An exploration of the relative influence of physical models for Omori’s law

Omori’s law states that the rate of aftershocks decays as a function of inverse time. There are multiple physical explanations that we reduce into a nonlinear mixed effects relation of three terms: (1) a Rate/State expression that can account for static/dynamic and viscoelastic triggering caused directly by the mainshock, (2) a fluid diffusion triggering term, and (3) a randomized secondary triggering (cascade) term. We fit free physical-model parameters to an observed aftershock sequence through two nonlinear regression methods to find the relative contributions of physics-based models in an observed aftershock sequence. Results from both methods show that Rate/State models overpredict aftershock rates by ∼0–30%. Secondary aftershocks cause a net negative contribution (seismicity rate reduction that corrects overprediction by other terms) ranging between ∼0 and 30%. All regression solutions yield negative secondary triggering contributions without being guided to do so. A physical explanation for this is that aftershock occurrence relieves stress from the crust, ultimately causing the sequence to extinguish itself. Fluid diffusion triggering contributions range from ∼0 to 20%. Diffusion processes are observed to be shorter in time than the full duration of an aftershock sequence and they are also spatially limited, diminishing their influence. Our results apply to an aftershock decay curve from the 2016 Central Apennines earthquake sequence, meaning that our specific results may not be general. Our primary conclusion is that any one physical model cannot alone fit the observed sequence as well as the combination of three we investigated.