Geomathematics: Theory and Applications (Volume III)
Geomathematics: Theory and Applications (Volume III)

Author: Virginia Williams

Publisher: Clanrye International

Published: 2023-09-19

Total Pages: 0

ISBN-13: 9781647266592

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Geomathematics is the application of mathematical methods to solve problems in geosciences, including geology and geophysics. It is also called mathematical geophysics. There are several applications of geomathematics in different areas such as data assimilation, geophysics, terrestrial tomography, crystallography, geomorphology, glaciology and geophysical statistics. The field of geomorphology involves the application of geomathematics by using mathematical methods related to soil and water. It includes the application of various mathematical concepts such as Darcy's law, Stoke's law, stream power and differential equations. Seismic tomography, a technique used for the imaging of the subsurface of the Earth by using seismic waves, also makes extensive use of geomathematics. This book provides a detailed explanation of geomathematics. Its extensive content provides the readers with a thorough understanding of the theory and applications of this field. Coherent flow of topics, student-friendly language, and extensive use of examples make this book an invaluable source of knowledge.

Geomathematics: Theory and Applications (Volume II)
Geomathematics: Theory and Applications (Volume II)

Author: Virginia Williams

Publisher: Clanrye International

Published: 2023-09-19

Total Pages: 0

ISBN-13: 9781647266585

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Geomathematics is the application of mathematical methods to solve problems in geosciences, including geology and geophysics. It is also called mathematical geophysics. There are several applications of geomathematics in different areas such as data assimilation, geophysics, terrestrial tomography, crystallography, geomorphology, glaciology and geophysical statistics. The field of geomorphology involves the application of geomathematics by using mathematical methods related to soil and water. It includes the application of various mathematical concepts such as Darcy's law, Stoke's law, stream power and differential equations. Seismic tomography, a technique used for the imaging of the subsurface of the Earth by using seismic waves, also makes extensive use of geomathematics. This book provides a detailed explanation of geomathematics. Its extensive content provides the readers with a thorough understanding of the theory and applications of this field. Coherent flow of topics, student-friendly language, and extensive use of examples make this book an invaluable source of knowledge.

Geomathematics: Theory and Applications (Volume IV)
Geomathematics: Theory and Applications (Volume IV)

Author: Virginia Williams

Publisher: Clanrye International

Published: 2023-09-12

Total Pages: 0

ISBN-13: 9781647266608

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Geomathematics is the application of mathematical methods to solve problems in geosciences, including geology and geophysics. It is also called mathematical geophysics. There are several applications of geomathematics in different areas such as data assimilation, geophysics, terrestrial tomography, crystallography, geomorphology, glaciology and geophysical statistics. The field of geomorphology involves the application of geomathematics by using mathematical methods related to soil and water. It includes the application of various mathematical concepts such as Darcy's law, Stoke's law, stream power and differential equations. Seismic tomography, a technique used for the imaging of the subsurface of the Earth by using seismic waves, also makes extensive use of geomathematics. This book provides a detailed explanation of geomathematics. Its extensive content provides the readers with a thorough understanding of the theory and applications of this field. Coherent flow of topics, student-friendly language, and extensive use of examples make this book an invaluable source of knowledge.

Geomathematics: Theory and Applications (Volume I)
Geomathematics: Theory and Applications (Volume I)

Author: Virginia Williams

Publisher: Clanrye International

Published: 2023-09-12

Total Pages: 0

ISBN-13: 9781647266578

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Geomathematics is the application of mathematical methods to solve problems in geosciences, including geology and geophysics. It is also called mathematical geophysics. There are several applications of geomathematics in different areas such as data assimilation, geophysics, terrestrial tomography, crystallography, geomorphology, glaciology and geophysical statistics. The field of geomorphology involves the application of geomathematics by using mathematical methods related to soil and water. It includes the application of various mathematical concepts such as Darcy's law, Stoke's law, stream power and differential equations. Seismic tomography, a technique used for the imaging of the subsurface of the Earth by using seismic waves, also makes extensive use of geomathematics. This book provides a detailed explanation of geomathematics. Its extensive content provides the readers with a thorough understanding of the theory and applications of this field. Coherent flow of topics, student-friendly language, and extensive use of examples make this book an invaluable source of knowledge.

