Deep seismic faulting triggered by nano- 2 crystallization of wadsleyite from olivine 3


 Activity of deep earthquakes, which increases with depth from ~400 km to a peak at ~600 km and abruptly decreases to zero at 680 km, is enigmatic, because brittle failure is unlikely to occur under the corresponding pressures of 13−24 GPa. It has been suggested that pressure-induced phase transformations of olivine in subducted slabs are responsible for occurrence of the deep earthquakes, based on deformation experiments under pressure. However, most experiments were made using analogue materials of mantle olivine and at pressures below ~5 GPa, which are not applicable directly to the actual slabs. Here we report the results of deformation experiments combined with in situ X-ray observations and acoustic emission measurements on (Mg,Fe)2SiO4 olivine at 11−17 GPa and 960−1250 K. We find that shear cracking followed by rapid formation of nano-crystalline wadsleyite on the crack surface is essential for the occurrence of faulting, which is observed only at temperatures around 1160 K. The faulting is accompanied by intense acoustic emissions and partial melting, which is likely to be induced by rapid sliding and adiabatic shear heating along the weak layer of nano-crystalline wadsleyite. In contrast, the olivine to ringwoodite transformation in (Mg,Fe)2SiO4 olivine would not cause such faulting because of the slow diffusion creep of ultrafine-grained ringwoodite. Our findings suggest the transformational faulting occurs on the surface of the metastable olivine wedge in subducted slabs, leading to deep earthquakes in the limited depth range.

In the deformation stage of M2676 and M3100 conducted at 1160 K, the semi-brittle 102 flow was terminated by faulting followed by a sudden large pressure drop (blow-out), 103 while no faulting was observed in other 11 deformation runs. Yield strength of the faulted 104 samples (1.5−1.8 GPa) is lower than that of many other samples deformed at 1160 K ( Fig.   105 2a), suggesting that larger stress is not necessarily required for the occurrence of faulting. 106 In these two runs with faulting, intense AEs (amplitude >1V) are radiated not only from 107 inside but outside of the sample, and the hypocenters locate along the fault plane crossing 108 the sample ( Fig. 1b and Extended Data Fig. 4f), showing occurrence of a fault-slip 109 associated rupture. A shear crack, which occurred 9 minutes before the rapture in M2676 110 (at a strain of 0.14: Fig. 1), is thought to be the precursor of the faulting.  In general, mode-II shear cracks can be formed by the coalescence of interacting 141 mode-I (opening mode) tensile cracks 21 occurring at the initial stage of brittle failure 22 . 142 Considering that volume expansion by opening of mode-I cracks is inhibited at elevated surface, as is the case for M2676 and M3100. 152 We estimate the nucleation rate of wadsleyite ( ) and the rate constant of the olivine-153 wadsleyite phase transformation (k) for two typical pressures of 13 and 15.5 GPa in the 154 wadsleyite stability field assuming that preferential nucleation proceeds on the crack 155 surface 23 (see Supplementary Information). The results (Extended Data Fig.7) show that 156 the interfacial nucleation of wadsleyite is effective in a narrow temperature window of 157 ~1160 K at 13 GPa on crack surfaces, while the transformation on both grain boundaries 158 and crack surfaces is accelerated with increasing temperatures at 15.5 GPa. As 159 microcracking would not occur at temperatures above 1200 K, indicated by the very low 160 values of the AE rate (Fig. 2b) where h is work hardening coefficient (=1), ρ is density (=3.6 g·cm -3 at 13.5 GPa) 26 , cp is 170 specific heat (=817 J·kg -1 K -1 ) 27 , κ is thermal diffusivity (=0.7 mm 2 ·s -1 ) 28 , H * is activation 171 enthalpy for deformation (=907 kJ·mol -1 for the Peierls creep at 13.5 GPa) 12,29 , and L is 172 sample size (=1.2 mm in length). Substituting these parameters of olivine for Eq. (1), we 173 obtain a critical strain rate of 1.2×10 -2 s -1 at a differential stress of 1.5 GPa to initiate 174 adiabatic shear heating at the background temperature of 1160 K (Fig. 4a). Instantaneous 175 strain rate of the damage zone (or gouge layer) (thickness Ld ~20 µm: Extended Data Fig.   176 6b) may reach ~0.1−2 s -1 during the faulting of ~10 s, as estimated from the stroke sensors 177 of the anvils in M2676 and M3100, under the assumption that strain was localized with a 178 factor of L/Ld. Thus, the adiabatic instability can be initiated by rapid nucleation of 179 wadsleyite on crack surface followed by diffusion creep of wadsleyite 30 with grain sizes 180 of ~20 nm ( Fig. 4b and Extended Data Fig. 6e).

