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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. 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In fact, it is the intrinsic and indispensable means to handle geoscient- cally relevant data sets of high quality within high accuracy and to improve signi?cantly modeling capabilities in Earth system research.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52675539403025,"sku":"NLS9783540851110","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783540851110.jpg?v=1762302139"},{"product_id":"dekorrelative-gravimetrie-book-willi-freeden-9783662619070","title":"Dekorrelative Gravimetrie","description":"Die Entwicklung immer leistungsfähigerer absoluter wie auch relativer Gravimeter mit deutlich verbesserter Messgenauigkeit ermöglicht es, dass sich künftig nicht nur prägnante Schwereanomalien (wie z. B. die eines Salzstocks), sondern auch schwächere Signaturen erfassen und modellieren lassen. Mehr noch, die rasante Entwicklung der Computer führt zu neuartigen Methoden der Datendekomposition, wie z. B. Waveletdekorrelation. Dekorrelative Gravimetrie ist somit eine neue Explorationstechnik, die als kanonische Innovation aus der Verbindung neuartiger Mess- und Modellierungstechniken resultiert.  Dekorrelative Gravimetrie dient  der Reduzierung des Fündigkeitsrisikos von Aquiferen sowie von Gas- und Öllagerstätten, auch durch Vergleich und Zusammenschau alternativer, aber strukturell ähnlich gelagerter, dekorrelativer Verfahren wie etwa Magnetometrie und Seismik. Hier setzt dieses Buch mit einem exemplarischen Überblick über die neuartige Dekorrelationsmethoden der heutigenGeomathematik mit Hauptgewicht für den Fall der Gravimetrie an. Wesentliches mathematisches Hilfsmittel ist die Regularisierung des Newtonschen Volumenintegrals durch taylorisierte Mollifier-Varianten des Newton-Kerns.  Ziel des vorliegenden Buches ist somit die Vermittlung des Grundverständnisses, dass Zooming-In Mollifier-Potentialmethoden wie etwa dekorrelative Gravimetrie neue wichtige Anwendungsfelder in der heutigen Geoexploration eröffnen, insbesondere für Gebiete mit bergbaubedingten Hohlräumen oder sehr dichter Bebauung wie etwa das Saarland oder Sachsen, die den Einsatz von reflexionsseismischen Messungen erschweren oder sogar unmöglich machen.  Zusammenfassend lässt sich für dieses Buchprojekt festhalten, dass es einen Einblick in den aktuellen Stand gravimetrischer Multiskalenforschung vermittelt. Als  wesentliches Resultat  ergibt sich, dass die Schlüsseltechnologie Geomathematik in der Tat in der Lage ist, die Gravimetrie auf einfache, für Explorationszwecke zugängliche und somit rechenbare Dekorrelationsmodelle zu reduzieren. Mehr noch, das  Buch macht auf diese Weise ein breites  Publikum mit den  vielfältigen Fragen und Problemen der heutigen Gravimetrie vertraut und setzt Denkanstöße  für eine erfolgreiche Weiterentwicklung und eine adäquate praxisrelevante Anwendbarkeit von Potentialmethoden in der Exploration in Gang.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52684286492945,"sku":"NLS9783662619070","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662619070.jpg?v=1762322689"},{"product_id":"metaharmonic-lattice-point-theory-book-willi-freeden-9781138382107","title":"Metaharmonic Lattice Point Theory","description":"Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of weighted lattice point numbers, in particular the non-uniform distribution of lattice points.  The author explains how to obtain multi-dimensional generalizations of the Euler summation formula by interpreting classical Bernoulli polynomials as Green’s functions and linking them to Zeta and Theta functions. To generate multi-dimensional Euler summation formulas on arbitrary lattices, the Helmholtz wave equation must be converted into an associated integral equation using Green’s functions as bridging tools. After doing this, the weighted sums of functional values for a prescribed system of lattice points can be compared with the corresponding integral over the function.  Exploring special function systems of Laplace and Helmholtz equations, this book focuses on the analytic theory of numbers in Euclidean spaces based on methods and procedures of mathematical physics. It shows how these fundamental techniques are used in geomathematical research areas, including gravitation, magnetics, and geothermal.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52691073302801,"sku":"NLS9781138382107","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53368613175569,"sku":"NIN9781138382107","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781138382107.jpg?v=1762338987"},{"product_id":"handbook-of-geomathematics-book-willi-freeden-9783642015458","title":"Handbook of Geomathematics","description":"Geomathematics is becoming increasingly important. The 'Handbook of Geomathematics' is a central reference work and fills the gap of a basic reference work in this area. The contributions are well-structured and informative.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52705131954449,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":52705132085521,"sku":"GOR014588266","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642015458.jpg?v=1762684961"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-willi-freeden.oembed","provider":"World of Books ","version":"1.0","type":"link"}