Controlling Anthropogenic and Natural Seismicity: Insights From Active Stabilization of the Spring-Slider Model

摘要

We present a theoretical study focusing on exploring the possibility of controlling anthropogenic and natural seismicity.We actively control the pressure of injected fluids using a negative-feedback control system. Our analysis is based on the spring-slider model for modeling the earthquake instability.We use a general Coulomb-type rheology for describing the frictional behavior of a fault system. This model leads to a nonautonomous system, whose steady state and stability are studied using a double-scale asymptotic analysis. This approach renders the dominant order of the system time invariant. Established tools from the classical mathematical theory of control are used for designing a proper stabilizing controller.We show that the system is stabilizable by controlling fluid pressure. This is a central result for industrial operations. A stabilizing controller is then designed and tested. The controller regulates in real time the applied pressure in order to assure stability, avoid unwanted seismicity, and drive the system from unstable states of high potential energy, to stable ones of low energy. The controller performs well even in the absence of complete knowledge of the frictional properties of the system. Finally, we present two numerical examples (scenarios) and illustrate how anthropogenic and natural earthquakes could be, in theory, prevented.