Cross-scale dynamic interactions in compacting porous geomaterials as a trigger to instabilities

Abstract

We present an approach to model material bifurcations derived from the dynamic interplay of at least two coupled reaction-diffusion processes dur-ing compaction of porous media. Our new approach introduces nonlocal terms that describe the coupling between scales through mutual cross-diffusivities and regularize the ill-posedness of the reaction-self-diffusion system. Applying bifurcation theory, we suggest that geological patterns can be interpreted as physical representations of two classes of well-known instabilities, i.e., Turing instability, Hopf bifurcation, and a new class of complex soliton-like waves. The new class appears for small fluid release reactions rates which may, with negligible self-diffusion, lead to an extreme focusing of wave intensity into a short sharp earthquake-like event. Here we investigate the phenomenon of episodic tremor and slip instability of time-periodic slip events recorded in subduction zones. It is shown that the instability is a Hopf bifurcation and our inversion of the recorded events conclusively shows that episodic fluid release from serpentinite dehydra-tion is the cause for the sudden slip events as postulated earlier. Our analy-sis further allows derivation of chemical reaction rates under geodynamic loading conditions opening the path for physics/chemistry-based forecast-ing of catastrophic instabilities in nature.