Deep-Focus Earthquake Analogs Recorded at High Pressure and Temperature in the Laboratory

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Science  20 Sep 2013:
Vol. 341, Issue 6152, pp. 1377-1380
DOI: 10.1126/science.1240206

Delineating Deep Faults

Most large, damaging earthquakes initiate in Earth's crust where friction and brittle fracture control the release of energy. Strong earthquakes can occur in the mantle too, but their rupture dynamics are difficult to determine because higher temperatures and pressures play a more important role. Ye et al. (p. 1380) analyzed seismic P waves generated by the 2013 Mw 8.3 Sea of Okhotsk earthquake—the largest deep earthquake recorded to date—and its associated aftershocks. The earthquake ruptured along a fault over 180-kilometer-long and structural heterogeneity resulted in a massive release of stress from the subducting slab. In a set of complementary laboratory deformation experiments, Schubnel et al. (p. 1377) simulated the nucleation of acoustic emission events that resemble deep earthquakes. These events are caused by an instantaneous phase transition from olivine to spinel, which would occur at the same depth and result in large stress releases observed for other deep earthquakes.


Phase transformations of metastable olivine might trigger deep-focus earthquakes (400 to 700 kilometers) in cold subducting lithosphere. To explore the feasibility of this mechanism, we performed laboratory deformation experiments on germanium olivine (Mg2GeO4) under differential stress at high pressure (P = 2 to 5 gigapascals) and within a narrow temperature range (T = 1000 to 1250 kelvin). We found that fractures nucleate at the onset of the olivine-to-spinel transition. These fractures propagate dynamically (at a nonnegligible fraction of the shear wave velocity) so that intense acoustic emissions are generated. Similar to deep-focus earthquakes, these acoustic emissions arise from pure shear sources and obey the Gutenberg-Richter law without following Omori’s law. Microstructural observations prove that dynamic weakening likely involves superplasticity of the nanocrystalline spinel reaction product at seismic strain rates.

The origin of deep-focus earthquakes fundamentally differs from that of shallow (<100 km) earthquakes (1), for which theories of rock fracture rely on the properties of coalescing cracks and friction (24). As pressure and temperature increase with depth, intracrystalline plasticity dominates the deformation regime so that rocks yield by creep or flow rather than by brittle fracturing (4). Polymorphic phase transitions in olivine have provided an attractive alternative mechanism for deep-focus earthquakes (5, 6). For instance, transformation of olivine to its high-pressure polymorphs could induce faulting in polycrystalline Mg2GeO4 olivine (7, 8). This was further confirmed on silicate olivine, (Mg,Fe)2SiO4, during the olivine-wadsleyite transition (9). Additional experiments demonstrated that the mechanism produced acoustic emissions (AEs) (10).

In total, we performed eight experiments on both powdered and sintered Ge-olivine samples in the stability field of the spinel polymorph, at confining pressures from 2 to 5 GPa and temperatures between 973 and 1573 K (fig. S2). Sintered samples consisted of fully densified “rocks” of isostatically hot pressed polycrystalline Mg2GeO4 (Ge-olivine) containing minor amounts of Ge-pyroxene (<5 vol %) (11). We used the germanate analog of Mg2SiO4 olivine because transformation into its denser polymorph can be reached at pressures routinely achievable in the deformation apparatus. Stress, transformation progress, and strain were measured in situ by using x-ray powder diffraction (XRD) and radiographic imaging, respectively. AEs were recorded continuously on six channels. Description of the set-up is given in the supplementary materials (fig. S1) (12).

Differential stress, strain, and acoustic activity for sample D1247 evolved as a function of time (Fig. 1). The sample was first pressurized to 4 GPa at room temperature then deformed at a constant temperature of 973 K with a strain rate of 5 ± 1 × 10−5 s−1. Differential stress built up to 2.75 GPa [discussion of uncertainties of stress measurement in synchrotron experiments can be found in (12, 13)] at 10% strain, followed by temperature ramping to 1173 K, which induced some softening. No spinel was detected in XRD patterns, and no AE was observed up to this point. Beyond 20% strain, however, AEs were triggered; their release rate peaked at time (t) ∼ 4200 s, coinciding with an abrupt increase in strain rate, to 1 ± 0.1 × 10−4 s−1, a stress drop of ≈100 MPa and a large burst of intense AEs. The sources of these AEs were located inside the sample (fig. S3) (12). XRD data collected toward the end of the experiment revealed the presence of a small amount (<5%) of spinel.

Fig. 1 Stress, strain and acoustic emission.

Evolution of temperature, differential stress, strain, and AE rate during experiment D1247 performed at 4 GPa effective mean stress.

