Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences

Open Access Published by De Gruyter 2013

Large Scale Inverse Problems

Computational Methods and Applications in the Earth Sciences

Edited by: Mike Cullen , Melina A Freitag , Stefan Kindermann and Robert Scheichl

Volume 13 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110282269

Overview
Contents

About this book

This book is the second volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.

The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary.

This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 10⁷ and 10⁸ degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 10⁶ and 10⁷ observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters.

The book records the achievements of Workshop 2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". It involves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Author / Editor information

Mike Cullen, MET Office, Exeter, UK; Melina Freitag, University of Bath, UK; Stefan Kindermann, Johann Kepler University Linz, Austria; Robert Scheichl, University of Bath, UK.

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Preface Open Access Download PDF	v
Contents Publicly Available Download PDF	vii
Synergy of inverse problems and data assimilation techniques Melina A. Freitag and Roland W. E. Potthast Open Access Download PDF	1
Variational data assimilation for very large environmental problems Amos S. Lawless Open Access Download PDF	55
Ensemble filter techniques for intermittent data assimilation Sebastian Reich and Colin J. Cotter Open Access Download PDF	91
Inverse problems in imaging Martin Burger, Hendrik Dirks and Jahn Müller Open Access Download PDF	135
The lost honor of ℓ₂-based regularization Kees van den Doel, Uri M. Ascher and Eldad Haber Open Access Download PDF	181
List of contributors Open Access Download PDF	204
Backmatter Open Access Download PDF	205

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Academics, graduate students, industry, universities, government labs, research institutes
Pages
- Front matter: 9
- Main content: 203
Keywords: Ill-Posed Inverse Problems; Data Assimilation; Regularization; Optimization; Geosciences

eBook

Published: August 29, 2013
ISBN: 9783110282269

Hardcover

Published: August 19, 2013
ISBN: 9783110282221