Decorrelative Mollifier Gravimetry

Basics, Ideas, Concepts, and Examples

Willi Freeden (Autor)

Buch | Softcover

XIX, 482 Seiten

2022 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-69911-6 (ISBN)

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This monograph presents the geoscientific context arising in decorrelative gravitational exploration to determine the mass density distribution inside the Earth. First, an insight into the current state of research is given by reducing gravimetry to mathematically accessible, and thus calculable, decorrelated models. In this way, the various unresolved questions and problems of gravimetry are made available to a broad scientific audience and the exploration industry. New theoretical developments will be given, and innovative ways of modeling geologic layers and faults by mollifier regularization techniques are shown.
This book is dedicated to surface as well as volume geology with potential data primarily of terrestrial origin. For deep geology, the geomathematical decorrelation methods are to be designed in such a way that depth information (e.g., in boreholes) may be canonically entered.
Bridging several different geo-disciplines, this book leads in a cycle from the potential measurements made by geoengineers, to the cleansing of data by geophysicists and geoengineers, to the subsequent theory and model formation, computer-based implementation, and numerical calculation and simulations made by geomathematicians, to interpretation by geologists, and, if necessary, back. It therefore spans the spectrum from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back.
Using the German Saarland area for methodological tests, important new fields of application are opened, particularly for regions with mining-related cavities or dense development in today's geo-exploration.

Introductory Remarks.- Part I: Gravitation and Gravimetry.- Gravitation.- Gravimetry.- Part II: Potential Theory.- Classical Context.- Newton-Haar Mollifier Theory and Application.- Disturbing Potential.- Part III: Surface Decorrelation.- Space versus Frequency Surface Modeling.- Surface Applications.- Part IV: Inverse Potential Theory.- Gravimetry as an Ill-Posed Inverse Problem.- Part V: Volume Decorrelation.- Volume Methodology.- Volume Applications.- Part VI: Decorrelative Potential Methods.- Decorrelative Monopole Potential Based Gravimetry.- Decorrelative Dipole Potential Based Magnetometry.- Decorrelative Acoustic Potential Based Exploration.- Decorrelative Elastic Potential Based Exploration.- Concluding Remarks.

"Graduate students in Geodesy interested in gravimetry, colleagues and researchers working in this field should read this book but also other geodesists, who are interested in modelling geodetic problems ... . This book, which allows readers to detect local structures provides them with all the necessary mathematical theories and concepts. ... the book can be recommended for all colleagues in Geophysics, Geology, and Geodesy, who deal with the various questions of inverse gravimetry" (Bertold Witte, Journal of Geodesy, Vol. 95 (8), 2021)

“Graduate students in Geodesy interested in gravimetry, colleagues and researchers working in this field should read this book but also other geodesists, who are interested in modelling geodetic problems … . This book, which allows readers to detect local structures provides them with all the necessary mathematical theories and concepts. … the book can be recommended for all colleagues in Geophysics, Geology, and Geodesy, who deal with the various questions of inverse gravimetry” (Bertold Witte, Journal of Geodesy, Vol. 95 (8), 2021)

Erscheinungsdatum	15.05.2022
Reihe/Serie	Geosystems Mathematics
Zusatzinfo	XIX, 482 p. 196 illus., 168 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	765 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Geowissenschaften ► Geologie
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Decorrelative Gravimetry • Geological Exploration • Mollifier Potential Methods • Potential Splines • Potential Wavelets
ISBN-10	3-030-69911-0 / 3030699110
ISBN-13	978-3-030-69911-6 / 9783030699116
Zustand	Neuware