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Inverse Magnetometry

Author: Christian Blick

Publisher: Springer Nature

Published: 2021-09-08

Total Pages: 114

ISBN-13: 303079508X

This monograph presents the geoscientific context arising in decorrelative geomagnetic exploration. First, an insight into the current state of research is given by reducing magnetometry to mathematically accessible, and thus calculable, decorrelated models. In this way, various questions and problems of magnetometry are made available to a broad scientific audience and the exploration industry. New stimuli are given, and innovative ways of modeling geologic strata by mollifier magnetometric techniques are shown. Potential data sets primarily of terrestrial origin constitute the main data basis in the book. For deep geology, the geomathematical decorrelation methods are designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Overall, this book provides pioneering and ground-breaking innovative mathematical knowledge as a transfer methodology from the “reality space” of magnetometric measurements into the “virtual space” of mathematical-numerical modeling structures and mollifier solutions with novel geological application areas. It pursues a double goal: On the one hand, it represents a geoscientific set of rules for today's geoengineering, interested in the application of innovative modelling and simulation techniques to promising data sets and structures occurring in geomagnetics. On the other hand, the book serves as a collection of current material in Applied Mathematics to offer alternative methodologies in the theory of inverse problems.

Applied Inverse Problems

Author: Larisa Beilina

Publisher: Springer Science & Business Media

Published: 2013-08-15

Total Pages: 206

ISBN-13: 1461478162

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This proceedings volume is based on papers presented at the First Annual Workshop on Inverse Problems which was held in June 2011 at the Department of Mathematics, Chalmers University of Technology. The purpose of the workshop was to present new analytical developments and numerical methods for solutions of inverse problems. State-of-the-art and future challenges in solving inverse problems for a broad range of applications was also discussed. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.

Anomalous Magnetic Field of the World Ocean

Author: Alexander M. Gorodnitsky

Publisher: CRC Press

Published: 1994-10-12

Total Pages: 270

ISBN-13: 9780849389375

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This book investigates the anomalous magnetic field of the ocean and its connection with geological structure, tectonic evolution of the oceanic lithosphere, and magnetic properties of different rock types in the oceanic crust. The book describes new instruments and techniques of gradient magnetic measurements with three sensors, as well as the new technique of processing and interpretating hydromagnetic data on the basis of adoptive filtration and reparametrization. The text provides unique data of geomagnetic surveys carried out by Russian research vessels in different regions of the World Ocean, including submersible apparatus and ingenious theoretical and experimental technology of the magnetic modeling and investigations of the nature of magnetic anomalies. The results of systems analysis of geochemical content and composition during the mid-oceanic ridge basalt are presented.

Decorrelative Mollifier Gravimetry

Author: Willi Freeden

Publisher: Springer Nature

Published: 2021-05-12

Total Pages: 482

ISBN-13: 3030699099

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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.

Recovery Methodologies: Regularization and Sampling

Author: Willi Freeden

Publisher: American Mathematical Society

Published: 2023-08-21

Total Pages: 505

ISBN-13: 1470473453

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The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.

Pragmatic Inversion of Geophysical Data

Author: Sven-Erik Hjelt

Publisher: Springer

Published: 2006-04-10

Total Pages: 268

ISBN-13: 3540472630

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Geophysical measurements are not done for the sake of art only. The ultimategoal is to solve some well-defined geological, tectonical or structural problems. For this purpose, the data have to be interpreted, translated, into a physical model of the subsurface. ... This book describes some ofthe most important common features of different geophysical data sets. (fromthe Introduction) Users at universities but also practitioners in exploration, physics or environmental sciences, wherever signal processing is necessary, will benefit from this textbook.

