Microscopic Evolution of Laboratory Volcanic Hybrid Earthquakes

Characterizing the interaction between fluids and microscopic defects is one of the long-standing challenges in understanding a broad range of cracking processes, in part because they are so difficult to study experimentally. We address this issue by reexamining records of emitted acoustic phonon events during rock mechanics experiments under wet and dry conditions. The frequency spectrum of these events provides direct information regarding the state of the system. Such events are typically subdivided into high frequency (HF) and low frequency (LF) events, whereas intermediate “Hybrid” events, have HF onsets followed by LF ringing. At a larger scale in volcanic terranes, hybrid events are used empirically to predict eruptions, but their ambiguous physical origin limits their diagnostic use. By studying acoustic phonon emissions from individual microcracking events we show that the onset of a secondary instability–related to the transition from HF to LF–occurs during the fast equilibration phase of the system, leading to sudden increase of fluid pressure in the process zone. As a result of this squeezing process, a secondary instability akin to the LF event occurs. This mechanism is consistent with observations of hybrid earthquakes.


1-1-
Time is the global time of the tests (loading instrument time) in seconds. The evaluated events for both and wet are from the highlighted interval. The rate of microcracking during loading is indicated by the AE hit rate, defined as bulk AE "hits" averaged over the 16 AE sensors per second, with a "hit" defined as every instance that a pre-set number of sensors (6) register voltage above a set threshold (60 mV). (e) A schematic picture of Experimental setup [modified from (2)]. Standard triaxial deformation experiments were performed in which the sample is loaded at a constant strain rate until failure occurs. At this stage the fault plane, which forms typically at an inclination angle of approximately 30°, is connected to the conduit (see details in Benson et al. 2010). For watersaturated experiments, an additional experimental step was carried out, in which the deviatoric stress is lowered until a hydrostat of 40 MPa effective pressure is achieved is order to ensure that no slip occurs on the fault plane.

1-2-On dry micro-acoustic ultrasound events-
To analyze the recorded micro-excitations, we use the relations between different phases as defined in terms of network parameters (Fig.   S2a,b) S2c). Assuming that the D-phase represents the nearly steady-state regime in comparison with the rate of the preceding phases, we interpret this parameter space as the bridge between the fast weakening rate (i.e., fast relaxation state) and steady-state stress: faster weakening rate yields smaller D R (Fig. S2c). Therefore, we infer a microscopic weakening law where steady state resistance (i.e., R) is scaled inversely with weakening velocity.   The transition from S to W is reflected in <k(t)> which is clearly related to a transition to another energy level. In (c), we show the 3D representation of signal power-frequency-<k(t)>. The S-phase coincides with the lower signal power and the transition to W-phase occurs rapidly.  Hybrid (a,b) and Dry (c,d) events with associated spectrograms and Q(t). The insets show the spectral amplitudes versus frequency and time. With this comparison, we find that the onset of the high-frequency regime corresponds to with the W-phase in Q(t). P is the power spectral density. The onset of the W-phase is also roughly coincident with the broadening of the power spectrum. An overlapped (80%) 2,048-point fast Fourier transform is used to calculate the power spectral density. (e,f) another example from a dry cracking event with the corresponding spectrum.

