Analyzing Earthquake Energy: Unveiling the Spectrum of Fault Behavior in Terms of Moment, Duration, and Rupture Speed

Seismic observations confirm that natural fault systems radiate waves across a continuum of frequency and amplitude. Within this spectrum, faulted systems exhibit a continuous range of slip rates, allowing them to irreversibly dissipate energy stored in rocks over a broad range of seismic moment. Despite advancements in observations and numerical modeling models, the question on how a given fault system can host such a wide range of ruptures, including slow ruptures, VLFEs, LFEs, and fast earthquakes needs a careful attention. Addressing this question requires a framework rooted in fracture mechanics, which explores the rate at which energy provided to a crack drives the rupture front forward and how this process radiates energy throughout the medium. This work delves into the question of how frictional instability and mechanical interactions between faults and fractures, particularly concerning the geometrical distribution of off-fault damage, can generate observed rupture patterns in seismic catalogs. A model of a representative fault system is proposed, featuring a main fault embedded within a fractured zone where all fractures can slip independently. The length distribution of the off-fault fractures follows a power-law. The study then explores the fracture processes within the system, examining rupture speed from an energetic standpoint and exploring the impact of the damaged zone on the supply or reduction of energy to the process zone, ultimately influencing whether ruptures propagate rapidly or slowly. The influence of this process is further examined by analyzing the amount of energy radiated away from the fault system. Moment-radiated energy and moment-fracture energy scaling relationships will be presented as mechanical quantities that both slow and fast earthquakes adhere to on a common curve. We will discuss radiation efficiency as a function of rupture speed to illustrate how a fault adjusts its rupture speed according to the energy provided to it and the amount of its breakdown work. The effect of damage on the process zone of the rupture will be discussed to examine how interactions between multiple fractures supply or detract energy to an active process zone, affecting its rupture speed and, consequently, the fast or slow advancement of the front.