Ship Magnetism and the Magnetic Compass

Author: F. G. Merrifield

Publisher: Elsevier

Published: 2014-05-09

Total Pages: 198

ISBN-13: 1483180549

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Ship Magnetism and the Magnetic Compass deals with the magnetism of ships and the deviation of the magnetic compass produced by this magnetism. Emphasis is placed on the distinction between the deviation itself and what causes the deviation. Numerous worked examples for exercise are found at the end of each chapter. Comprised of 15 chapters, this volume begins with an introduction to magnetometry, paying particular attention to the magnitude of the forces involved in magnetism and the manner in which these forces act. The strength of a magnetic pole is also considered, along with the angle of deflection of the needle when in two magnetic fields. Subsequent chapters offer a thorough treatment of the strength of the magnetic field and the magnet's moment of inertia and magnetic moment; the earth's magnetic force; and how the different parts of the ship's magnetic force give different types of deviation. The book also explains the heeling error and its causes; the principle underlying successful compass adjustment; the effect of the ship's magnetic forces on the directive force felt by the compass needles; and sub-permanent magnetism. This monograph will be of value to students and practitioners interested in ship magnetism and the magnetic compass.

Principles and Methods of Quantum Information Technologies

Author: Yoshihisa Yamamoto

Publisher: Springer

Published: 2015-12-30

Total Pages: 615

ISBN-13: 4431557563

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This book presents the research and development-related results of the “FIRST” Quantum Information Processing Project, which was conducted from 2010 to 2014 with the support of the Council for Science, Technology and Innovation of the Cabinet Office of the Government of Japan. The project supported 33 research groups and explored five areas: quantum communication, quantum metrology and sensing, coherent computing, quantum simulation, and quantum computing. The book is divided into seven main sections. Parts I through V, which consist of twenty chapters, focus on the system and architectural aspects of quantum information technologies, while Parts VI and VII, which consist of eight chapters, discuss the superconducting quantum circuit, semiconductor spin and molecular spin technologies. Readers will be introduced to new quantum computing schemes such as quantum annealing machines and coherent Ising machines, which have now arisen as alternatives to standard quantum computers and are designed to successfully address NP-hard/NP-complete combinatorial optimization problems, which are ubiquitous and relevant in our modern life. The book offers a balanced mix of theory-based and experimentation-based chapters written by leading researchers. Extensive information is provided on Quantum simulation, which focuses on the implementation of various many-body Hamiltonians in a well-controlled physical system, Quantum key distribution, Quantum repeaters and quantum teleportation, which are indispensable technologies for building quantum networks with various advanced applications and require far more sophisticated experimental techniques to implement.

Deconvolution and Inverse Theory

Author: V. Dimri

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 249

ISBN-13: 1483291375

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This is the first study to present simultaneously both deconvolution and inversion, two powerful tools of data analysis. Featured within this volume are various geophysical convolution models and a treatment of deconvolution for a time-varying signal. The single channel time-varying deconvolution is shown equivalent to the multichannel time-invariant deconvolution, thus a formalism and associated algorithms can handle both. Inverse theory as well as various inversion schemes are presented on the basis of a relationship between a small perturbation to the model and its effects on the observation. The information theory inversion scheme is discussed, and several types of norm of minimization presented. Additionally, concepts and results of inverse theory are applied to design a new deconvolution operator for estimating magnetization and density distribution, and the constraint of the Backus-Gilbert formalism of inverse theory is used to design a new prediction error filter for maximum entropy spectral estimates. Maximum likelihood, another high resolution method is also presented. This volume can be utilised as a graduate-level text for courses in Geophysics. Some chapters will be of use for graduate courses in Applied Mathematics, Applied Statistics, and Oceanography.

Principles of the Magnetic Methods in Geophysics

Author:

Publisher: Elsevier

Published: 2008-11-21

Total Pages: 320

ISBN-13: 0080931855

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Magnetic methods are widely used in exploration, engineering, borehole and global geophysics, and the subjects of this book are the physical and mathematical principles of these methods regardless of the area of application. Beginning with Ampere's law, the force of interaction between currents is analyzed, and then the concept of the magnetic field is introduced and the fundamental features are discussed. Special attention is paid to measurements of relaxation processes, including topics as the spin echoes or refocusing. Also the special role of the magnetic method in the development of the plate tectonic theory is described. * covers all the physical and mathematical principles of magnetic methods regardless of the area of application. * presents thorough developments of magnetic methods.