2-1-
This statement also is true for the DW regime where at the onset of this phase the porepressure is in its maximum value, inducing secondary weakening, and at the end of this phase the pore-pressure approaches zero: The coefficients where 0.8   (Fig.2c-main text). We can assume a linear growth of pore-fluid pressure in the RS regime: Plugging (4) in (2) and (3)   ). This damaged node acts similar to a kink, separating zones with up and down nodes. In Fig.S13, we have shown that creation and annihilation of kinks-antikinks (i.e., pairing mechanics) govern the transitions between main phases of Q(t) (or <K(t)>).  . At the third time interval, the system is in a fully polarized (ordered) state. Transition from fully ordered state (e.g., S-phase) to another fully ordered state (e.g., W-phase) is associated with the creation of "kinks" as the flipped nodes.  [8]). The phase singularity at point A is manifested in a binary network structure as the flipping the node (spin) leading to formation of kink (domain wall) in K-chain.  -cracking noises. (a,b) the mean degree of all nodes for a hybrid event and the corresponding correlation length of K-chains . (c) Highly fluctuating order parameter in DW phase drives the system in to the next degenerate state. This signature distinguishes the physics of the secondary weakening phase from the W-phase. We assign this fluctuation to discrete process of squeezing-out of the liquid. The frequency of this almost periodic oscillation is around 200-300kHz. A double peak in RS phase-exhibited in m(t) and () t  -induces sequence of stiffening-softening-like feature with durations less than 2µs (red dotted-circles). Figure S.15 (also Fig S.16-17). The nodes with the healing-like characteristics in a way that many nodes become polarized in the same outward direction such that they elongate circumferentially forming large domains in the RS phase, covering a large fraction of the chain's circumference (The dotted red-line around the chain). We have illustrated this characteristic in Fig.S18. Transition from the initial S-phase to fast relaxation regime (W-phase) marks different signatures of kink distribution in comparison with transition from W to RS phase. Approaching fixed points from below or above yields different defect structures. If k i < k max (stage 1), kinks form in a finite size (smaller than the system size-also see [5], [7]). This is the situation for S to W transition and we have described this feature in [5]. In contrast, if k i < k min (stage 2) , a major fraction of the elements form as string that spans the whole system and they survive in RS-phase. We have illustrated this feature in Fig.S19 and Fig.4 of the main text. The transition to the RS phase resembles the partial healing of defects (contraction of flipped nodes).  Figure S.18|The crack-like excitation relaxes through at least two fixed points. Approaching fixed points from below or above yields different defects structures. If k i < k max (stage 1) , kinks form in a finite size (smaller than the system size-also see [5], [7]). In contrast, if k i < k min (stage 2) , a major fraction of the elements form as string that spans the system and they survive in RS-phase. Nodes that span the majority of the system disappear at a slower rate leading to stability of RS phase. transition to RS-phase is accompanied with the extension of "healed elements" (as blue arrow) as a major fraction of the system size form as string that spans the system.

3-3-The pair-correlation function (node-node correlation):
The discrete equivalent of the autocorrelation function is the two-point correlation function. First we calculate the two-point correlation function (G(x)) in a given time step based on binary-K chains (i.e. fictitious spins). For the calculated functions (for example see [5]), We can fit a correlation function in the form of ( ) (1 ) exp( ) where L is the total number of the nodes, x is distance, and  is the correlation length. Correlation length  is the cut-off length of the correlation function where for distances shorter than the correlation length, G(x) can be fit by a power law function. For a fully ordered state a triangular function (i.e., fully coherent system and  ) is given. In Fig.S20, we show the evolution of W-RS and DW-L transitions and the counterpart correlation length evolution. The transition from the W to RS phase accompanies the fast decline of the correlation length ( Fig.S20d-e). The RS-phase is characterized by the extended (proliferated) re-pinning of elements forming a string like structure in K-chains (i.e., outward blue arrows in Fig.S20c) that spans the whole system. As the system approaches the DW phase, the correlation length slowly declines.
A similar pattern of a sudden increase and then slow decline of  is observed for the L-phase (Fig.S20e-between 65-80µs). In the context of configurations of K-chains and the observed relaxation phases, we need to suppress slow relaxation phases (D-phase) either intrinsically or extrinsically; the vibrating part of the crack must be confined between the rupture front and repining (i.e., healing) point. For a crack-like excitation the healing occurs when the system approaches thermal equilibrium. To visualize the onset of such re-pining, we might use the states of the nodes in K-chains (Fig.S20). The results shown in Fig.S19-S20 indicates that re-pining process clearly is visualized in K-chain structures as "healed"like sites in the form of proliferated or extended healed-like elements. The inner (blue) and outer strings (red) are at ~20µs (as the reference point) and ~30µ, respectively. The extended (proliferated) repinning elements form a string like structure (outward blue arrows) that spans the major fraction of the system.
(d-e) Correlation length (  ) in W-RS and L phases. Sudden transition from W to RS phase accompanies with almost constant correlation length (frozen correlation length) immediately follows by an enhanced correlation length which decays as the system enters into the DW regime. Note that at~40µs a strong spike appears in DW phase. A similar trend is observed for the L-phase (e). (f) shows the four reordered waveforms for this single event.