Preface ......................................................... v
About the Editors ............................................. vii
Contributors ................................................. xiii
Volume 1
General Issues, Key Technologies, Data Acquisition,
Modeling the System Earth
1 Geomathematics: Its Role, Its Aim, and Its Potential ......... 3
Willi Freeden
2 Navigation on Sea: Topics in the History of
Geomathematics .............................................. 43
Thomas Sonar
3 Earth Observation Satellite Missions and Data Access ........ 71
Henri Laur, Volker Liebig
4 GOCE: Gravitational Gradiometry in a Satellite .............. 93
Reiner Rummel
5 Sources of the Geomagnetic Field and the Modern Data That
Enable Their Investigation ................................. 105
Nils Olsen, Gauthier Hulot Terence Sabaka
6 Classical Physical Geodesy ................................. 127
Helmut Moritz
7 Spacetime Modelling of the Earth's Gravity Field by
Ellipsoidal Harmonics ...................................... 159
Erik W. Grafarend, Matthias Klapp, Zdenek Martinec
8 Time-Variable Gravity Field and Global Deformation of
the Earth .................................................. 253
Jürgen Kusche
9 Satellite Gravity Gradiometry (SGG): From Scalar to
Tensorial Solution ......................................... 269
Willi Freeden, Michael Schreiner
10 Gravitational Viscoelastodynamics .......................... 303
Detlef Wolf
11 Multiresolution Analysis of Hydrology and Satellite
Gravitational Data ......................................... 333
Helga Nutz, Kerstin Wolf
12 Time Varying Mean Sea Level ................................ 353
Luciana Fenoglio-Marc, Erwin Groten
13 Unstructured Meshes in Large-Scale Ocean Modeling .......... 371
Sergey Danilov, Jens Schroter
14 Numerical Methods in Support of Advanced Tsunami Early
Warning .................................................... 399
Jörn Behrens
15 Efficient Modeling of Flow and Transport in Porous Media
Using Multiphysics and Multiscale Approaches ............... 417
Rainer Helmig, Jennifer Niessner, Bernd Flemisch, Markus
Wolff, Jochen Fritz
16 Numerical Dynamo Simulations: From Basic Concepts to
Realistic Models ........................................... 459
Johannes Wicht, Stephan Stellmach, Helmut Harder
17 Mathematical Properties Relevant to Geomagnetic Field
Modeling ................................................... 503
Terence J. Sabaka, Gauthier Hulot, Nils Olsen
18 Multiscale Modeling of the Geomagnetic Field and
Ionospheric Currents ....................................... 539
Christian Gerhards
19 The Forward and Adjoint Methods of Global Electromagnetic
Induction for CHAMP Magnetic Data .......................... 565
Zdeněk Martinec
20 Asymptotic Models for Atmospheric Flows .................... 625
Rupert Klein
21 Modern Techniques for Numerical Weather Prediction:
A Picture Drawn from Kyrill ................................ 649
Nils Dorband, Martin Fengler, Andreas Gumann, Stefan Laps
22 Modeling Deep Geothermal Reservoirs: Recent Advances and
Future Problems ............................................ 679
Maxim Ilyasov, Isabel Ostermann, Alessandro Punzi
23 Phosphorus Cycles in Lakes and Rivers: Modeling,
Analysis, and Simulation ................................... 713
Andreas Meister, Joachim Benz
Volume 2
Modeling the System Earth, Analytical and Statistical
Methods, Computational and Numerical Algorithms
24 Noise Models for Ill-Posed Problems ........................ 741
Paul N. Eggermont, Vincent LaRiccia, M. Zuhair Nashed
25 Sparsity in Inverse Geophysical Problems ................... 763
Markus Grasmair, Markus Haltmeier, Otmar Scherzer
26 Quantitative Remote Sensing Inversion in Earth Science:
Theory and Numerical Treatment ............................. 785
Yanfei Wang
27 Multiparameter Regularization in Downward Continuation of
Satellite Data ............................................. 813
Shuai Lu, Sergei V. Pereverzev
28 Correlation Modeling of the Gravity Field in Classical
Geodesy .................................................... 833
Christopher Jekeli
29 Modeling Uncertainty of Complex Earth Systems in Metric
Space ...................................................... 865
Jef Caers, Kwangwon Park, Céline Scheldt
30 Slepian Functions and Their Use in Signal Estimation
and Spectral Analysis ...................................... 891
Frederik J. Simons
31 Special Functions in Mathematical Geosciences: An Attempt
at a Categorization ........................................ 925
Willi Freeden, Michael Schreiner
32 Tomography: Problems and Multiscale Solutions .............. 949
Volker Michel
33 Material Behavior: Texture and Anisotropy .................. 973
Ralf Hielscher, David Mainprice, Helmut Schaeben
34 Dimensionality Reduction of Hyperspectral Imagery Data
for Feature Classification ................................ 1005
Charles K. Chui, Jianzhong Wang
35 Oblique Stochastic Boundary-Value Problem ................. 1051
Martin Grothaus, Thomas Raskop
36 Geodetic Deformation Analysis with Respect to an
Extended Uncertainty Budget ............................... 1077
Hansjörg Kutterer
37 Mixed Integer Estimation and Validation for Next
Generation GNSS ........................................... 1101
Peter J.G. Teunissen
38 Mixed Integer Linear Models ............................... 1129
Peiliang Xu
39 Statistical Analysis of Climate Series .................... 1159
Helmut Pruscha
40 Numerical Integration on the Sphere ....................... 1187
Kerstin Hesse, Ian H. Sloan, Robert S. Womersley
41 Multiscale Approximation .................................. 1221
Stephan Dahlke
42 Sparse Solutions of Underdetermined Linear Systems ........ 1243
Inna Kozlov, Alexander Petukhov
43 Multidimensional Seismic Compression by Hybrid Transform
with Multiscale Based Coding .............................. 1261
Amir Z. Averbuch, Valery A. Zheludev, Dan D. Kosloff
44 Cartography ............................................... 1289
Liqiu Meng
45 Geoinformatics ............................................ 1313
Monika Sester
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