Continuously Sheared Granular Matter Reproduces in Detail Seismicity Laws

We introduce a shear experiment that quantitatively reproduces the main laws of seismicity. By continuously and slowly shearing a compressed monolayer of disks in a ringlike geometry, our system delivers events of frictional failures with energies following a Gutenberg-Richter law. Moreover, foreshocks and aftershocks are described by Omori laws and interevent times also follow exactly the same distribution as real earthquakes, showing the existence of memory of past events. Other features of real earthquakes qualitatively reproduced in our system are both the existence of a quiescence preceding some main shocks, as well as magnitude correlations linked to large quakes. The key ingredient of the dynamics is the nature of the force network, governing the distribution of frictional thresholds.

Figure 1

Setup and raw data analysis. (a) Sketch of the setup. (b) Photograph of the setup, displaying the mechanical and acoustic sensors. Inset: force chains in the granular layer observed thanks to photoelasticity. (c),(d) Respectively, torque signal and torque difference on 0.1-s intervals on a 1-h window. Detected torque drops have been highlighted by $\times$. (e) Typical acoustic event. (f) Result of the discrete wavelet transform on the acoustic event, resulting in a power spectrogram, with a color proportional to the logarithm of the energy value.

Figure 2

Quantitative reproduction of main seismicity laws. (a) Probability distribution of energies, either acoustic $E_a$ or mechanical $E_m$ for a 24-h experiment. Both distributions follow Gutenberg-Richter-like laws $P(E)\sim E^{-\beta }$ with an exponent $\beta =1.71$ (solid lines). (b) normalized probability distribution of $\theta ={\tau }_{E\ge E_0}/{\tau }_{E\ge E_0}^{*}$. Solid symbols: considering all the events. It follows the universal function $f(\theta )\sim {\theta }^{-0.3}\exp (-\theta /1.5)$ (solid line). Open symbols: considering different threshold values $E_0$. (c) Average acoustic emissions rates respectively before (squares) and after (circles) a main shock. They follow Omori laws, respectively, $n(t_{-})=9.05+2.78/(0.22+t_{-}{)}^{0.8}$ for foreshocks and $n(t_{+})=8.22+7.81/(0.12+t_{+})$ for aftershocks.

Figure 3

Around main shocks. (a) Local power-law exponent computed on all acoustic foreshocks or aftershocks detected in fixed 200-ms windows centered at a given time from the main shock. (b) Histogram of acoustic emissions energies on 2-ms intervals during $\pm 200\mathrm{ms}$ around a large acoustic emission. The AE rate is displayed as shades of color, with a corresponding numerical value averaged over the 4500 main shocks. We observe an abundance of high amplitudes right after the main shock, with a decrease of the logarithm of the most probable acoustic energy value as a power law of time (with an offset) $5.33+{[60.34/(t+44.91)]}^{4.82}$, also displayed as a white solid line.