Subsurface propagation of thermomechanical kinks through hydrothermal fluid‐saturated porous horizons

Abstract

In this paper a one‐dimensional nonlinear analytical model for the mechanism of subsurface fluid‐rock coupling dynamics in hydrothermal systems is proposed. The model is based upon the modern thermoporoelasticity theory and its two nonlinear heatlike equations, namely, the stress diffusion equation and the fluid‐rock energy equation. On the lower boundary of a subsurface fluid‐saturated porous horizon a buried thermomechanical source is supposed to build up so that coupled fluid‐rock temperature and pore fluid pressure changes are generated. These changes are thought of as being related to the Heaviside step function, which is here adopted as the initial condition to be combined with Burgers' equation, obtained in the case of small fluid diffusivity in the stress diffusion equation. By using the Hopf‐Cole transformation an analytical solution corresponding to a solitary wave such as a thermomechanical kink is found that propagates upward through the fluid‐saturated thermoelastically reactive porous horizon, thus supplying changes in the thermomechanical properties of the fluid emissions as the wave approaches the ground surface. Some cases of episodes of unrest are considered for some hydrothermal systems, showing the agreement between our theoretical curves of fluid surface signals and the enhanced activity in the fluid emissions. In this connection the upsurge of thermomechanical solitary shock waves such as kinks can be used as an indicator of thermal energy buildup and approaching mechanical destabilization at depth in both volcanic and geothermal systems.