Frictional heating processes and energy budget during laboratory earthquakes

During an earthquake, part of the released elastic strain energy is dissipated within the slip zone by frictional and fracturing processes, the rest being radiated away via elastic waves. Frictional heating thus plays a crucial role in the energy budget of earthquakes, but, to date, it cannot be resolved by seismological data. Here we investigate the dynamics of laboratory earthquakes by measuring frictional heat dissipated during the propagation of shear instabilities at typical seismogenic depth stress conditions. We perform, for the first time, the full energy budget of earthquake rupture and demonstrate that increasing the radiation efficiency, i.e. the ratio of energy radiated away via elastic waves compared to that dissipated locally, increases with increasing thermal - frictional - weakening. Using an in-situ carbon thermometer, we map frictional heating temperature heterogeneities - ‘heat’ asperities - on the fault surface. Combining our microstructural, temperature and mechanical observations, we show that an increase in fault strength corresponds to a transition from a weak fault with multiple strong asperities, but little overall radiation, to a highly radiative fault, which behaves as a single strong asperity.

💡 Research Summary

This paper presents a comprehensive experimental investigation of the energy budget of earthquakes by measuring frictional heat generated during laboratory stick‑slip events that simulate natural seismic ruptures. The authors used Westerly granite samples subjected to confining pressures of 45, 90, and 180 MPa, corresponding to crustal depths of roughly 1.7, 3.4, and 6.8 km. For each stick‑slip event they recorded static stress drop, co‑seismic slip, and temperature evolution 5 mm from the fault plane.

A key innovation is the development of an in‑situ carbon thermometer. Amorphous carbon was deposited on the fault surface, and post‑mortem Raman micro‑spectroscopy was used to map the degree of carbonization, which correlates with peak temperature above ~700 °C. This technique revealed “heat asperities” – elongated high‑temperature patches (≈100–300 µm long, ≈100 µm wide) that persist over multiple stick‑slip cycles, indicating that they are repeatedly re‑heated.

The total elastic strain energy released, W, was calculated as (τ₀ + τ_r)·d/2, where τ₀ and τ_r are the initial and final shear stresses and d is the co‑seismic slip. Frictional heat, Q_th, was obtained by inverting the measured temperature curves with a simple heat‑diffusion model assuming a constant heat source lasting 20 µs and a diffusion length √(k t). The model fits well for the 45 and 90 MPa experiments; at 180 MPa deviations suggest longer heating durations or latent‑heat effects.

Results show that Q_th increases with slip, reaching up to 37 kJ m⁻² for the largest events. Comparison with independently measured fracture energy (Gc) indicates that at low normal and shear stresses, frictional heat dominates the energy dissipation, whereas at higher stresses and larger slips, Q_th and Gc become comparable, and most of the released energy is radiated as seismic waves. The authors infer a radiation efficiency (E_R/W) approaching 0.9 for the high‑stress, large‑slip cases.

A “heating efficiency” R = Q_th/W was defined and found to scale with the inverse square root of slip (R ∝ d⁻¹/²). This scaling arises because heat production per unit area scales as Q_th ∝ √d when slip is proportional to the duration of sliding. Consequently, as slip grows, a smaller fraction of the total work is converted into heat, and a larger fraction is radiated. Moreover, R decreases with the number of stick‑slip cycles, reflecting a “memory effect”: repeated events rework the fault surface, flattening asperities and reducing subsequent heat generation.

Scanning electron microscopy revealed progressive melting of fault‑rock minerals. At 45 MPa only biotite and a few plagioclase/k‑feldspar grains melted; at 90 and 180 MPa essentially all minerals, including quartz (fusion temperature ≈ 1650 °C), were molten. This transition from localized flash melting at asperity contacts to bulk melting of the entire fault surface corresponds to a mechanical shift from a weak fault composed of many small asperities (high heating efficiency, low radiation) to a strong fault dominated by a single large asperity (low heating efficiency, high radiation).

The authors argue that this laboratory‑based transition explains the wide range of seismic radiation efficiencies observed in nature (h = E_R/(E_R + G_c) ≈ 0.3–0.8) and even cases where h > 1 (e.g., the 1992 Landers and 1994 North Ridge earthquakes). In such events, a single dominant asperity can radiate disproportionately large energy relative to the overall fault area, while the rest of the fault experiences limited stress drop and little radiation. The study demonstrates that apparent radiation efficiencies greater than one do not require invoking frictional heating as a dominant sink; rather, they arise naturally from the spatial heterogeneity of stress and temperature on the fault.

In summary, the paper provides the first full accounting of elastic, radiated, fracture, and frictional‑heat energies in laboratory earthquakes, introduces a novel carbon‑based temperature mapping technique, and shows how the evolution from multiple micro‑asperities to a single dominant asperity controls the balance between heat dissipation and seismic radiation. These findings offer a new physical framework for interpreting seismic efficiency variations and underscore the importance of fault‑scale temperature heterogeneity and memory effects in earthquake dynamics.