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The dynamics of melt and shear localization in partially molten aggregates

Abstract

The volcanoes that lie along the Earth's tectonic boundaries are fed by melt generated in the mantle. How this melt is extracted and focused to the volcanoes, however, remains an unresolved question. Here we present new theoretical results with implications for melt focusing beneath mid-ocean ridges. By modelling laboratory experiments1,2, we test a formulation for magma dynamics and provide an explanation for localized bands of high-porosity and concentrated shear deformation observed in experiments. These bands emerge and persist at 15°–25° to the plane of shear. Past theoretical work on this system predicted the emergence of melt bands3,4 but at an angle inconsistent with experiments. Our results suggest that the observed band angle results from a balance of porosity-weakening and strain-rate-weakening deformation mechanisms. Lower band angles are predicted for greater strain-rate weakening. From these lower band angles, we estimate the orientation of melt bands beneath mid-ocean ridges and show that they may enhance magma focusing toward the ridge axis.

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Figure 1: A comparison of experimental and numerical results.
Figure 2: Results from linear analysis and numerical simulations, showing the effect of stress exponent n on the angular dependence of porosity of melt bands.
Figure 3: Estimated orientation of melt bands beneath a mid-ocean ridge from a two-dimensional, steady-state simulation of mantle flow23.

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Acknowledgements

This work was supported by the Department of Energy Computational Science Graduate Fellowship Program of the Office of Science and National Nuclear Security Administration in the Department of Energy, and the NSF. We thank B. Smith, M. Knepley and the PETSc team at Argonne National Laboratory. We are also grateful to E. Coon, P. Kelemen and the solid Earth geodynamics group at LDEO for discussions. Comments by M. Jellinek helped to improve the manuscript.

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Correspondence to Richard F. Katz.

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Supplementary Notes

This file contains Supplementary Discussion with equations. This section contains text detailing the derivation of linear analysis results presented in the text. The text also describes the methods, boundary and initial conditions and results of numerical simulations. This file also contains Supplementary Figures 1–4. These figures help to elucidate the behavior of the numerical and analytical models for different values of the non-linear parameter n. This file also contains Supplementary Movie Legend and additional references. (PDF 904 kb)

Supplementary Movie 1

This movie shows the results of a numerical simulation as described in the text and movie caption. This simulation progresses to a shear strain of about 2.75. High porosity bands develop and shear strain is concentrated onto these bands, as shown by the black strain markers. Band reconnection and realignment may be observed in the porosity field. (MOV 2543 kb)

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Katz, R., Spiegelman, M. & Holtzman, B. The dynamics of melt and shear localization in partially molten aggregates. Nature 442, 676–679 (2006). https://doi.org/10.1038/nature05039

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