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Data-Driven Numerical Modelling in Geodynamics: Methods and Applications
1. Introduction1.1 Inverse problems in geodynamics1.2 Forward and backward modelling and source of errors1.3 Data assimilation methods
2. Backward advection method and its application to salt tectonics2.1 Basic idea of the backward advection (BAD) method2.2 Modelling of salt diapirism2.3 Mathematical statement2.4 Solution method2.5 Forward and backward model results
3. Variational method and its application to mantle plume evolution3.1 Basic idea of the variational (VAR) method3.2 Mathematical statement3.3 Objective functional3.4 Adjoint problem3.5 Solution method3.6 Restoration of mantle plumes3.7 Challenges in variational data assimilation4. Application of the VAR method to volcanic lava dynamics4.1 Volcanic lava flow4.2 Reconstruction of volcanic lava properties4.3 Mathematical statement4.4 Minimisation problem4.5 Adjoint problem4.6 Numerical approach4.7 Model results and discussion
5. Quasi-reversibility method and its applications5.1 Basic idea of the quasi-reversibility (QRV) method5.2 Mathematical statement5.3 Optimisation problem and numerical approach5.4 Restoration of mantle plumes5.5 Restoration of descending lithosphere evolution6. Application of the QRV method to reconstruction of plate subduction6.1 Plate subduction beneath the Japanese islands6.2 Mathematical statement6.3 Input Seismic temperature model6.4 Boundary conditions6.5 Rheological model6.6 Numerical approach6.7 Model results6.8 Data uncertainties
7. Comparison of data assimilation methods for mantle convection models
2. Backward advection method and its application to salt tectonics2.1 Basic idea of the backward advection (BAD) method2.2 Modelling of salt diapirism2.3 Mathematical statement2.4 Solution method2.5 Forward and backward model results
3. Variational method and its application to mantle plume evolution3.1 Basic idea of the variational (VAR) method3.2 Mathematical statement3.3 Objective functional3.4 Adjoint problem3.5 Solution method3.6 Restoration of mantle plumes3.7 Challenges in variational data assimilation4. Application of the VAR method to volcanic lava dynamics4.1 Volcanic lava flow4.2 Reconstruction of volcanic lava properties4.3 Mathematical statement4.4 Minimisation problem4.5 Adjoint problem4.6 Numerical approach4.7 Model results and discussion
5. Quasi-reversibility method and its applications5.1 Basic idea of the quasi-reversibility (QRV) method5.2 Mathematical statement5.3 Optimisation problem and numerical approach5.4 Restoration of mantle plumes5.5 Restoration of descending lithosphere evolution6. Application of the QRV method to reconstruction of plate subduction6.1 Plate subduction beneath the Japanese islands6.2 Mathematical statement6.3 Input Seismic temperature model6.4 Boundary conditions6.5 Rheological model6.6 Numerical approach6.7 Model results6.8 Data uncertainties
7. Comparison of data assimilation methods for mantle convection models
116 pages, Paperback
Published May 21, 2016
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