Willi Freeden Books

Focusing on gravimetric and magnetometric exploration, this book delves into the geoscientific context by employing mathematics for modeling and interpreting complex geological data. It emphasizes the analysis of precise gravitational and magnetic measurements, addressing both surface and deep geological features. The content is primarily centered on terrestrial data, making it a valuable resource for understanding the intricacies of geological exploration through advanced mathematical techniques.

The book delves into the geoscientific aspects of decorrelative gravitational exploration, focusing on mass density distribution within the Earth. It simplifies gravimetry to create mathematically accessible models, addressing unresolved issues in the field. The text introduces new theoretical advancements and innovative modeling techniques for geological layers and faults using mollifier regularization. This work aims to make complex gravimetric concepts understandable for a wider scientific audience and the exploration industry.

The book offers a comprehensive overview of the theory of spherical functions, emphasizing a transition from scalar to vectorial and tensorial theories of spherical harmonics within a coordinate-free framework. It discusses key concepts such as the addition theorem, Funk-Hecke formulas, and Helmholtz decompositions. Additionally, it explores the shift from spherical harmonics to zonal functions and the Dirac kernel, linking these to an uncertainty principle relevant for data analysis in geosciences. The structured collection of spherical functions aims to aid in modeling Earth's system phenomena, making it significant for both research and education.

Die Fortschritte in der Gravimetrie, insbesondere durch leistungsfähigere Gravimeter und verbesserte Messgenauigkeit, ermöglichen die Erfassung sowohl starker als auch schwächerer Schwereanomalien. Die Entwicklung innovativer Computertechnologien führt zu neuen Methoden wie der Waveletdekorrelation, die die Datendekomposition revolutionieren. Diese Fortschritte machen die dekorrelative Gravimetrie zu einer richtungsweisenden Explorationstechnik, die auf der Kombination neuartiger Mess- und Modellierungstechniken basiert.