Spatiotemporal Evolution of Seismic Swarms in the light of the Continuous Time Random Walk Model

Seismic swarms are characterized by intense seismic activity strongly clustered in time and space and without the occurrence of a major event that can be considered as the mainshock. Such intense seismic activity is most commonly associated with external aseismic factors, as pore-fluid pressure diffusion, aseismic creep, or magmatic intrusion that can perturb the regional stresses locally triggering the observed seismicity. These factors can control the spatiotemporal evolution of seismic swarms, frequently exhibiting spatial expansion and migration of event hypocenters with time. This phenomenon, termed as earthquake diffusion, can be highly anisotropic and complex, with earthquakes occurring preferentially along fractures and zones of weakness within the heterogeneous crust, presenting anisotropic diffusivities that may locally vary over several orders of magnitude. The efficient modelling of the complex spatiotemporal evolution of seismic swarms, thus, represents a major challenge. Herein, we develop a stochastic framework based on the well-established Continuous Time Random Walk (CTRW) model, to map the spatiotemporal evolution of seismic swarms. Within this context, earthquake occurrence is considered as a point-process in space and time, with jump lengths and waiting times between successive earthquakes drawn from a joint probability density function. The spatiotemporal evolution of seismicity is then described with an appropriate master equation and the time-fractional diffusion equation (TFDE). The applicability of the model is demonstrated in the 2014 Long Valley Caldera (California) seismic swarm, which has been associated with a pore-fluid pressure triggering mechanism. Statistical analysis of the seismic swarm in the light of the CTRW model shows that the mean squared distance of event hypocenters grows slowly with time, with a diffusion exponent much lower than unity, as well as a broad waiting times distribution with asymptotic power law behavior. Such properties are intrinsic characteristics of anomalous earthquake diffusion and particularly subdiffusion. Furthermore, the asymptotic solution of the TFDE can successfully capture the main features of earthquake progression in time and space, showing a peak of event concentration close to the initial source of the stress perturbation and a stretched relaxation of seismicity with distance. Overall, the results demonstrate that the CTRW model and the TFDE can efficiently be used to decipher the complex spatiotemporal evolution of seismic swarms.

Acknowledgements

The research project was supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “2nd Call for H.F.R.I. Research Projects to support Post-Doctoral Researchers” (Project Number: 00256).