point of view and on the adopted definition of earthquake. If an earthquake is defined to be the slip on a fault (or faults) that produces the observed seismic wavefield, then we have a good understanding of earthquakes. In contrast to the earthquake kinematics, however, it is indisputable that there is not yet a satisfactory understanding of the physical processes in the lithosphere that cause slip on faults and are, thus, responsible for the dynamics of earthquakes. This dynamics involves a vast range of space- and timescales and manifests itself in a number of empirical and emergent features of earthquake occurrence including spatiotemporal clustering, long-range space-time correlations, as well as self-similar scaling laws like the Gutenberg-Richter law giving rise to a worldwide dispute about their reason. The origin of these non-trivial emergent features of earthquake occurrence is one of the main unresolved problems in the field.

Resolving this issue may require measuring the internal state variables – the stress and strain at every point within the earth along active earthquake faults – and their exact microscopic dynamics. This is (currently) impossible. Yet, the associated earthquake patterns are readily observable making macroscopic approaches based on the concept of spatiotemporal point processes feasible, where the description of each earthquake is reduced to its size or magnitude, its epicenter and its time of occurrence. Describing the patterns of seismicity may shed light on the fundamental physics since these patterns are emergent processes of the underlying many-body nonlinear system.

Utilizing such an approach, Davidsen & Goltz (2004); Davidsen & Paczuski (2005, 2007); Davidsen et al. (2006, 2008b) have discovered new key features of the dynamics of seismicity, which can conceivably be exploited for earthquake prediction in the future. The observed spatiotemporal clustering of earthquakes indicates that the usual mainshock/aftershock scenario — where each event has at most one correlated predecessor — is too simplistic and the causal structure of seismicity extends beyond immediately subsequent events. This paradigm shift was especially supported by a unique approach to quantify non-trivial spatiotemporal clustering and to infer the causal structure of seismicity based on the view that any suitable definition of clustering should be purely contextual and depend only on the actual history of events. The approach utilizes the notion of space-time records and maps seismicity onto a graph providing a new and independent estimate of the rupture length and its scaling with magnitude.

To put the findings for seismicity into a broader perspective, it is essential to compare them with theoretical models (Peixoto & Davidsen, 2008) as well as anthropogenically induced seismicity and rock fracture processes. Recent laboratory studies of rock fracture (Davidsen et al., 2007) indicate that acoustic emissions due to microcracks can be considered analogous to earthquake sequences and share many of the same behaviors despite the vastly different length, time and energy scales involved. In particular, the precise microscopic details of the material or the way of fracturing does not play a significant role. The scale-invariance suggests that it is sufficient to study fracture at the scale of lab experiments to understand these features at the scale of earthquakes.