Preprints
https://doi.org/10.5194/egusphere-2023-2683
https://doi.org/10.5194/egusphere-2023-2683
17 Nov 2023
 | 17 Nov 2023

Automatic adjoint-based inversion schemes for geodynamics: Reconstructing the evolution of Earth’s mantle in space and time

Siavash Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham

Abstract. Reconstructing the thermo-chemical evolution of Earth's mantle and its diverse surface manifestations is a widely-recognised grand challenge for the geosciences. It requires the creation of a digital twin: a digital representation of Earth's mantle across space and time that is compatible with available observational constraints on the mantle's structure, dynamics and evolution. This has led geodynamicists to explore adjoint-based approaches that reformulate mantle convection modelling as an inverse problem, in which unknown model parameters can be optimised to fit available observational data. Whilst recent years have seen a notable increase in the use of adjoint-based methods in geodynamics, the theoretical and practical challenges of deriving, implementing and validating adjoint systems for large-scale, non-linear, time-dependent problems, such as global mantle flow, has hindered their broader use. Here, we present the Geoscientific Adjoint Optimisation Platform (G-ADOPT), an advanced computational modelling framework that overcomes these challenges for coupled, non-linear, time-dependent systems. By integrating three main components: (i) Firedrake, an automated system for the solution of partial differential equations using the finite element method; (ii) Dolfin-Adjoint, which automatically generates discrete adjoint models in a form compatible with Firedrake; and (iii) the Rapid Optimisation Library, ROL, an efficient large-scale optimisation toolkit; G-ADOPT enables the application of adjoint methods across geophysical continua, showcased herein for geodynamics. Through two sets of synthetic experiments, we demonstrate application of this framework to the initial condition problem of mantle convection, in both square and annular geometries, for both isoviscous and non-linear rheologies. We confirm the validity of the gradient computations underpinning the adjoint approach, for all cases, through second-order Taylor remainder convergence tests, and subsequently demonstrate excellent recovery of the unknown initial conditions. Moreover, we show that the framework achieves theoretical computational efficiency. Taken together, this confirms the suitability of G-ADOPT for reconstructing the evolution of Earth's mantle in space and time. The framework overcomes the significant theoretical and practical challenges of generating adjoint models, and will allow the community to move from idealised forward models to data-driven simulations that rigorously account for observational constraints and their uncertainties using an inverse approach.

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Journal article(s) based on this preprint

03 Jul 2024
Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and time
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024,https://doi.org/10.5194/gmd-17-5057-2024, 2024
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.

Short summary
We introduce the Geoscientific Adjoint Optimisation Platform (G-ADOPT), designed to improve our...
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