Many contemporary problems within the Earth sciences are complex, and require an interdisciplinary approach. This book provides a comprehensive reference on data assimilation and inverse problems, as well as their applications across a broad range of geophysical disciplines. With contributions from world leading researchers, it covers basic knowledge about geophysical inversions and data assimilation and discusses a range of important research issues and applications in atmospheric and cryospheric sciences, hydrology, geochronology, geodesy, geodynamics, geomagnetism, gravity, near-Earth electron radiation, seismology, and volcanology. Highlighting the importance of research in data assimilation for understanding dynamical processes of the Earth and its space environment and for predictability, it summarizes relevant new advances in data assimilation and inverse problems related to different geophysical fields. Covering both theory and practical applications, it is an ideal reference for researchers and graduate students within the geosciences who are interested in inverse problems, data assimilation, predictability, and numerical methods.

1 AUK ISMAIL-ZADEH ,2, TOM BEER3 1 International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Warshavskoye shosse 79-2, Moscow 113556, Russia; e-mail: [email protected] 2 Geophysikalisches Institut, Universittit Karlsruhe, Hertzstr. 16, Karlsruhe 76187, Germany; e-mail: [email protected] 3 CSIRO Environmental Risk Network, CSIRO Atmospheric Research, Aspendale, Vic. 3195 Australia; e-mail: [email protected] The world faces major threats to the sustainability of our planet. These threats are accompanied by the immediate dangers of natural and man-made disasters. Our vulnerability to them is greatly magnified with each passing year undermining our ability to maintain a sustainable and productive world into the 21st Century and beyond. Both history and common sense teach us that science has a tremendous potential to find ways to cope with these threats. 1 The EUROSCIENCE working group "Science and Urgent Problems of Society" 2 and the IUGG Commission on Geophysical Risk and Sustainability were initiators of the EUROSCIENCE - IUGG Advanced Research Workshop "Science for Reduction of Risk and Sustainable Development of Society" sponsored by the NATO Science Program. The Workshop was held on 15-16 June 2002 in Budapest, Hungary. More than 40 participants from 17 countries took part in the Workshop. Talks and discussions addressed mainly the question of how science can help in reduction of risk and sustainable development of society.

1 AUK ISMAIL-ZADEH ,2, TOM BEER3 1 International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Warshavskoye shosse 79-2, Moscow 113556, Russia; e-mail: [email protected] 2 Geophysikalisches Institut, Universittit Karlsruhe, Hertzstr. 16, Karlsruhe 76187, Germany; e-mail: [email protected] 3 CSIRO Environmental Risk Network, CSIRO Atmospheric Research, Aspendale, Vic. 3195 Australia; e-mail: [email protected] The world faces major threats to the sustainability of our planet. These threats are accompanied by the immediate dangers of natural and man-made disasters. Our vulnerability to them is greatly magnified with each passing year undermining our ability to maintain a sustainable and productive world into the 21st Century and beyond. Both history and common sense teach us that science has a tremendous potential to find ways to cope with these threats. 1 The EUROSCIENCE working group "Science and Urgent Problems of Society" 2 and the IUGG Commission on Geophysical Risk and Sustainability were initiators of the EUROSCIENCE - IUGG Advanced Research Workshop "Science for Reduction of Risk and Sustainable Development of Society" sponsored by the NATO Science Program. The Workshop was held on 15-16 June 2002 in Budapest, Hungary. More than 40 participants from 17 countries took part in the Workshop. Talks and discussions addressed mainly the question of how science can help in reduction of risk and sustainable development of society.

Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master cutting-edge techniques. Links to supplementary computer codes are available online.