Data-Driven Numerical Modelling in Geodynamics: Methods and Applications (eBook)

Alik Ismail-Zadeh is a Chief Scientist / Research Professor of the Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences (RusAS) at Moscow, Russia, and a Senior Scientist at the Institute of Applied Geosciences, Karlsruhe Institute of Technology, Germany. He graduated from the Baku State and Lomonossov Moscow State Universities (mathematics and physics) and received his PhD and Doctor of Science degrees (in geophysics) from RusAS. He has been lecturing on computational geodynamics at the University of Karlsruhe, Abdus Salam International Center for Theoretical Physics in Trieste, and Moscow State University of Oil and Gas, and working as visiting scholar/professor in the universities of California (UCLA), Cambridge, Paris (IPGP), Stockholm (KTH), Tokyo, Trieste, and Uppsala. His scientific interests cover studies of the crust and mantle dynamics, basin evolution, salt tectonics, and seismic hazard through theoretical analysis and numerical modelling. He is an author of over 100 peer-reviewed papers and four books. Alik Ismail-Zadeh is an honorary fellow of the Royal Astronomical Society and has been awarded the Academia Europaea Medal, AGU International Award, and several prestigious fellowships including Alexander von Humboldt, Royal Society of London, Royal Swedish Academy of Sciences, and Russian President.Alexander Korotkii is Head of the Department of Applied Problems of the Institute of Mathematics and Mechanics, Russian Academy of Sciences at Yekaterinburg, Russia. He graduated from Ural State University (mathematics and mechanics) and received his PhD and Doctor of Science degrees (in mathematics) from RusAS. He is also Professor in Mathematics at the Chair of Numerical Mathematics of the Ural Federal University and teach on computational methods and mathematical modeling. His scientific interests cover studies of partial differential equations, optimal control theory, systems of distributed parameters with uncertainties and conflicts, direct and inverse problems in fluid dynamics. He is an author and co-author of 80 research papers.Igor Tsepelev is a Senior Scientist of the Department of Applied Problems of the Institute of Mathematics and Mechanics, RusAS at Yekaterinburg, Russia. He graduated from the Ural State University (mathematics and mechanics) and received his PhD in mathematics (differential equations and inverse problems) from RusAS. His scientific interests cover studies of inverse ill-posed problems, development of numerical methods for solving systems of partial differential equations and algorithms for parallel computing, and mathematical and numerical modeling in geophysics. He is an author and co-author of more than 50 research papers. 

1.Introduction1.1Inverse problems in geodynamics1.2Forward and backward modelling and source of errors1.3Data assimilation methods2.Backward advection method and its application to salt tectonics2.1Basic idea of the backward advection (BAD) method2.2Modelling of salt diapirism2.3Mathematical statement2.4Solution method2.5Forward and backward model results3.Variational method and its application to mantle plume evolution3.1Basic idea of the variational (VAR) method3.2Mathematical statement3.3Objective functional3.4Adjoint problem3.5Solution method3.6Restoration of mantle plumes3.7Challenges in variational data assimilation4.Application of the VAR method to volcanic lava dynamics4.1Volcanic lava flow4.2Reconstruction of volcanic lava properties4.3Mathematical statement4.4Minimisation problem4.5Adjoint problem4.6Numerical approach4.7Model results and discussion5.Quasi-reversibility method and its applications5.1Basic idea of the quasi-reversibility (QRV) method5.2Mathematical statement5.3Optimisation problem and numerical approach5.4Restoration of mantle plumes5.5Restoration of descending lithosphere evolution6. Application of the QRV method to reconstruction of plate subduction6.1Plate subduction beneath the Japanese islands6.2Mathematical statement6.3Input data: Seismic temperature model6.4Boundary conditions6.5Rheological model6.6Numerical approach6.7Model results6.8Data uncertainties7.Comparison of data assimilation methods for mantle convection models