Data-driven numerical modelling in geodynamics [electronic resource] : methods and applications / Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev.

Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Inverse Problems in Geodynamics; 1.2 Forward and Backward Modelling and Source of Errors; 1.3 Data Assimilation Methods; References; 2 Backward Advection Method and Its Application to Modelling of Salt Tectonics; 2.1 Basic Idea of the Backward Advection (BAD) Method; 2.2 Modelling of Salt Diapirism; 2.3 Mathematical Statement; 2.4 Solution Method; 2.5 Forward and Backward Model Results; References; 3 Variational Method and Its Application to Modelling of Mantle Plume Evolution; 3.1 Basic Idea of the Variational (VAR) Method

3.2 Mathematical Statement3.3 Objective Functional; 3.4 Adjoint Problem; 3.5 Solution Method; 3.6 Restoration of Mantle Plumes; 3.6.1 Model and Methods; 3.6.2 Forward Modelling; 3.6.3 Backward Modelling; 3.6.4 Performance of the Numerical Algorithm; 3.7 Challenges in VAR Data Assimilation; 3.7.1 Data Smoothness; 3.7.2 Numerical Noise; References; 4 Application of the Variational Method to Lava Flow Modelling; 4.1 Lava Flow; 4.2 Reconstruction of Lava Properties; 4.3 Mathematical Statement; 4.4 Minimisation Problem; 4.5 Adjoint Problem; 4.6 Numerical Approach; 4.7 Model Results and Discussion

6.1 Plate Subduction Beneath the Japanese Islands6.2 Mathematical Statement; 6.3 Input Data: Seismic Temperature Model; 6.4 Boundary Conditions; 6.5 Rheological Model; 6.6 Numerical Approach; 6.7 Model Results; 6.8 Data Uncertainties; References; 7 Comparison of Data Assimilation Methods; References