Handbook of Geomathematics / edited by Willi Freeden, M. Zuhair Nashed, Thomas Sonar.

Format:

Book

Contributor:

Freeden, Willi., Editor.

Nashed, M. Zuhair., Editor.

Sonar, Thomas., Editor.

Language:

English

Subjects (All):

Mathematics.

Earth sciences.

Mathematics, general.

Earth Sciences, general.

Local Subjects:

Mathematics, general.

Earth Sciences, general.

Physical Description:

1 online resource (778 illus., 523 illus. in color. eReference.)

Edition:

2nd ed. 2015.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.

Language Note:

English

Summary:

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.

Contents:

Part 1: General Issues, Historical Background, and Future Perspectives

Geomathematics: Its Role, Its Aim, and Its Potential

Navigation on Sea: Topics in the History of Geomathematics

Gauss and Weber’s “Atlas des Erdmagnetismus” (1840) Was Not the First: History of the Geomagnetic Atlases

Part 2: Observational and Measurement Key Technologies

Earth Observation Satellite Missions and Data Access

Satellite-to-Satellite Tracking (Low-Low/High-Low SST)

GOCE: Gravitational Gradiometry in a Satellite

Sources of the Geomagnetic Field and the Modern Data That Enable Their Investigation

Part 3: Modeling of the System Earth (Geosphere, Cryosphere, Hydrosphere, Atmosphere, Biosphere, Anthroposphere)

Classical Physical Geodesy

Geodetic Boundary Value Problem

Time-Variable Gravity Field and Global Deformation of the Earth

Satellite Gravity Gradiometry (SGG): From Scalar to Tensorial Solution

Spacetime Modelling of the Earth’s Gravity Field by Ellipsoidal Harmonics

Multiresolution Analysis of Hydrology and Satellite Gravitational Data Time Varying Mean Sea Level

Self-Attraction and Loading of Oceanic Masses

Unstructured Meshes in Large-Scale Ocean Modeling.- Numerical Methods in Support of Advanced Tsunami Early Warning

Gravitational Viscoelastodynamics

Elastic and Viscoelastic Reaction of the Lithosphere to Loads

Use of Multiscale Methods in Geomathematics

Efficient Modeling of Flow and Transport in Porous Media Using

Multiphysics and Multiscale Approaches

Convection Structures of Binary Fluid Mixtures in Porous Media

Numerical Dynamo Simulations: From Basic Concepts to Realistic Models

Mathematical Properties Relevant to Geomagnetic Field Modeling

Multiscale Modeling of the Geomagnetic Field and Ionospheric Currents

Toroidal - Poloidal Decompositions of Electromagnetic Green's Functions in Geomagnetic Induction

Using B-Spline Expansions for Ionosphere Modeling

The Forward and Adjoint Methods of Global Electromagnetic Induction for CHAMP Magnetic Data

Climate Dynamics

Modern Techniques for Numerical Weather Prediction: A Picture Drawn from Kyrill

Radio Occultation via Satellites

Asymptotic Models for Atmospheric Flows

Stokes Problem, Layer Potentials and Regularizations, Multiscale Applications

On High Reynolds Number Aerodynamics - Separated Flows.-Turbulence Theory

Analysis of Forest Fire Spreading Theory

Phosphorus Cycles in Lakes and Rivers: Modeling, Analysis, and Simulation

Model-based Visualization of Instationary Geo-Data with Application to Volcano Ash Data

Modeling of Fluid Transport in Geothermal Research

Fractional Diffusion and Wave Propagation

Modeling Deep Geothermal Reservoirs: Recent Advances and Future Problems

Part 4: Analytic, Algebraic, and Operator Theoretical Methods

Noise Models for Ill-Posed Problems

Sparsity in Inverse Geophysical Problems

Multiparameter Regularization in Downward Continuation of Satellite Data

Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics

Quantitative Remote Sensing Inversion in Earth Science: Theory and Numerical Treatment

Correlation Modeling of the Gravity Field in Classical Geodesy

Inverse Resistivity Problems in Computational Geoscience

Identification of Current Sources in 3D Electrostatics

Numerical Simulation and Inversion for Geo-Electromagnetic Methods

Transmission Tomography in Seismology

Numerical Algorithms for Non-Smooth Optimization Applicable to Seismic Recovery

Strategies in Adjoint Tomography

Potential-field Estimation using Scalar and Vector Slepian Functions at Satellite Altitude

Multidimensional Seismic Compression by Hybrid Transform with Multiscale Based Coding Tomography: Problems and Multiscale Solutions

RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences

Material Behavior: Texture and Anisotropy

Rayleigh Wave Dispersive Properties of a Vector Displacement as a Tool for P- and S-wave Velocities Near Surface Profiling

Dynamic Simulation of Land Use Change and Management Effects on Soil N2O Emissions

Part 5: Statistical and Stochastic Methods

Selected Statistical Methods

Statistical Analysis of Climate Series

Oblique Stochastic Boundary-Value Problem

Geodetic Deformation Analysis with Respect to an Extended Uncertainty Budget)

It's All About Statistics Global Gravity Field Modeling from GOCE and Complementary Data

Mixed Integer Estimation and Validation for Next Generation GNSS

Mixed Integer Linear Models

Part 6: Special Function Systems and Methods

Special Functions in Mathematical Geosciences: An Attempt at a Categorization

Clifford Analysis and Harmonic Polynomials

Splines and Wavelets on Geophysically Relevant Manifolds

Slepian Functions and Their Use in Signal Estimation and Spectral Analysis

Dimension Reduction and Remote Sensing Using Modern Harmonic Analysis

Low Discrepancy Methods

Part 7: Computational and Numerical Methods

Radial Basis Function-generated Finite Differences: A Mesh-free Method for Computational Geosciences

Numerical Integration on the Sphere

Fast Spherical/Harmonic Spline Modeling

Multiscale Approximation

Sparse Solutions of Underdetermined Linear Systems

Nonlinear Methods for Dimensionality Reduction

Part 8: Cartographic, Photogrammetric, Information Systems and Methods

Cartography

Map Projections: Cartographic Information Systems

Modeling Uncertainty of Complex Earth Systems in Metric Space

Geometrical Reference System

Analysis of Data from Multi-Satellite Geospace Missions

Geodetic World Height System Unification

Mathematical Foundations of Photogrammetry

Potential Methods and Geoinformation Systems

Geoinformatics.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-642-54551-3

OCLC:

1076258568