Fault state evolution governed by cumulative slip history.

Given the significant risk that earthquakes pose to society, understanding the spatiotemporal evolution of slip rates on natural faults has been a central research objective over recent decades. Geological and geophysical observations indicate that fault slip is accommodated by multiple deformation mechanisms operating both on the fault plane and within the surrounding damage zone. At the outcrop scale, structures formed by seismic and aseismic slip commonly coexist within the same fault system, implying that fault displacement involves a combination of deformation processes controlled by mineral-specific rheology. At larger scales, however, these processes may be masked by the limited spatial and temporal resolution of geophysical and geodetic observations.

From a theoretical and experimental perspective, rate-and-state friction (RSF) laws have been widely used to explain unstable fault slip through velocity-weakening behaviour, in which fault strength decreases with increasing slip rate. In this framework, fault friction is governed by slip velocity and a single state parameter that evolves with time and slip, commonly expressed either through an aging law, where fault healing occurs primarily during stationary contact, or a slip law, where state evolution is driven by slip-dependent renewal of contacts. Because both formulations are typically expressed as local, slip-rate-dependent laws, the explicit role of cumulative slip history in controlling the fault state remains implicit.

To investigate the effect of cumulative slip history, we perform a suite of 3D quasi-dynamic simulations assuming a homogeneous distribution of rate-weakening frictional properties, in which fault slip is governed by a classical RSF formulation. By systematically decreasing effective normal stress from 50 to 10 MPa and explicitly rewriting the aging law in a slip-dependent, event-integrated form, we show that the well-documented transition from characteristic earthquake behaviour to deterministic chaotic slip (e.g., Rubin, 2008; Cattania, 2019; Barbot, 2019) is accompanied by a change in the role of the state variable. Specifically, state evolution becomes increasingly governed by cumulative slip history and slip-filtered healing, which inhibits convergence toward a unique healed state and results in incomplete state recovery between successive events. Importantly, this behaviour arises without prescribing any spatial heterogeneity in frictional properties or fault-zone structure.

These results have direct implications for the interpretation of fault kinematics. While regions where slip rates remain below the prescribed background velocity may persist constant over interseismic periods, the shear stress within those regions in models of low effective normal stress need not be stationary. Instead, shear stress can evolve significantly because of incomplete state recovery driven by cumulative slip history and slip-limited healing, leading to temporally heterogeneous mechanical behaviour despite stable kinematic expression.

References

Rubin, A. M. (2008). Episodic slow slip events and rate‐and‐state friction. Journal of Geophysical Research: Solid Earth, 113(B11).

Cattania, C. (2019). Complex earthquake sequences on simple faults. Geophysical Research Letters, 46(17-18), 10384-10393.

Barbot, S. (2019). Slow-slip, slow earthquakes, period-two cycles, full and partial ruptures, and deterministic chaos in a single asperity fault. Tectonophysics, 768, 228171.