Geomathematics: modelling and solving mathematical problems in geodesy and geophysics
Language: English Publication details: United Kingdom: Cambridge University Press, 2022. Description: viii, 457p.; 23cmsISBN: 9781108419444Subject(s): Mathematical basics | Basic functions -- The magnetic field | Gravitation, Harmonic functions | Mathematical models in seismologyDDC classification: 550.151 M53| Item type | Current library | Call number | Status | Date due | Barcode |
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| 550 L69, 3:4 Fundamentals of geophysics | 550 R63 Basic geophysics | 550 S54 Essentials of geology | 550.151 M53 Geomathematics: modelling and solving mathematical problems in geodesy and geophysics | 550.151474 T87, 2 Fractals and chaos in geology and geophysics | 550.15195 M35 Geostatistics explained: An introductory guide for earth scientists | 550.285 G87, 3 Remote sensing geology |
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.
A self-consistent reference work on the mathematical modelling in gravimetry, geomagnetics and seismology
Aims to show interconnections of mathematical concepts between different scientific areas and encourage further interdisciplinary research
Provides a comprehensive explanation of complicated and sophisticated mathematical propositions, proofs and concepts in the Earth Sciences