Geomathematics: Theoretical Foundations, Applications and Future Developments
Geomathematics: Theoretical Foundations, Applications and Future Developments

Author: Frits Agterberg

Publisher: Springer

Published: 2014-07-14

Total Pages: 569

ISBN-13: 3319068741

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This book provides a wealth of geomathematical case history studies performed by the author during his career at the Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC). Several of the techniques newly developed by the author and colleagues that are described in this book have become widely adopted, not only for further research by geomathematical colleagues, but by government organizations and industry worldwide. These include Weights-of-Evidence modelling, mineral resource estimation technology, trend surface analysis, automatic stratigraphic correlation and nonlinear geochemical exploration methods. The author has developed maximum likelihood methodology and spline-fitting techniques for the construction of the international numerical geologic timescale. He has introduced the application of new theory of fractals and multi fractals in the geostatistical evaluation of regional mineral resources and ore reserves and to study the spatial distribution of metals in rocks. The book also contains sections deemed important by the author but that have not been widely adopted because they require further research. These include the geometry of preferred orientations of contours and edge effects on maps, time series analysis of Quaternary retreating ice sheet related sedimentary data, estimation of first and last appearances of fossil taxa from frequency distributions of their observed first and last occurrences, tectonic reactivation along pre-existing schistosity planes in fold belts, use of the grouped jackknife method for bias reduction in geometrical extrapolations and new applications of the theory of permanent, volume-independent frequency distributions.

An Invitation to Geomathematics
An Invitation to Geomathematics

Author: Willi Freeden

Publisher: Springer

Published: 2019-05-17

Total Pages: 140

ISBN-13: 3030130541

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The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackle geoscientific problems in the mathematical language. Chapter 3 contains some exemplary applications as novel exploration methods. Particular importance is laid on the change of language when it comes to translate measurements to mathematical models. New solution methods like the multiscale mollifier technique are presented. Further applications discussed are aspects of reflection seismics. Chapter 4 is devoted to the short description of recent activities in geomathematics. The Appendix (Chapter 5) is devoted to the GEM – International Journal on Geomathematics founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of all papers published in former issues is given.

Geomathematics: Theoretical Foundations, Applications and Future Developments
Geomathematics: Theoretical Foundations, Applications and Future Developments

Author: Frits Agterberg

Publisher: Springer

Published: 2016-09-17

Total Pages: 0

ISBN-13: 9783319349473

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This book provides a wealth of geomathematical case history studies performed by the author during his career at the Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC). Several of the techniques newly developed by the author and colleagues that are described in this book have become widely adopted, not only for further research by geomathematical colleagues, but by government organizations and industry worldwide. These include Weights-of-Evidence modelling, mineral resource estimation technology, trend surface analysis, automatic stratigraphic correlation and nonlinear geochemical exploration methods. The author has developed maximum likelihood methodology and spline-fitting techniques for the construction of the international numerical geologic timescale. He has introduced the application of new theory of fractals and multi fractals in the geostatistical evaluation of regional mineral resources and ore reserves and to study the spatial distribution of metals in rocks. The book also contains sections deemed important by the author but that have not been widely adopted because they require further research. These include the geometry of preferred orientations of contours and edge effects on maps, time series analysis of Quaternary retreating ice sheet related sedimentary data, estimation of first and last appearances of fossil taxa from frequency distributions of their observed first and last occurrences, tectonic reactivation along pre-existing schistosity planes in fold belts, use of the grouped jackknife method for bias reduction in geometrical extrapolations and new applications of the theory of permanent, volume-independent frequency distributions.

The Advanced Geometry of Plane Curves and Their Applications
The Advanced Geometry of Plane Curves and Their Applications

Author: C. Zwikker

Publisher: Courier Corporation

Published: 2011-11-30

Total Pages: 316

ISBN-13: 0486153436

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"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.

Decorrelative Mollifier Gravimetry
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.

Geomathematically Oriented Potential Theory
Geomathematically Oriented Potential Theory

Author: Willi Freeden

Publisher: CRC Press

Published: 2012-10-30

Total Pages: 470

ISBN-13: 1439895422

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As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today’s satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth’s gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphere-oriented potential theoretic methods as well as classical space potential theory.