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Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity

Li, Dunzhu and Gurnis, Michael and Stadler, Georg (2017) Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity. Geophysical Journal International, 209 (1). pp. 86-105. ISSN 0956-540X. doi:10.1093/gji/ggw493.

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We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature-dependent and strain-rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a pre-conditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.

Item Type:Article
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URLURL TypeDescription
Li, Dunzhu0000-0003-3149-0236
Gurnis, Michael0000-0003-1704-597X
Additional Information:© 2017 The Authors. Published by Oxford University Press on behalf of The Royal Astronomical Society. Accepted 2017 January 3. Received 2016 December 5; in original form 2016 July 8; Published: 13 January 2017. DL and MG were supported by the National Science Foundation under EAR-1247022. We would like to thank Mark Simons for comments and suggestions and David May and Alik Ismail-Zadeh for detailed and careful reviews that helped us to significantly improve the manuscript.
Group:Seismological Laboratory
Funding AgencyGrant Number
Subject Keywords:Inverse theory; Dynamics of lithosphere and mantle
Issue or Number:1
Record Number:CaltechAUTHORS:20170417-074407210
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Official Citation:Dunzhu Li, Michael Gurnis, Georg Stadler; Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity. Geophys J Int 2017; 209 (1): 86-105. doi: 10.1093/gji/ggw493
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76584
Deposited By: Tony Diaz
Deposited On:24 Apr 2017 17:09
Last Modified:15 Nov 2021 17:01

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