Non-local reaction-diffusion instabilities in geomaterials and geosystems : modeling and potential applications

Abstract

Reaction-diffusion instabilities are ubiquitous in geological and geophysical con- texts, where the underlying THMC processes can be driven out of equilibrium, resulting in self-regulated spatial or temporal patterns. Such pattern formation instabilities are crucial for the modulation of strain partitioning and mass transport within geomaterials, and may also serve as precursors to catastrophic events in geosystems. Hence, it is of paramount importance to understand the mechanisms underpinning these instability phenomena.

This thesis proposes a generalized reaction-diffusion model for the investigation of pattern formation instabilities in geomaterials and geosystems. The model extends classical formulations by incorporating non-local feedback, which regularises the ill-posedness for post-instability evolution. With the combination of theoretical and numerical analyses, the proposed model unlocks a rich solution space of instabilities and provides an enhanced perspective on the pat- tern formation covering both quasi-static and dynamic regimes.

The derived model has been used to elucidate a wide spectrum of patterns observed in experimental and field studies, including compaction bands in porous rocks, melt segregation channels in migmatites, and episodic tremor and slip events in subduction zones. The findings illustrate that the non-local reaction-diffusion formalism can effectively capture the spatio-temporal characteristics of the instabilities of various sorts, highlighting the role that the nonlocal interaction plays in the pattern formation process.

This study provides a solidifying step towards a new reaction-diffusion based framework for the modelling of geological and geophysical patterns. The results have the potential to shed light on the evolution and development of terrestrial instabilities and hence aid in the mitigation of natural hazards and the efficient management of geological resources in the long run.