Handbook of Geomathematics, 2nd edition

Автор: Willi Freeden; M. Zuhair Nashed; Thomas Sonar
Название: Handbook of Geomathematics, 2nd edition
Язык: English
Издательство: Berlin: Springer
Год: 2015
Формат: pdf
Размер: 69,4 mb
Страниц: 3170
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as space borne data of better and better quality explain the strong need of new mathematical structures, tools and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important.
The ‘Handbook of Geomathematics’ deals with the qualitative and quantitative properties for the current and possible structures of the system Earth. As a central reference work it comprises the following geoscientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
 Table of contents:
Volume 1
Part I General Issues, Historical Background, and Future Perspectives . . . . . . . . . . . . . . . . . . .1
Geomathematics: Its Role, Its Aim, and Its Potential . . . . . . . . . . . . . . . . . 3
Willi Freeden
Navigation on Sea: Topics in the History of Geomathematics . . . . . . . . . . 79
Thomas Sonar
Gauss’ andWeber’s “Atlas of Geomagnetism” (1840) Was not the first: the History of the Geomagnetic Atlases . . . . . . . . . . . . . . . . . . . . . 107
Karin Reich and Elena Roussanova
Part II Observational and Measurement Key Technologies . . . . . . . . . . 145
Earth Observation Satellite Missions and Data Access . . . . . . . . . . . . . . . . 147
Henri Laur and Volker Liebig
Satellite-to-Satellite Tracking (Low-Low/High-Low SST) . . . . . . . . . . . . . . 171
Wolfgang Keller
GOCE: Gravitational Gradiometry in a Satellite . . . . . . . . . . . . . . . . . . . . . 211
Reiner Rummel
Sources of the Geomagnetic Field and the Modern Data That
Enable Their Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Nils Olsen, Gauthier Hulot, and Terence J. Sabaka
Part III Modeling of the System Earth (Geosphere, Cryosphere, Hydrosphere, Atmosphere, Biosphere, Anthroposphere) . . . . 251
Classical Physical Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Helmut Moritz
Geodetic Boundary Value Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
F. Sansò
Time-Variable Gravity Field and Global Deformation of the Earth . . . . . 321
Jürgen Kusche
Satellite Gravity Gradiometry (SGG): From Scalar to Tensorial Solution . . . . . . . . . . . . . . . .339
Willi Freeden and Michael Schreiner
Spacetime Modeling of the Earth’s Gravity Field by Ellipsoidal Harmonics . . . . . . . . . . . . . . 381
Erik W. Grafarend, Matthias Klapp, and Zdenˇek Martinec
Multiresolution Analysis of Hydrology and Satellite Gravitational Data . . . . . . . . . . . . . . . 497
Helga Nutz and Kerstin Wolf
Time-VaryingMean Sea Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
Luciana Fenoglio-Marc and Erwin Groten
Self-Attraction and Loading of Oceanic Masses . . . . . . . . . . . . . . . . . . . . . . 545
Julian Kuhlmann, Maik Thomas, and Harald Schuh
Unstructured Meshes in Large-Scale Ocean Modeling . . . . . . . . . . . . . . . . 567
Sergey Danilov and Jens Schröter
Numerical Methods in Support of Advanced Tsunami Early Warning . . . . . . . . . . . . . . . . 601
Jörn Behrens
Gravitational Viscoelastodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Detlef Wolf
Elastic and Viscoelastic Response of the Lithosphere to Surface Loading . . . . . . . . . . . . 661
Volker Klemann, Maik Thomas, and Harald Schuh
Multiscale Model Reduction with Generalized Multiscale Finite Element Methods in Geomathematics . . . . . . . . . . . . . 679
Yalchin Efendiev and Michael Presho
Efficient Modeling of Flow and Transport in Porous Media Using Multi-physics and Multi-scale Approaches . . . . . . . . . . . . . . . . . . . . . 703
Rainer Helmig, Bernd Flemisch, Markus Wolff, and Benjamin Faigle
Convection Structures of Binary Fluid Mixtures in Porous Media . . . . . . 751
Matthias Augustin, Rudolf Umla, and Manfred Lücke
Numerical Dynamo Simulations: From Basic Concepts to Realistic Models . . . . . . . . . . . . .779
JohannesWicht, Stephan Stellmach, and Helmut Harder
Mathematical Properties Relevant to Geomagnetic Field Modeling . . . . . 835
Terence J. Sabaka, Gauthier Hulot, and Nils Olsen
Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents . . . . . . . . . . . . . . . . . 879
Christian Gerhards
Toroidal-Poloidal Decompositions of Electromagnetic Green’s Functions in Geomagnetic Induction . . . . . . . . . . . . . .921
