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A periodic shear-heating mechanism for intermediate-depth earthquakes in the mantle

Abstract

Intermediate-depth earthquakes1, at depths of 50–300 km in subduction zones, occur below the brittle–ductile transition, where high pressures render frictional failure unlikely. Their location approximately coincides with 600 to 800 °C isotherms in thermal models2, suggesting a thermally activated mechanism for their origin. Some earthquakes may occur by frictional failure owing to high pore pressure that might result from metamorphic dehydration2,3,4,5. Because some intermediate-depth earthquakes occur 30 to 50 km below the palaeo-sea floor6, however, the hydrous minerals required for the dehydration mechanism may not be present. Here we present an alternative mechanism to explain such earthquakes, involving the onset of highly localized viscous creep in pre-existing, fine-grained shear zones. Our numerical model uses olivine flow laws for a fine-grained, viscous shear zone in a coarse-grained, elastic half space, with initial temperatures from 600–800 °C and background strain rates of 10-12 to 10-15 s-1. When shear heating becomes important, strain rate and temperature increase rapidly to over 1 s-1 and 1,400 °C. The stress then drops dramatically, followed by low strain rates and cooling. Continued far-field deformation produces a quasi-periodic series of such instabilities.

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Figure 1: Schematic illustration of some numerical model conditions and results.
Figure 2: Numerical model results for T0 = 650 °C, wez = 1 km, wsz = 2 m, σ0 = 80 MPa, gs0 ≈ 50 μm, adjacent ‘wall rock’ grain size of 10 mm, and far-field velocity of 0.1 m yr-1.
Figure 3: Same model run as in Figs 2, 4 and Supplementary Fig. S1, but for a 30 s time interval centred on the maximum heating rate in the shear heating event at 8,040 years.
Figure 4: Results of steady-state analysis, with T 0 = 650 °C and 700 °C, w sz  ≈ 1 m and w dz  ≈ 10 and 100 m.

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Acknowledgements

Two colleagues were instrumental in helping with this paper: J. Whitehead guided us toward a steady state, and M. Spiegelman helped with a faster thermal diffusion code. In addition we gratefully acknowledge discussions with E. Coon, A. Rubin, P. Molnar, D. McKenzie, M. Billen, J. Gaherty, J. McGuire, L. Montesi, S. Kirby, B. Hacker and J. Warren. This work was supported, in part, by several NSF research grants, the Charles Francis Adams Chair at WHOI (P.B.K.), the Arthur D. Storke Chair at Columbia University (P.B.K.), and a Fellowship from the WHOI Deep Ocean Exploration Institute (G.H.).

Author Contributions While learning from G.H. about the weak fault controversy in Oman, P.B.K. proposed the possibility of a periodic shear heating instability in an upper mantle shear zone of fixed width. P.B.K. constructed the numerical model, and devised the analytical approximation. G.H. provided essential insight on rock mechanics, supplying formulations for olivine flow laws, grain size evolution, stress variation with and without inertial terms, elastic relaxation, and references to prior work on all these topics. G.H. proposed applying the model to intermediate-depth earthquakes. Both authors contributed equally to evaluating and extending model results within natural parameter ranges for temperature, stress, grain size, shear-zone width, and so on, based on our ongoing joint field work.

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Correspondence to Peter B. Kelemen.

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This file contains Supplementary Discussion, Supplementary Figures S1-S5 with Legends and additional references. (PDF 2638 kb)

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Kelemen, P., Hirth, G. A periodic shear-heating mechanism for intermediate-depth earthquakes in the mantle. Nature 446, 787–790 (2007). https://doi.org/10.1038/nature05717

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