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Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples

Ratnaswamy, V. and Stadler, G. and Gurnis, M. (2015) Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples. Geophysical Journal International, 202 (2). pp. 768-786. ISSN 0956-540X. doi:10.1093/gji/ggv166.

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We develop and validate a systematic approach to infer plate boundary strength and rheological parameters in models of mantle flow from surface velocity observations. Based on a realistic rheological model that includes yielding and strain rate weakening from dislocation creep, we formulate the inverse problem in a Bayesian inference framework. To study the distribution of parameters that are consistent with the observations, we compute the maximum a posteriori (MAP) point, Gaussian approximations of the parameter distribution around that MAP point, and employ Markov Chain Monte Carlo (MCMC) sampling methods. The computation of the MAP point and the Gaussian approximation require first and second derivatives of an objective function subject to non-linear Stokes equations; these derivatives are computed efficiently using adjoint Stokes equations. We set up 2-D numerical experiments with many of the elements expected in a global geophysical inversion. This setup incorporates three subduction zones with slab and weak zone (interplate fault) geometry consistent with average seismic characteristics. With these experiments, we demonstrate that when the temperature field is known, we can recover the strength of plate boundaries, the yield stress and strain rate exponent in the upper mantle. When the number of uncertain parameters increases, there are trade-offs between the inferred parameters. These trade-offs depend on how well the observational data represents the surface velocities, and on the weakness of plate boundaries. As the plate boundary coupling drops below a threshold, the uncertainty of the inferred parameters increases due to insensitivity of plate motion to plate coupling. Comparing the trade-offs between inferred rheological parameters found from the Gaussian approximation of the parameter distribution and from MCMC sampling, we conclude that the Gaussian approximation—which is significantly cheaper to compute—is often a good approximation, in particular locally around the MAP point. Thus, the method can be applied to the global problem of inferring non-linear constitutive parameters and plate coupling factors for each subduction zone in a global geophysical inversion with known slab structure.

Item Type:Article
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Gurnis, M.0000-0003-1704-597X
Additional Information:© 2015 The Authors. Published by Oxford University Press on behalf of The Royal Astronomical Society. Accepted 2015 April 14. Received 2015 March 31; in original form 2014 December 24. Supported by the National Science Foundation through EAR-1247022, EAR-1118239, and CMMI-1028978. We thank Noemi Petra and Johann Rudi for valuable discussions.
Group:Seismological Laboratory
Funding AgencyGrant Number
Subject Keywords:Inverse theory; Plate motions; Mantle processes; Rheology: mantle
Issue or Number:2
Record Number:CaltechAUTHORS:20150924-101837483
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Official Citation:Vishagan Ratnaswamy, Georg Stadler, and Michael Gurnis Adjoint-based estimation of plate coupling in a non-linear mantle flow model: theory and examples Geophys. J. Int. (August, 2015) 202 (2): 768-786 doi:10.1093/gji/ggv166
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60478
Deposited By: Tony Diaz
Deposited On:24 Sep 2015 23:59
Last Modified:10 Nov 2021 22:34

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