Jin Sun
Using B-Spline Expansions for Ionosphere Modeling . . . . . . . . . . . . . . . . . 939
Michael Schmidt, Denise Dettmering, and Florian Seitz
The Forward and Adjoint Methods of Global Electromagnetic Induction for CHAMP Magnetic Data . . . . . . . . . . . . . . . 985
Zdenˇek Martinec
Modern Techniques for Numerical Weather Prediction: A Picture Drawn from Kyrill . . . . . . .1057
Nils Dorband, Martin Fengler, Andreas Gumann, and Stefan Laps
Volume 2
Radio Occultation via Satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089
Christian Blick and Sarah Eberle
Asymptotic Models for Atmospheric Flows . . . . . . . . . . . . . . . . . . . . . . . . . . 1127
Rupert Klein
Stokes Problem, Layer Potentials and Regularizations, and Multiscale Applications . . . . . . . .1155
Carsten Mayer andWilli Freeden
On High Reynolds Number Aerodynamics: Separated Flows . . . . . . . . . . 1255
Mario Aigner
Turbulence Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297
Steffen Schön and Gaël Kermarrec
Forest Fire Spreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1349
Sarah Eberle,Willi Freeden, and Ulrich Matthes
Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation . . . . . . . . . . . .1387
Andreas Meister and Joachim Benz
Model-Based Visualization of Instationary Geo-Data with Application to Volcano Ash Data . . . . . . . . . . . . . . .1417
Martin Baumann, Jochen Förstner, Vincent Heuveline, Jonas Kratzke, Sebastian Ritterbusch, Bernhard Vogel, and Heike Vogel
Modeling of Fluid Transport in Geothermal Research . . . . . . . . . . . . . . . . 1443
Jörg Renner and Holger Steeb
Fractional Diffusion andWave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . 1507
Yuri Luchko
Modeling Deep Geothermal Reservoirs: Recent Advances and Future Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1547
Matthias Augustin, Mathias Bauer, Christian Blick, Sarah Eberle, Willi Freeden, Christian Gerhards, Maxim Ilyasov, René Kahnt, Matthias Klug, Sandra Möhringer, Thomas Neu, Helga Nutz, Isabel Michel née Ostermann, and Alessandro Punzi
Part IV Analytic, Algebraic, and Operator Theoretical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1631
Noise Models for Ill-Posed Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1633
Paul N. Eggermont, Vincent LaRiccia, and M. Zuhair Nashed
Sparsity in Inverse Geophysical Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 1659
Markus Grasmair, Markus Haltmeier, and Otmar Scherzer Multiparameter Regularization in Downward Continuation of Satellite Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1689
Shuai Lu and Sergei V. Pereverzev
Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 1713
Frank Bauer, Martin Gutting, and Mark A. Lukas
Quantitative Remote Sensing Inversion in Earth Science: Theory and Numerical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 1775
Yanfei Wang
CorrelationModeling of the Gravity Field in Classical Geodesy . . . . . . . . 1807
Christopher Jekeli
Inverse Resistivity Problems in Computational Geoscience . . . . . . . . . . . . 1845
Alemdar Hasanov (Hasanoˇglu) and Balgaisha Mukanova
Identification of Current Sources in 3D Electrostatics . . . . . . . . . . . . . . . . . 1863
Aron Sommer, Andreas Helfrich-Schkarbanenko, and Vincent Heuveline
Transmission Tomography in Seismology . . . . . . . . . . . . . . . . . . . . . . . . . . . 1887
Guust Nolet
Numerical Algorithms for Non-smooth Optimization Applicable to Seismic Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1905
Ignace Loris
Strategies in Adjoint Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1943
Yang Luo, Ryan Modrak, and Jeroen Tromp
Potential-Field Estimation Using Scalar and Vector Slepian Functions at Satellite Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2003
Alain Plattner and Frederik J. Simons
Multidimensional Seismic Compression by Hybrid Transform with Multiscale-Based Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2057
Amir Z. Averbuch, Valery A. Zheludev, and Dan D. Kosloff
Tomography: Problems and Multiscale Solutions . . . . . . . . . . . . . . . . . . . . 2087
Volker Michel
RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2121
Volker Michel
Material Behavior: Texture and Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . 2149
Ralf Hielscher, David Mainprice, and Helmut Schaeben
