An invitation to geomathematics
type: Item
instance of: scholarly article
title: An invitation to geomathematics
zbMATH Open document ID: 1422.86017
DOI: 10.1007/978-3-030-13054-1
author: Willi Freeden
author: Clemens Heine
author: M. Zuhair Nashed
published in: Lecture Notes in Geosystems Mathematics and Computing
publication date: 2019-02-25T00:00:00Z
review text: Geomathematics is a subject not see often enough in modern mathematics as many mathematicians are often not enthusiastic about observational concepts. Yet, at a professional level, the role of mathematics in geophysics has led to an increase in the relevance of mathematical intuition as a leading framwork for resolving complex geophysical problems, rather than merely acting a service function. An invitation is more than an introduction. Henceforth, appealing discussions are distributed throughout the text in ways that show how geomathematics can be very career enhancing, just as biologically and epidemiologically driven mathematics has been growing since the 1960s. Besides, the notes will be useful to geoscientists new to this subject, making them aware of new techniques and giving them a new perspective of how mathematics can explain observations. The second chapter starts with several important tools that are used to study terrestrial problems. Classical orthogonal spherical harmonics that use polynomials to the sphere in a Hilbert space are introduced. The reader is then delved further into the power and advantage of multiscale harmonic spherical wavelets that have the capability of breaking up the complicated geophysical structures with simple pieces defined at different scales and positions. The key novelty occurs in Chapter 3, where the authors present the mollifier procedure directly on two geoexploration applications:\begin{itemize}\item[1)] inverse gravimetry; and \item[2)] reflection seismology.\end{itemize} The mathematical analysis for gravimetry starts with standard Newtonian geopotential principles. In this way gravimetric observations are immediately transferred into the language of geomathematics using approximate integration inside a subarea of the Earth. Noting Hadamard's mathematical well-posedness notion on existence, uniqueness and stability of solutions, the authors discuss three multiscale mollifier regularisation inversion methods. Mollifiers…
reviewed by: Christopher Dimech
Mathematics Subject Classification ID: 86A22
Mathematics Subject Classification ID: 86A15
Mathematics Subject Classification ID: 31A10
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 49-04
zbMATH DE Number: 7029535
zbMATH Keywords: geomathematics
zbMATH Keywords: inhomogenous Helmholtz equation inversion
zbMATH Keywords: multiscale Mollifier regularisation
zbMATH Keywords: weak perturbation theory
zbMATH Keywords: first order born approximation
zbMATH Keywords: gravimetry
zbMATH Keywords: potential theory, Helmholtz wavelets
zbMATH Keywords: Haar wavelets
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-030-13054-1
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description: scientific article; zbMATH DE number 7029535