Decorrelative mollifier gravimetry : basics, ideas, concepts, and examples / Willi Freeden.

Format:

Book

Author/Creator:

Freeden, W. (Willi), author.

Series:

Geosystems Mathematics, 2510-1544

Language:

English

Subjects (All):

Potential theory (Mathematics).

Physical Description:

1 online resource (XIX, 482 p. 196 illus., 168 illus. in color.)

Edition:

1st ed. 2021.

Place of Publication:

Cham, Switzerland : Birkhäuser, [2021]

Summary:

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. .

Contents:

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.

Notes:

Description based on print version record.

ISBN:

3-030-69909-9

OCLC:

1256239615