Here, we extend the Fisher-Kolmogorov-Petrovsky-Piskunov equation to capture the interplay of multiscale and multiphysics coupled processes. We use a minimum of two coupled reaction-diffusion equations with additional nonlocal terms that describe the coupling between scales through mutual cross-diffusivities and regularise the ill-posed 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: 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, for negligible self-diffusion, lead to an extreme focusing of wave intensity into a short sharp earthquake-like event. We propose a first step approach for detection of these dissipative waves, expected to precede a large scale instability.

Here, we extend the Fisher-Kolmogorov-Petrovsky-Piskunov equation to capture the interplay of multiscale and multiphysics coupled processes. We use a minimum of two coupled reaction-diffusion equations with additional nonlocal terms that describe the coupling between scales through mutual cross-diffusivities. This system of equations incorporates the physics of interaction of thermo-hydro-chemo-mechanical processes and can be used to understand a variety of localisation phenomena in nature. Applying bifurcation theory to the system of equations suggests that geological patterns can be interpreted as physical representation of three classes of well-known instabilities: Turing instability, Hopf bifurcation, and a chaotic regime of complex soliton-like waves. For specific parameters, the proposed system of equations predicts all three classes of instabilities encountered in nature. The third class appears for small fluid release reactions rates as a slow quasi-soliton wave for which our parametric diagram shows possible transition into the Hopf- or Turing-style instability upon dynamic evolution of coefficients.