Geomathematics: Modelling and Solving Mathematical Problems in Geodesy and Geophysics

Geomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, explaining physical realities through basic laws and deriving and analyzing systems of basis functions. It covers inverse problems, the Laplace/Poisson equation, boundary-value problems, potential theory, spherical harmonics, and more, with review questions and solutions for instructors.

Format: Hardback
Length: 466 pages
Publication date: 28 April 2022
Publisher: Cambridge University Press

Geomathematics is a comprehensive and in-depth exploration of the mathematical foundations underlying key topics in geophysics and geodesy. It delves into the principles of gravimetry, geomagnetics, and seismology, providing a thorough understanding of the underlying mathematical concepts. Through theorems and their rigorous proofs, the book elucidates how physical realities in geoscience emerge as logical mathematical outcomes of fundamental laws. Furthermore, it derives and analyzes the theory and numerical aspects of established systems of basis functions, offering valuable insights into their properties and applications.

The book encompasses a wide range of topics, including 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, modeling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapter concludes with review questions, accompanied by solutions for instructors, making it an invaluable resource for graduate students and researchers seeking to deepen their knowledge in these fields.

By unraveling the mathematical intricacies behind geophysics and geodesy, Geomathematics serves as a crucial bridge between theory and practice, enabling scientists to make informed predictions and interpretations of Earth's physical phenomena. Its rigorous approach and comprehensive coverage make it an essential tool for anyone interested in advancing their understanding of the Earth's dynamic systems.

Weight: 1002g
Dimension: 177 x 251 x 30 (mm)
ISBN-13: 9781108419444