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19 - Data Assimilation in Geodynamics: Methods and Applications

from Part III - ‘Solid’ Earth Applications: From the Surface to the Core

Published online by Cambridge University Press:  20 June 2023

By
Alik Ismail-Zadeh ,
Igor Tsepelev  and
Alexander Korotkii
Edited by
Alik Ismail-Zadeh ,
Fabio Castelli ,
Dylan Jones  and
Sabrina Sanchez
Alik Ismail-Zadeh
Affiliation:
Karlsruhe Institute of Technology, Germany
Fabio Castelli
Affiliation:
Università degli Studi, Florence
Dylan Jones
Affiliation:
University of Toronto
Sabrina Sanchez
Affiliation:
Max Planck Institute for Solar System Research, Germany
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Summary

Abstract: In this chapter, we review basic methods for data assimilation used in geodynamic modelling: backward advection (BAD), variational/adjoint (VAR), and quasi-reversibility (QRV). The VAR method is based on a search for model parameters (e.g. mantle temperature and flow velocity in the past) by minimising the differences between present observations of the relevant physical parameters (e.g. temperature derived from seismic tomography, geodetic measurements) and those predicted by forward models for an initial guess temperature. The QRV method is based on introduction of the additional term involving the product of a small regularisation parameter and a higher-order temperature derivative into the backward heat equation. The data assimilation in this case is based on a search of the best fit between the forecast model state and the observations by minimising the regularisation parameter. To demonstrate the applicability of the considered data assimilation methods, a numerical model of the evolution of mantle plumes is considered. Also, we present an application of the data assimilation to dynamic restoration of the thermal state of the mantle beneath the Japanese islands and their surroundings. The geodynamic restoration for the last 40 million years is based on the assimilation of the present temperature inferred from seismic tomography, and constrained by the present plate movement derived from geodetic observations, and paleogeographic and paleomagnetic plate reconstructions. Finally, we discuss some challenges, advantages, and disadvantages of the data assimilation methods.

Keywords

adjoint problembackward advectiondynamic restorationlithospheric slabmantle plumeobjective functionaloptimizationquasi-reversibility methodvariational data assimilation
Type
Chapter
Information
Applications of Data Assimilation and Inverse Problems in the Earth Sciences , pp. 293 - 310
Publisher: Cambridge University Press
Print publication year: 2023

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