Dynamic Weakening by Acoustic Fluidization in a Model for Earthquake Occurrence
Authors: Eugenio Lippiello2,4, Ferdinando Giacco1,2, Massimo Pica Ciamarra1,5, Lucilla de Arcangelis3,4
1CNR-SPIN, Department of Physics, University of Naples “Federico II”, Italy
2Department of Mathematics and Physics, Second University of Naples and CNISM, Caserta, Italy
3Department of Industrial and Information Engineering, Second University of Naples and CNISM, Aversa (CE), Italy
4Kavli Institute for Theoretical Physics, University of California, Santa Barbara, USA
5Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore.
Many studies have shown that the frictional strength of fault systems is controlled by the rheology of crushed and ground-up rock produced during past sliding events, known as fault gouge. Treating the gouge as a granular material confined between two rough plates we started to think an earthquake as a transition from a jammed state, in which the gouge resists the existing stresses, to a flowing one. By connecting the physics of earthquakes to that of granular systems, the analogy allows to investigate -- from an original perspective -- an important geophysical question: why are earthquakes observed when the estimated shear to normal stress ratio is much smaller than the rock static Coulomb coefficient?
We have therefore developed a “granular” model for a seismic fault, where the tectonic drive is implemented by coupling the confining boundary to a spring whose free-end moves at constant velocity (Fig.1). The model exhibits alternations between very long stick (jammed) phases abruptly interrupted by jumps (slips), typical of earthquake sequences in real seismic faults . The jumps follow a broad distribution that is in agreement with the Gutenberg-Richter law for the organization of magnitude in instrumental catalogs .
Figure 1: The model consists of spherical grains, representing the fault gouge, confined between two rough rigid layers, at constant pressure P0. The grains interact through a normal viscoelastic interaction and a tangential frictional one. A stick slip dynamics is induced by driving the system via a spring mechanism along x at shear stress σ.
The numerical model allows for a detailed investigation of the evolution of the system as the shear stress increases and the failure is approached. While the structure remains essentially unchanged, we observe that the system's response to external perturbations increases: the fault becomes weaker on approaching a slip instability. Interestingly, this weakening only occurs for perturbations in a narrow range of frequency, independent of the fault orientation . In particular the weakening was observed also for perturbations which increase the confining pressure or reduce the shear stress, that is a kind of perturbation that should strengthen the system.
The mechanism of "acoustic fluidization" is the explanation of this unexpected behavior. This mechanism has been proposed by Melosh in 1979 [4,5] to justify why several major fault systems exhibit a resistance to shear stress much smaller than the one observed in experiments of rock-on-rock friction. According to this mechanism, during seismic fracture, a fraction of the total energy is released via elastic waves that diffuse inside the fault at short-wavelengths because of scattering due to small scale heterogeneities. These waves produce oscillations in the direction normal to the fault plane that can balance the confining normal pressure and eventually induce seismic failure.
In our model we explicitly show that the maximum response is obtained at a characteristic frequency ω*, typical of acoustic waves bouncing back-and-forth within the fault. The advantage of numerical simulations is that it is possible to turn back the clock arbitrarily and therefore to know in advance when the next slip will occur. In particular our study shows that even very small amplitude perturbations, at the characteristic frequency ω*, can induce failure. This could explain the observation of aftershocks at great distances (thousand of kilometers) from their triggering earthquake.
Furthermore, we have also found that acoustic waves at the same resonant frequency spontaneously emerge inside the model fault, even when no external perturbation is applied. The contour map of the power spectrum as function of the time, plotted in Fig. 2, shows that the characteristic frequency ω* is spontaneously excited as soon as the sliding starts. This suggests that acoustic oscillations reduce the confining pressure and promote failure at a shear stress value smaller than expected.
Figure 2: The map of the logarithm of the power spectral density, as function of the time t (horizontal axis) and frequency ω (vertical axis). The dashed vertical lines indicate the slip occurrence times. We observe the appearance of a peak in the characteristic frequency ω* immediately before the occurrence of each slip.
 Massimo Pica Ciamarra, Eugenio Lippiello, Cataldo Godano, Lucilla de Arcangelis, "Unjamming Dynamics: The Micromechanics of a Seismic Fault Model", Physical Review Letters, 104, 238001 (2010). Abstract.
 M. Pica Ciamarra, E. Lippiello, L. de Arcangelis, C. Godano, "Statistics of slipping event sizes in granular seismic fault models", Europhysics Letters, 95, 54002 (2011). Abstract.
 F. Giacco, L. Saggese, L. de Arcangelis, E. Lippiello, M. Pica Ciamarra, "Dynamic Weakening by Acoustic Fluidization during Stick-Slip Motion", Physical Review Letters, 115, 128001 (2015). Abstract.
 H. Jay Melosh, "Acoustic fluidization: A new geologic process?", Journal of Geophysical Research, 84, 7513 (1979). Abstract.
 H.J. Melosh, "Dynamical weakening of faults by acoustic fluidization", Nature, 379, 601 (1996). Abstract.