Complete AE waveform catalogs were built for two experiments (D1247 and D1253), at 4 and 5 GPa confining pressure, respectively. In total, more than 500 AEs were recorded. Waveforms, amplitude, and length of the AEs varied considerably (Fig. 2A), lasting from 10 μs to 4 ms. Generally, the recorded acoustic signals are a combination of the source, resonance of the sensors, and that of mechanical set-up, so that the duration of the AEs is not directly representative of that of the source but scales with the AE amplitude. Here, the longest AE events displayed amplitudes exceeding the voltage saturation limit of our recording system (5 V). These amplitudes are larger than those observed during cold compression of quartz at high pressure (14) and are comparable with those observed during brittle failure of centimeter-sized samples of pure glass (15). The frequency of relative moment magnitudes (MAE) for two AE catalogs follows a power law distribution (Fig. 2B), generally referred to as the Gutenberg-Richter (GR) law, that is systematically observed both in the field (1, 16) and in the laboratory (17). In consequence, there was a range of source sizes in our experiments—the upper limit being the length of the sample (3 mm)—which opens the possibility that the phenomenon could be scaled to much larger dimensions. Here, the power law exponent (or b-value) is on the order of 0.5 to 0.6—lower than 1, as often observed in the case of deep-focus earthquakes (1). The absence of long and sustained “aftershock” sequences (Omori-type sequence) after large AEs in our experiments also seems to correspond to a peculiarity of deep-focus earthquakes; for instance, the largest deep earthquake ever recorded [moment magnitude (Mw) 8.3 Sea of Okhotsk earthquake on 24 May 2013, 610 km depth] was followed by only a few aftershocks until now in the immediate vicinity of the rupture plane.

Fig. 2 AE magnitude catalog and GR distribution.

(A) Amplitude and duration of 5 AEs of relative magnitude equal to ≈0, ≈1, ≈2, ≈3 and ≈4, respectively, from bottom to top. The reference event MAE = 1 is shown. (B) Statistical distribution of the relative magnitudes within four magnitude bins (0 < MAE < 1, 1 < MAE < 2, 2 < MAE < 3, and 3 < MAE < 4) and for experiments D1247 (4 GPa) and D1253 (5 GPa). The moment magnitude completeness of each catalog is MAE > 0. A slope of 1 for the b value is displayed for reference.

With six recording sensor “stations” and using first-motion relative amplitudes (fig. S3), we performed moment tensor inversions (12) for 44 events with 1 < MAE < 2 (Fig. 3). Like deep-focus earthquakes, which invariably show the absence of volumetric component associated with the earthquake source (1), all 44 events exhibit a negligible isotropic component; no volumetric strain is associated with the source. AEs are more than 95% in shear (k < 0.05), some showing positive or negative compensated linear vector dipole (CLVD) component, which might be due to geometric complexities during source propagation (fig. S4). Some deep-focus earthquakes have also been reported as being up to 50% CLVD (1).

Fig. 3 AE moment tensor inversion.

Moment tensor inversions displayed within a T-K plot (1 < MAE < 2). The variables t and k represent the decomposition of the moment into a deviatoric (shear) and an isotropic (volumetric) component, respectively (12, 30). The ellipsoid of error indicates that the uncertainty on the ratio between isotropic and deviatoric components is low.

Sample D1253 is crosscut by a set of conjugate macroscopic faults (Fig. 4A) and displays typical barreling of the sides, as expected for a specimen deformed within the ductile regime. A close-up view of the fracture (Fig. 4B) reveals a pyroxene grain intensely sheared during fracture propagation. Using the grain as a marker, the total displacement across the fault is ≈30 μm. Transmission electron microscopy (TEM) examination of a focused ion beam foil (Fig. 4C) demonstrates that the fault is ~100 nm thick (Fig. 4D). The fault “gouge” consists of nanocrystalline spinel (Fig. 4E), the largest crystals measuring only 20 to 40 nm. No amorphous material was observed. On both sides of the fracture, high dislocation density indicates intense deformation. Selected area electron diffraction patterns collected on both sides of the fault plane demonstrated that the fracture walls consist of several large olivine grains, indicating that the fault has cut through multiple grains. These microstructural observations confirm our AE moment tensor inversion. Indeed, the faults being so narrow, the volumetric contraction induced by the solid-phase transformation (ΔV ≈ 7%) is negligible when compared with the shear across the fault. In such a way, AEs in our experiment have shear sources, yet their propagation does involve a—negligible—volumetric contraction.

Fig. 4 Microstructure of the transformed fault zone.

Electron micrographs of sample D1253, which failed at 5 GPa. (A) Full view of the sample (σ1 is vertical). Horizontal fractures are likely to have been caused during decompression. The red box corresponds to the location of (B). (B) High-magnification view of one of the fracture planes. The white grains are Ge-enstatite (MgGeO3), and the gray grains are Ge-olivine, the grain size of which are <10 and 150 μm, respectively. The red box corresponds to the location of (C). (C) A narrow band of light gray material highlights the fault. The red line indicates the location of the FIB section (D). (D) Close-up TEM view of the fault zone. Dashed lines highlight the main fault, only 100 nm thick. The gouge consists of fully crystalline nanometric material. The fracture walls are intensely deformed. (E) Electron diffraction patterns of the gouge and adjacent wall rock display bright olivine spots and numerous spinel spots emanating from the gouge itself.

