Seismic Energy Partitioning Across the Continuum of Laboratory Fault Slip Modes

Technical Summary: Seismic Energy Partitioning Across the Continuum of Laboratory Fault Slip Modes

Problem Statement
The transition between slow and fast earthquakes remains a fundamental unresolved challenge in earthquake physics. While the existence of a continuum of slip modes—from slow slip events lasting days to dynamic ruptures lasting seconds—is well-established, the physical conditions governing the transition between these modes are not fully understood. A central debate persists regarding whether slow and fast slip arise from distinct physical mechanisms or represent different expressions of a single underlying process. Specifically, it is unclear if a unified constitutive framework can explain both phenomena, particularly given that slow and fast slip frequently coexist on the same fault segments in nature.

Methodology
The authors conducted a series of laboratory experiments using a servo-controlled biaxial deformation apparatus at Sapienza University of Rome. The study utilized a double-direct shear geometry with Min-U-Sil 10 quartz powder as the fault gouge material. The experimental design focused on systematically varying the elastic loading stiffness ($k$) of the system while maintaining constant normal stress ($\sigma_n$) and background loading rate.

Three distinct stiffness configurations were employed ($k_1 > k_2 > k_3$) across normal stresses ranging from 8 to 22 MPa. This approach allowed the researchers to modulate the stability ratio ($k/k_c$), where $k_c$ is the critical stiffness determined by the fault's constitutive frictional properties. The experiments were monitored using:

1. High-resolution mechanical sensors: To measure shear stress, fault displacement, and slip velocity.
2. Continuous acoustic emission (AE) monitoring: Calibrated piezoelectric transducers recorded AE signals at 3.125 MHz to capture seismic radiation.

The study analyzed the full spectrum of slip behaviors by calculating key parameters including stress drop, peak slip velocity, co-seismic slip ($\delta$), breakdown work ($W_b$), and seismic moment ($M_0$) derived from AE spectral analysis. Statistical scaling relationships were evaluated using power-law regressions and non-parametric bootstrap resampling to ensure robustness.

Key Results

1. Continuum of Slip Modes: The experiments demonstrated that the same fault patch, under identical normal stress and loading rate conditions, can exhibit stable sliding, slow slip events, and fast dynamic ruptures solely by varying the loading stiffness.
   • Stable sliding occurs when $k/k_c > 1.4$.
   • Slow slip events (peak velocities < cm/s) cluster around $k/k_c \sim 1$.
   • Fast slip events (peak velocities > cm/s) occur when $k/k_c < 0.8$.
2. Distinct Seismic Signatures:
   • Slow slip is characterized by swarms of low-amplitude, high-frequency acoustic emissions distributed throughout the acceleration phase, indicating distributed microseismic failure.
   • Fast slip generates high-amplitude, clustered energy bursts concentrated at the peak slip velocity, indicating coherent rupture.
   • In both regimes, AE activity is confined to the acceleration phase, while the deceleration phase remains aseismic.
3. Scaling Relationships:
   • Breakdown Work vs. Seismic Moment: A continuous power-law scaling was observed across all slip modes ($W_b \propto M_0^{0.26}$). The sub-linear exponent suggests that larger events radiate a greater fraction of energy seismically. When corrected to isolate the seismically coupled fraction of $W_b$, the exponent aligns with self-similar rupture predictions ($\alpha \approx 0.6$).
   • Moment vs. Slip: Seismic moment scales with co-seismic slip as $M_0 \propto \delta^{3.53}$, consistent with theoretical predictions for self-similar sources.
   • Temporal Efficiency: A temporal seismic efficiency proxy ($\eta_t = T_{AE}/T_{slip}$) reveals a systematic shift in energy partitioning. In slow events, detectable acoustic radiation accounts for a negligible fraction of slip duration (0.002%), whereas in fast events, it constitutes a substantial portion (7%).

Key Contributions

• Unified Mechanism: The study provides experimental evidence that slow and fast earthquakes are not distinct phenomena requiring separate physical descriptions but are end-members of a continuous spectrum of fault slip.
• Elastodynamic Control: The transition between slip modes is shown to be governed primarily by the elastodynamic interaction between the fault and its surroundings (specifically the stability ratio $k/k_c$), rather than by changes in stress conditions or specific constitutive mechanisms alone.
• Energy Partitioning: The research quantifies the continuous evolution of energy partitioning, demonstrating a shift from predominantly aseismic deformation in slow events to efficient radiative failure in fast events.

Significance
The paper claims that its findings offer a unified physical framework for understanding fault slip dynamics. By demonstrating that the same fault can host a spectrum of behaviors under constant stress, the authors suggest that the apparent variability in rupture behavior on natural faults arises from differences in how energy is accumulated and released (modulated by system stiffness, fluid pressure, or damage zones) rather than from fundamental changes in fault mechanics. This supports the hypothesis that slow and fast slip represent a continuum, where the elastodynamic coupling dictates the interplay between recurrence intervals, frictional restrengthening, and the partitioning of seismic versus aseismic energy. The results imply that slow slip events may arise from cascades of small asperity failures driven by aseismic fronts, sharing a common scaling mechanism with regular earthquakes.