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

Dunzhu Li, Michael Gurnis, Georg Stadler

Research output: Contribution to journalArticle

Abstract

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 preconditioned 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.

Original languageEnglish (US)
Pages (from-to)86-105
Number of pages20
JournalGeophysical Journal International
Volume209
Issue number1
DOIs
StatePublished - Apr 1 2017

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mantle convection
Earth mantle
convection
viscosity
Viscosity
inversions
plate motion
temperature
subduction
Temperature
recovery
mantle
inversion
Convection
Recovery
gradients
sinking
optimization
pulse detonation engines
Constrained optimization

Keywords

  • Dynamics of lithosphere and mantle
  • Inverse theory

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology

Cite this

Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity. / Li, Dunzhu; Gurnis, Michael; Stadler, Georg.

In: Geophysical Journal International, Vol. 209, No. 1, 01.04.2017, p. 86-105.

Research output: Contribution to journalArticle

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