For a rupture to radiate acoustic waves during propagation, it must travel at a velocity that is a nonnegligible fraction (>10%) of the shear wave velocity cs, which for Ge-olivine in these conditions is ~5 km/s. Assuming a rupture propagation velocity of 0.2 cs only (18) and considering the millimeter size of our specimens, the source duration of the largest AEs must be on the order of a few microseconds only. The offsets of the largest fault observed within the specimen being of ~10 μm, and assuming only 10% of that slip as “coseismic,” the minimum bound for the sliding velocity is on the order of ~1 m/s (for a crack-like rupture), which is comparable with slip velocities typically inferred during earthquakes (19). Considering that the fault extends over ~1 mm, the stress drop Δσ = CμD/L [where μ is the shear modulus (~100 GPa), C is a geometric constant on the order of 1, D is the coseismic slip, and L is the fault length] (20) inferred on this large fault is on the order of 100 MPa. This is consistent with the stress drop observed in our stress-strain record. It corresponds to maximum values inferred by seismologic studies of deep (18, 20) and intermediate (21) earthquakes up to date. A large number of smaller faults could be observed (fig. S4) for which the ratio of slip versus fault length may indicate smaller stress drops. If some of these complex systems of parallel and conjugate faults were propagating contemporaneously—meaning that if the source consisted of not a singular fault plane but several segments propagating together—these could possibly be at the origin of the large CLVD components observed.

No evidence of melting or amorphous material (19) was found at any scale, implying that the phase transformation must have been essentially instantaneous during fault propagation. Because of high normal stress, this observation not only implies that little frictional heating occurred (dynamic friction coefficient of ≈0.1 at most) (supplementary text) but also that dynamic weakening occurred during fracture propagation in the absence of fluids or melt.

In these experiments, AEs were observed only after a certain level of axial strain (10 to 20%). High dislocation density within Ge-olivine grains promotes spinel nucleation at dislocation pile-ups or tangles. Stress concentrations due to volumetric contraction are likely also playing an important role (6), as well as reaction-driven latent heat release. Our observations suggest that instabilities are triggered when nucleation is the dominant control mechanism (relatively cold conditions and large pressure overstepping) so that the grain size of the (spinel) reaction product is on the nanometer scale (Fig. 4D). Superplastic flow is commonly observed in ultrafine-grained materials (22), and a crude extrapolation of superplastic flow laws in olivine (23) shows that under these conditions (high stresses and extremely fine grains), grain boundary sliding can accommodate strain rates as high as 103 to 104 s−1 (supplementary text). These are compatible with seismic strain rates, implying that the dynamic weakening mechanism is superplastic flow. The paradox between the observation of extreme dynamic weakening and partial stress drops, also true in brittle materials (24), implies extremely fast fault strength recovery. Superplastic flow may only be active at the rupture tip and within the breakdown zone, where the stress concentrations are high enough. Last, the paucity of aftershocks may be explained by the fact that rupture nucleation and propagation are intrinsically linked to the phase transformation, which is irreversible.

In all eight experiments, the temperature range (fig. S2A) at which we observed AEs was narrow (1000 to 1250 K) over a wide range of confining pressure conditions (2 to 5 GPa), which extends former experimental observations (7, 8) to higher pressures, suggesting that transformational faulting is controlled by spinel nucleation kinetics and therefore by absolute temperature rather than homologous temperature (ratio of absolute temperature to melting temperature). The direct implication is that deep-focus seismicity depth range and rate should, at least in part, correlate with the subducted lithosphere temperature, and thus its age.

Although in our experiments the absolute stress value remains high (fig. S2B) compared with stresses expected within the cold core of subducted slabs (25), the observed stress drops are broadly consistent with those calculated for deep earthquakes (1, 18, 20, 21). Constant differential stress conditions at failure over a wide range of confinement (2 to 5 GPa) strongly suggest that transformational faulting is largely independent of normal stress and thus involves nonfrictional processes. We suggest that rupture nucleation is controlled by dislocation density and spinel nucleation kinetics, whereas propagation is controlled by superplastic flow. High-stress and high–dislocation density conditions can be met in a cold subducting slab full of metastable olivine (2628) owing to stress concentrations at the micro- and mesoscopic scales because of buckling, folding, and/or inherited fractures (29). This is particularly true in the Tonga-Kermadec region, for instance (28, 29), for which the largest catalog of deep-focus earthquakes is available (1).

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S4

Data Files S1 and S2

References (3150)

Movies S1 and S2

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: We thank A. Addad, D. Deldicque, I. Estève, E. Larue, and Y. Pinquier for technical support and three reviewers for their constructive remarks, which helped to improve this work. This work was funded through Institut National des Sciences de l’Univers (project “Deep Quakes”) and L’Agence Nationale de la Recherche (project “DELF”). GeoSoilEnviroCARS is supported by the National Science Foundation–Earth Sciences (EAR-1128799) and U.S. Department of Energy–Geosciences (DE-FG02-94ER14466). Use of the Advanced Proton Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357. Part of the AE technical development was made possible by the National Science Foundation grant EAR-0968456 (Y.W.). Data are available in the supplementary materials.
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