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It has been reported that the latent heat release associated with phase transformation 182 enhances deep earthquake activity 31,32 . A net temperature increment ΔT by the latent heat 183 release across the phase transformation is given as 33 : where ΔSr is the entropy change of reaction, ΔGv is the free energy change of reaction, 186 and Cp is isobaric heat capacity. ΔGv is approximated as ΔP·ΔV/V0, where ΔP is the 187 overpressure from the equilibrium and ΔV/V0 is the fractional volume change 16  1160 K, where the nano-crystallization of wadsleyite occurs followed by the faulting due 208 to shear instability, although this critical temperature may be slightly lower in the 209 geological time scale (Extended Data Fig. 7). In fact, the observed deep earthquakes are 210 reported to locate along an isotherm of ~1000 K in deep slabs 39 . It has been widely 211 recognized that some characteristics of deep earthquake, such as the frequency of 212 aftershocks and the Gutenberg-Richter b-value, reflect thermal structures of deep slabs 8 .

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The very small aftershock rate and higher b-values of deep earthquakes in warmer slabs 40

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can be attributed to a smaller number of the earthquake nucleation in their thinner MOW 41 .

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Numerical studies based on experimental kinetic data show that metastable olivine in cold 216 slabs probably persist to depths of ~600 km, below which ringwoodite is the major phase 217 down to ~700 km (ref. 8,42 ). Our results show that the deep earthquakes in the mantle 218 transition zone is mainly caused by the metastable olivine to wadsleyite transformation 219 along the isothermal regions in the MOW, and the corresponding transformation to 220 ringwoodite would play no major roles in occurrence of the deep earthquakes, consistent 221 with the rapid decrease in seismicity from ~600 km to 680 km (ref. 43 ).        Kilosa, Tanzania) was put into a nickel capsule (inner diameter: 8 mm; length: 11 mm).

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The olivine and olivine-orthoenstatite powders were sintered at 4 GPa and 1073 K for 297 1.5 hour using a Kawai-type multi-anvil apparatus at Ehime University. The average 298 grain size of olivine in the sintered sample is ~15 µm. The sintered sample was core-299 drilled to a rod with a diameter of 1 mm and a length of 0.6 mm. Melting of the OL100 300 and OL92 samples is used for estimation of a peak temperature during faulting (e.g.,

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OL100: >2500 K at 15.5 GPa; OL92: ~2170 K at 13 GPa) 18,20 . Mechanical behavior of 302 the OL92 sample was found to be almost the same as that of the OL100 sample because 303 92 wt.% of olivine forms the load-bearing framework 46 , suggesting that the present 304 discussion and conclusions are independent on these two samples. 305 We conducted deformation experiments on the OL100 and OL92 samples using a 306 deformation-DIA apparatus combined with the large-volume MA-6-6 system at the 307 edge length of 5 mm was used as the pressure medium, which was surrounded by five 309 tungsten carbide anvils (with a truncated edge length of 3 mm) and an X-ray transparent 310 cubic boron nitride (cBN) (or sintered diamond) anvil placed on the down-stream side.  were replaced by an amorphous boron powder cemented with epoxy resin (at a ratio of 325 4:1 by wt.) to maximize the intensity of the diffracted X-rays.

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The cell assembly was first pressurized hydrostatically up to 0.6 MN in the main-327 ram load and temperature was raised to 1470 K at a rate of ~50 K/min. A thermocouple  showed that the peak was detectable when the volume fraction of wadsleyite is higher 374 than 5 vol.%.

