Volker Michel

Geomathematics (eBook, PDF)

Modelling and Solving Mathematical Problems in Geodesy and Geophysics

• Format: PDF

Produktbeschreibung

Geomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, covering the foundations of gravimetry, geomagnetics and seismology. Theorems and their proofs explain why physical realities in geoscience are the logical mathematical consequences of basic laws. The book also derives and analyzes the theory and numerical aspects of established systems of basis functions; and presents an algorithm for combining different types of trial functions. Topics cover inverse problems and their regularization, the Laplace/Poisson equation, boundary-value problems, foundations of potential theory, the Poisson integral formula, spherical harmonics, Legendre polynomials and functions, radial basis functions, the Biot-Savart law, decomposition theorems (orthogonal, Helmholtz, and Mie), basics of continuum mechanics, conservation laws, modelling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapter ends with review questions, with solutions for instructors available online, providing a valuable reference for graduate students and researchers.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 31. März 2022
• Englisch
• ISBN-13: 9781108321686
• Artikelnr.: 66177913

Autorenporträt

Volker Michel is a mathematics professor at the University of Siegen where he founded the geomathematics group. He is also an editor-in-chief of the 'International Journal on Geomathematics' and a member of the editorial boards of the Journal of Geodesy and Mathematics of Computation and Data Science. Previous works include Lectures on Constructive Approximation (Springer, 2013) and 'Multiscale Potential Theory' (Birkhauser, 2004) with Willi Freeden. Michel has organised several conferences on inverse problems and geomathematics.

Inhaltsangabe

1. Introduction
2. Required Mathematical Basics
3. Gravitation and Harmonic Functions
4. Basis Functions
5. Inverse Problems
6. The Magnetic Field
7. Mathematical Models in Seismology
Appendix A. Hints for the Exercises
Appendix B. Questions for Understanding
References
Index.