Book contents
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Series page
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Copyright page
- Contents
- Contributors
- Preface
- Acknowledgements
- Part I Introduction
- 1 Inverse Problems and Data Assimilation in Earth Sciences
- 2 Emerging Directions in Geophysical Inversion
- 3 A Tutorial on Bayesian Data Assimilation
- 4 Third-Order Sensitivity Analysis, Uncertainty Quantification, Data Assimilation, Forward and Inverse Predictive Modelling for Large-Scale Systems
- Part II ‘Fluid’ Earth Applications: From the Surface to the Space
- Part III ‘Solid’ Earth Applications: From the Surface to the Core
- Index
- References
1 - Inverse Problems and Data Assimilation in Earth Sciences
from Part I - Introduction
Published online by Cambridge University Press: 20 June 2023
Book contents
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Series page
- Applications of Data Assimilation and Inverse Problems in the Earth Sciences
- Copyright page
- Contents
- Contributors
- Preface
- Acknowledgements
- Part I Introduction
- 1 Inverse Problems and Data Assimilation in Earth Sciences
- 2 Emerging Directions in Geophysical Inversion
- 3 A Tutorial on Bayesian Data Assimilation
- 4 Third-Order Sensitivity Analysis, Uncertainty Quantification, Data Assimilation, Forward and Inverse Predictive Modelling for Large-Scale Systems
- Part II ‘Fluid’ Earth Applications: From the Surface to the Space
- Part III ‘Solid’ Earth Applications: From the Surface to the Core
- Index
- References
Summary
Abstract: We introduce direct and inverse problems, which describe dynamical processes causing change in the Earth system and its space environment. A well-posedness of the problems is defined in the sense of Hadamard and in the sense of Tikhonov, and it is linked to the existence, uniqueness, and stability of the problem solution. Some examples of ill- and well-posed problems are considered. Basic knowledge and approaches in data assimilation and solving inverse problems are discussed along with errors and uncertainties in data and model parameters as well as sensitivities of model results. Finally, we briefly review the book’s chapters which present state-of-the-art knowledge in data assimilation and geophysical inversions and applications in many disciplines of the Earth sciences: from the Earth’s core to the near-Earth environment.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2023
References
Asch, M., Bocquet, M., and Nodet, M. (2016). Data Assimilation: Methods, Algorithms, and Applications. Philadelphia, PA: Society of Industrial and Applied Mathematics.Google Scholar
Aster, R. C., Borchers, B., and Thurber, C. H. (2005). Parameter Estimation and Inverse Problems, vol. 90. San Diego, CA: Elsevier.Google Scholar
Backus, G. E., and Gilbert, F. (1968). The resolving power of gross Earth data. Geophysical Journal of the Royal Astronomical Society, 16, 169–205.Google Scholar
Bennett, A. F. (1992). Inverse Methods in Physical Oceanography. Cambridge: Cambridge University Press.Google Scholar
Blayo, E., Bocquet, M., Cosme, E., and Cugliandolo, L. F., eds. (2014). Advanced Data Assimilation for Geosciences. Oxford: Oxford University Press.CrossRefGoogle Scholar
Bunge, H.-P., Hagelberg, C. R., and Travis, B. J. (2003). Mantle circulation models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography. Geophysical Journal International, 152, 280–301.Google Scholar
Fletcher, S. J. (2017). Data Assimilation for the Geosciences: From Theory to Application. Amsterdam: Elsevier.Google Scholar
Fournier, A., Eymin, C., and Alboussiere, T. (2007). A case for variational geomagnetic data assimilation: Insights from a one-dimensional, non-linear, and sparsely observed MHD system. Nonlinear Processes in Geophysics, 14(3), 163–80.Google Scholar
Ghil, M., and Malanotte-Rizzoli, P. (1991). Data assimilation in meteorology and oceanography. Advances in Geophysics, 33, 141–266.Google Scholar
Hadamard, J. (1902). Sur les problèmes aux dérivées partielles et leur signification physique. Princeton University Bulletin, XIII(4), 49–52.Google Scholar
Hier-Majumder, C. A., Travis, B. J., Belanger, E. et al. (2006). Efficient sensitivity analysis for flow and transport in the Earth’s crust and mantle. Geophysical Journal International, 166, 907–22.Google Scholar
Ismail-Zadeh, A., and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge: Cambridge University Press.Google Scholar
Ismail-Zadeh, A. T., Korotkii, A. I., Naimark, B. M., and Tsepelev, I. A. (2003). Three-dimensional numerical simulation of the inverse problem of thermal convection. Computational Mathematics and Mathematical Physics, 43(4), 587–99.Google Scholar
Ismail-Zadeh, A., Schubert, G., Tsepelev, I., and Korotkii, A. (2004). Inverse problem of thermal convection: Numerical approach and application to mantle plume restoration. Physics of the Earth and Planetary Interiors, 145, 99–114.Google Scholar
Ismail-Zadeh, A., Korotkii, A., and Tsepelev, I. (2016). Data-Driven Numerical Modeling in Geodynamics: Methods and Applications. Heidelberg: Springer.Google Scholar
Kabanikhin, S.I. (2011). Inverse and Ill-Posed Problems. Theory and Applications. Berlin: De Gruyter.Google Scholar
Kalnay, E. (2003). Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press.Google Scholar
Kirsch, A. (1996). An Introduction to the Mathematical Theory of Inverse Problems. New York: Springer.Google Scholar
Lahoz, W., Khattatov, B., and Menard, R., eds. (2010). Data Assimilation: Making Sense of Observations. Berlin: Springer.Google Scholar
Law, K., Stuart, A., and Zygalakis, K. (2015). Data Assimilation: A Mathematical Introduction. Berlin: Springer.Google Scholar
Le Dimet, F.-X., Navon, I. M., and Daescu, D. N. (2002). Second-order information in data assimilation. Monthly Weather Review, 130, 629–48.Google Scholar
Liu, D., Tangborn, A., and Kuang, W. 2007. Observing system simulation experiments in geomagnetic data assimilation. Journal of Geophysical Research, 112. https://doi.org/10.1029/2006JB004691.Google Scholar
McLaughlin, D. (2002). An integrated approach to hydrologic data assimilation: Interpolation, smoothing, and forecasting. Advances in Water Research, 25, 1275–86.Google Scholar
Park, S. K., and Xu, L., eds. (2009). Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Berlin: Springer.Google Scholar
Saltus, R. W., and Blakely, R. J. (2011). Unique geologic insights from ‘non-unique’ gravity and magnetic interpretation. GSA Today, 21(12), 4–11. https://doi.org/10.1130/G136A.1Google Scholar
Samarskii, A. A., and Vabishchevich, P. N. (2007). Numerical Methods for Solving Inverse Problems of Mathematical Physics. Berlin: De Gruyter.Google Scholar
Tikhonov, A. N. (1963). Solution of incorrectly formulated problems and the regularization method. Doklady Akademii Nauk SSSR, 151, 501–4 (Engl. transl.: Soviet Math. Dokl. 4, 1035–8).Google Scholar
Weyl, H. (1911). Über die asymptotische Verteilung der Eigenwerte: Nachrichten der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Naturwissenschaftliche Klasse, 110–17.Google Scholar