Geomathematics
Modelling and Solving Mathematical Problems in Geodesy and Geophysics

A comprehensive summary of the fundamental mathematical principles behind key topics in geophysics and geodesy.

Volker Michel (Author)

9781108419444, Cambridge University Press

Hardback, published 28 April 2022

466 pages
25.1 x 17.4 x 2.6 cm, 1 kg

'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

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.

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.

Subject Areas: Geodesy & surveying for maps & charts [RGY], Volcanology & seismology [RBC], Geophysics [PHVG], Mathematical modelling [PBWH]