Geomathematics: Modelling and Solving Mathematical Problems in Geodesy and Geophysics

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Volker Michel

Geomathematics

Modelling and Solving Mathematical Problems in Geodesy and Geophysics

Volker Michel

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English

Cambridge University Press
28 April 2022

Mathematical modelling; Geophysics; Volcanology & seismology; Geodesy & surveying for maps & charts

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.

By: Volker Michel
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 251mm, Width: 174mm, Spine: 26mm
Weight: 1.000kg
ISBN: 9781108419444
ISBN 10: 1108419445
Pages: 466
Publication Date: 28 April 2022
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Geomathematics: Modelling and Solving Mathematical Problems in Geodesy and Geophysics

'Volker does a good job of presenting thorough associated proofs. These chapters serve much as a mathematical methods survey course would in a physics curriculum, presenting the needed mathematics without unduly burdening the reader with the breadth that would normally be offered in a mathematics course ... Recommended.' E. Kincanon, Choice