Geomathematics

Modelling and Solving Mathematical Problems in Geodesy and Geophysics
Erscheinungsjahr 2022
ISBN: 978-1-108-41944-4
Verlag: Cambridge University Press

Buch, Englisch, 400 Seiten, Format (B × H): 179 mm x 249 mm, Gewicht: 1007 g

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.

Autoren/Hrsg.

Michel, Volker

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Geowissenschaften Geologie Vulkanologie, Seismologie
• Geowissenschaften Geologie Geophysik
• Geowissenschaften Geologie Geodäsie, Kartographie, Fernerkundung
• Naturwissenschaften Physik Angewandte Physik Geophysik
• Geowissenschaften Geographie | Raumplanung Geodäsie, Kartographie, GIS, Fernerkundung

Inhaltsverzeichnis

1. Introduction; 2. Required Mathematical Basics; 3. Gravitation and Harmonic Functions; 4. Basis Functions; 5. Inverse Problems; Appendix A; Appendix B; References; Index.

Über Autor(innen)

Michel, Volker
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.