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.

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.

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.

This book constitutes the refereed proceedings of the 11th International Conference on Parallel Computational Technologies, PCT 2017, held in Kazan, Russia, in April 2017. The 24 revised full papers presented were carefully reviewed and selected from 167 submissions. The papers are organized in topical sections on high performance architectures, tools and technologies; parallel numerical algorithms; supercomputer simulation.

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.

The book provides the geoscientific context, that arises in gravimetric/magnetometric exploration. It essentially uses mathematics as a key technology for modeling issues on the basis of analysis and interpretation according to dense and precise gravitational/magnetic measurements. It is dedicated to surface and deep geology with potential data primarily of terrestrial origin. The book spans the interdisciplinary arc from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back again. It presents the recently published pioneering and groundbreaking multiscale mollifier methodologies realizing the bridging transfer from gravitational/magnetic measurements to approximative/numerical mollifier wavelet decorrelations with novel geologic prospects and layer-structure determination as outcome. Using the specific example of the German Saarland region, new important fields of application, especially for areas with mining-related cavities, will be opened up and subjected to an in-depth geologic detection.

This volume offers an overview of the state-of-the-art theoretical and practical approaches currently used for geophysical data interpretation. It includes new methods and techniques for solving data processing problems, and an analysis of geopotential fields by international researchers. It discusses topics such as: 1. Theoretical issues of interpretation of gravitational, magnetic and electric fields, including general methods of interpreting potential fields and other geophysical data. 2. Modern algorithms and computer technologies for interpretating geophysical fields. 3. The study of Earth deep structure using terrestrial and satellite potential field anomalies. 4. Geological interpretation of gravitational, magnetic and electric fields. This proceedings book is of interest to all geophysical researchers.

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.

This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.

This book treats permanent magnet (hard) materials, magnetically soft materials for low-frequency applications and for high-frequency electronics, magnetostrictive materials, superconductors, magnetic-thin films and multilayers, and ferrofluids. Chapters are dedicated to magnetic recording, the role of magnetism in magnetic resonance imaging (MRI), and instrumentation for magnetic measurements.