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The strain ε of a deforming sample was evaluated from the distance between two 376 platinum strain-markers placed between the sample and an alumina piston, which was 377 monitored by in-situ monochromatic X-ray radiography. Each radiograph image (30 378 seconds of exposure time) was taken just before the acquisition of the 2-D X-ray 379 diffraction pattern. Natural strain (i.e., ε = -ln (l/l0), where l0 is the initial length of the 380 sample; l: the length of the sample during deformation) was adopted to evaluate the 381 sample strain. The uncertainty in the strain mainly due to the shape of strain marker is 382 within 10%. A sudden splitting of a platinum strain marker monitored by in-situ 383 observations was interpreted as the occurrence of faulting 45 , which was confirmed in the 384 recovered sample. 385 386 AE monitoring and data processing 387 We monitored AEs as a proxy of fracture propagation at high pressure and 388 temperature. AE monitoring was combined with in-situ X-ray diffraction/imaging where vp is the averaged P-wave velocity in the sample, and Ri is the distance between X 422 and Pi. In the calculation, we obtained the best location of X' that gives the minimum 423 residual of Eq. (3) under the assumption that the velocity structure of the cell assembly 424 was homogeneous and the averaged P-wave velocity was equal to that for olivine (e.g., 425 9.1 kmꞏs -1 at 14 GPa and 1160 K) 48 in the cell assembly. In this study, the location 426 uncertainty is defined as the root mean square of the right side of Eq. (3).  is also shown. The timings of shear cracking, rupture, and blow-out are shown by thin-dashed, thick-dashed and dotted lines, respectively. b, Two-dimensional views of AE hypocenters in the deforming sample (blue cylinder) and the pressure medium (black square) during periods of each 5 (or 2) minutes. The black cross shows typical errors for the location of hypocenter. A brown-dashed line shows the seismic plane observed at the timing of rupture. Arrows represent the compressional direction. c, X-ray radiographs of the deforming sample at each strain ε. Positions of platinum strain markers are shown by arrows. Splitting of the middle strain marker (ε =0.14 at 62 min) suggests shear cracking followed by faulting. Direction of the incident X-ray is perpendicular to the radiograph images. where a0 and b0 are constants, ϕ is a shape factor, ΔG * hom is the activation energy for 17 homogeneous nucleation, ΔGr is the free energy change of reaction, Q is the activation 18 energy for growth, k is the Boltzmann constant, and R is the molar gas constant. We  before the deformation stage. Square, triangle, and diamond represent the P-T-t path#1 (normal), #2 (overpressurized just before the deformation), and #3 (annealing in the wadsleyite-stability field before the deformation), respectively. Solid and open symbols represent the runs in which the OL100 and OL92 samples were used, respectively. The equilibrium boundaries of α (olivine), β (wadsleyite), and γ (ringwoodite) for Mg1.8Fe0.2SiO4 are shown by gray solid lines (Kerschhofer et al. 6 ). In a, partial melting of the OL92 sample is possible above the solidus curve (orange) for dry lherzolite (Takahashi 7 ). Note that the conditions for incongruent melting of γ-Fe2SiO4 to a liquid phase and stishovite (Sti) for fayalite (Ohtani 8 ) shown by the red line gives the lower limit of the melting temperature of β/γ-Mg1.8Fe0.2SiO4. In b, the P-T condition for deformation of the M2955 sample, in which a mode-II throughgoing crack occurred, is highlighted by a large symbol. were obtained from the first motions of six waveforms, equals to 1 and -1 in the cases of isotropic volume increase (i.e., explosion) and decrease (i.e., compaction), respectively. Double couple source is expected when the absolute value of polarity is less than 1 (i.e., both positive and negative polarities are detected in an AE event).   (solid curves) and the rate constant for the olivine-wadsleyite transformation k (dashed curves) are calculated from Eqs. (S1) and (S3), respectively. We considered two cases for the calculations: reactions on grain boundaries (GBs: blue) and on interfaces (orange). Shape factors (ϕ) for GB nucleation and interfacial nucleation are assumed as 6×10 -4 and 1×10 -4 , respectively. The values of and k are normalized by their maximum values of the GB case at 13 GPa (i.e., Ngb-max-13GPa and kgb-max-13GPa). The olivine-wadsleyite transformation is so sluggish that no wadsleyite grain was expected on olivine GBs, as observed in the M2676 sample. Numerous wadsleyite grains on olivine GBs in the M3100 sample are explained by the elevated transformation rate on GBs at 15.5 GPa. Semi-brittle flow associating AEs controls the sample shortening at temperatures below 1200 K. On the other hand, aseismic plastic deformation is dominant at higher temperatures. Faulting can proceed only when both microcracking and fast transition of olivine-wadsleyite transformation are possible at temperatures ~1160 K (pale-red area). The cell assembly viewed in cross section from the direction parallel to the X-ray path (dashed yellow circle). Note that the tungsten (W) rings and the thermocouple wires (TC) were not used for the deformation runs. b, Calibration of central temperature in the cell vs. furnace power under 0.6 MN main-ram load (corresponding to ~13 GPa at 1250 K). The three calibration runs (M2286, M2296, and M2290) were conducted at the BL04B1 beamline, SPring-8. c, A one-dimensional diffraction pattern integrated from a half ring of the two-dimensional diffraction pattern taken at 13.6 GPa and 1160 K (M2446). Diffraction patterns of olivine (Ol), wadsleyite (Wad), the MgO sleeve, a nickel capsule (Ni) are observed. d-e, Schematic representation of the experimental setup showing the positions of six PZT crystals (i.e., transducers) mounted on the sidewall surface of 2 nd -stage anvils. Views from the directions perpendicular (d) and parallel (e) to the compressional direction. f, Sample waveforms of an AE radiated from an OL100 sample deformed at ~15 GPa and 1160 K (M2446). The AE event was monitored by two transducers: one was connected to a low-noise 30 dB preamplifier via an ultra-small pre-amplifiers (20 dB gain) (this study), and the other was connected to a low-noise 40 dB pre-amplifier used in our previous studies (Ohuchi et al. 9 ). Extended