Geomathematics
Modelling and Solving Mathematical Problems in Geodesy and Geophysics
Published on 28. April 2022
Book
Hardback
466 pages
978-1-108-41944-4 (ISBN)
Description
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.
Reviews / Votes
'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, ChoiceMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Product notice
Laminated cover
Illustrations
Worked examples or Exercises
Dimensions
Height: 249 mm
Width: 179 mm
Thickness: 30 mm
Weight
1007 gr
ISBN-13
978-1-108-41944-4 (9781108419444)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
04/2022
Cambridge University Press
€63.49
Available for download
E-Book
03/2022
Cambridge University Press
€63.49
Available for download
Person
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.
Content
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.