RayleighWave Dispersive Properties of a Vector Displacement as a Tool for P- and S-Wave Velocities Near Surface Profiling . . . . . . . . . . 2189
Andrey Konkov, Andrey Lebedev, and Sergey Manakov
Simulation of Land Management Effects on Soil N2O Emissions Using a Coupled Hydrology-BiogeochemistryModel on the Landscape Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2207
Martin Wlotzka, Vincent Heuveline, Steffen Klatt, Edwin Haas, David Kraus, Klaus Butterbach-Bahl, Philipp Kraft, and Lutz Breuer
Volume 3
Part V Statistical and StochasticMethods . . . . . . . . . . . . . . . . . . . . . . . . 2233
An Introduction to PredictionMethods in Geostatistics . . . . . . . . . . . . . . . 2235
Ralf Korn and Alexandra Kochendörfer
Statistical Analysis of Climate Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2257
Helmut Pruscha
Oblique Stochastic Boundary-Value Problem . . . . . . . . . . . . . . . . . . . . . . . . 2285
Martin Grothaus and Thomas Raskop
Geodetic Deformation Analysis with Respect to an Extended Uncertainty Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2317
Hansjörg Kutterer
It’s All About Statistics: Global Gravity Field Modeling from GOCE and Complementary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2345
Roland Pail
Mixed Integer Estimation and Validation
for Next Generation GNSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2373
Peter J.G. Teunissen
Mixed Integer Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2405
Peiliang Xu

Part VI Special Function Systems andMethods . . . . . . . . . . . . . . . . . . . 2453
Special Functions in Mathematical Geosciences: An Attempt at a Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2455
Willi Freeden and Michael Schreiner
Clifford Analysis and Harmonic Polynomials . . . . . . . . . . . . . . . . . . . . . . . . 2483
Klaus Gürlebeck andWolfgang Sprößig Splines and Wavelets on Geophysically Relevant Manifolds . . . . . . . . . . . . 2527
Isaac Pesenson
Scalar and Vector Slepian Functions, Spherical Signal Estimation and Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2563
Frederik J. Simons and Alain Plattner
Dimension Reduction and Remote Sensing Using Modern Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2609
John J. Benedetto andWojciech Czaja
Part VII Computational and Numerical Methods . . . . . . . . . . . . . . . . . . 2633
Radial Basis Function-Generated Finite Differences: A Mesh-Free Method for Computational Geosciences . . . . . . . . . . . . . . . . . 2635
Natasha Flyer, Grady B. Wright, and Bengt Fornberg
Numerical Integration on the Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2671
Kerstin Hesse, Ian H. Sloan, and Robert S. Womersley
Fast Spherical/Harmonic Spline Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 2711
Martin Gutting
Multiscale Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2747
Stephan Dahlke
Sparse Solutions of Underdetermined Linear Systems . . . . . . . . . . . . . . . . 2773
Inna Kozlov and Alexander Petukhov
Nonlinear Methods for Dimensionality Reduction . . . . . . . . . . . . . . . . . . . . 2799
Charles K. Chui and JianzhongWang
Part VIII Cartographic, Photogrammetric, Information Systems and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2853
Cartography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2855
Liqiu Meng
Theory of Map Projection: From Riemann Manifolds to Riemann Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2883
Erik W. Grafarend
Modeling Uncertainty of Complex Earth Systems in Metric Space . . . . . . 2965
Jef Caers, Kwangwon Park, and Céline Scheidt
Geometrical Reference Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2995
Manuela Seitz, Detlef Angermann, Michael Gerstl, Mathis Bloßfeld, Laura Sánchez, and Florian Seitz
Analysis of Data from Multi-satellite GeospaceMissions . . . . . . . . . . . . . . 3035
Joachim Vogt
GeodeticWorld Height System Unification . . . . . . . . . . . . . . . . . . . . . . . . . . 3067
Michael Sideris
Mathematical Foundations of Photogrammetry . . . . . . . . . . . . . . . . . . . . . . 3087
Konrad Schindler
Potential Methods and Geoinformation Systems . . . . . . . . . . . . . . . . . . . . . 3105
Hans-Jürgen Götze
Geoinformatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3131
Monika Sester
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3151
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