Applied Mathematical Problems In Geophysics

Author : Massimo Chiappini,Vincenzo Vespri
Publisher : Springer Nature
Page : 211 pages
File Size : 42,6 Mb
Release : 2022-07-23
Category : Mathematics
ISBN : 9783031053214

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Applied Mathematical Problems in Geophysics by Massimo Chiappini,Vincenzo Vespri Pdf

This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes. This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.

Author : William Hill Reid
Publisher : American Mathematical Society(RI)
Page : 392 pages
File Size : 49,8 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015004618453

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Mathematical Problems in the Geophysical Sciences: Inverse problems, dynamo theory, and tides by William Hill Reid Pdf

Author : Massimo Chiappini,Vincenzo Vespri
Publisher : Unknown
Page : 0 pages
File Size : 51,5 Mb
Release : 2022
Category : Electronic books
ISBN : 8303105329

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Applied Mathematical Problems in Geophysics by Massimo Chiappini,Vincenzo Vespri Pdf

This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes. This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.

Author : Dale R. Durran
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 42,8 Mb
Release : 2010-09-14
Category : Mathematics
ISBN : 9781441964120

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Numerical Methods for Fluid Dynamics by Dale R. Durran Pdf

This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

Author : Yanfei Wang,Anatoly G. Yagola,Changchun Yang
Publisher : Walter de Gruyter
Page : 552 pages
File Size : 54,5 Mb
Release : 2012-10-30
Category : Mathematics
ISBN : 9783110259056

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Computational Methods for Applied Inverse Problems by Yanfei Wang,Anatoly G. Yagola,Changchun Yang Pdf

Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.

Author : Heinz W. Engl,Alfred Karl Louis,William Rundell
Publisher : Society for Industrial and Applied Mathematics (SIAM)
Page : 318 pages
File Size : 43,8 Mb
Release : 1997
Category : Geophysics
ISBN : UCSD:31822026085126

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Inverse Problems in Geophysical Applications by Heinz W. Engl,Alfred Karl Louis,William Rundell Pdf

The papers in this volume describe recent accomplishments in the area, and also give pointers for future research, thereby prompting questions that advance the science and lead to open questions about the underlying mathematics. This volume should be of interest to mathematicians who wish to know more about this application area, and to geophysicists interested in theoretical analysis.

Author : N. Bleistein,J.K. Cohen,John W. Jr. Stockwell
Publisher : Springer Science & Business Media
Page : 537 pages
File Size : 45,7 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9781461300014

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Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion by N. Bleistein,J.K. Cohen,John W. Jr. Stockwell Pdf

For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.

Author : Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl
Publisher : Walter de Gruyter
Page : 212 pages
File Size : 44,6 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9783110282269

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Large Scale Inverse Problems by Mike Cullen,Melina A Freitag,Stefan Kindermann,Robert Scheichl Pdf

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Author : Roger M. Samelson,Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 55,9 Mb
Release : 2006-11-24
Category : Mathematics
ISBN : 9780387462134

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Lagrangian Transport in Geophysical Jets and Waves by Roger M. Samelson,Stephen Wiggins Pdf

Written jointly by a specialist in geophysical fluid dynamics and an applied mathematician, this is the first accessible introduction to a new set of methods for analysing Lagrangian motion in geophysical flows. The book opens by establishing context and fundamental mathematical concepts and definitions, exploring simple cases of steady flow, and touching on important topics from the classical theory of Hamiltonian systems. Subsequent chapters examine the elements and methods of Lagrangian transport analysis in time-dependent flows. The concluding chapter offers a brief survey of rapidly evolving research in geophysical fluid dynamics that makes use of this new approach.

Author : Gottfried Anger
Publisher : Wiley-VCH
Page : 336 pages
File Size : 51,7 Mb
Release : 1993-09
Category : Mathematics
ISBN : UOM:39015032213194

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Inverse Problems by Gottfried Anger Pdf

Most mathematical problems in science, technology, and medicine are inverse problems. Studying such problems is the only way of completely analyzing experimental results. Inverse problems may be considered among the pressing problems of current mathematical research.

Author : Willi Freeden,Martin Gutting
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 48,6 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9783034805636

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Special Functions of Mathematical (Geo-)Physics by Willi Freeden,Martin Gutting Pdf

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Author : Yanfei Wang,Anatoly G. Yagola,Changchun Yang
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 51,9 Mb
Release : 2011-06-29
Category : Mathematics
ISBN : 9783642137426

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Optimization and Regularization for Computational Inverse Problems and Applications by Yanfei Wang,Anatoly G. Yagola,Changchun Yang Pdf

"Optimization and Regularization for Computational Inverse Problems and Applications" focuses on advances in inversion theory and recent developments with practical applications, particularly emphasizing the combination of optimization and regularization for solving inverse problems. This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quantitative remote sensing inversion, seismic inversion using the Lie group method, and the gravitational lensing problem. Scientists, researchers and engineers, as well as graduate students engaged in applied mathematics, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book. Dr. Yanfei Wang is a Professor at the Institute of Geology and Geophysics, Chinese Academy of Sciences, China. Dr. Sc. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonosov Moscow State University, Russia. Dr. Changchun Yang is a Professor and Vice Director of the Institute of Geology and Geophysics, Chinese Academy of Sciences, China.

Author : Kalyan Kumar Roy
Publisher : Springer Science & Business Media
Page : 661 pages
File Size : 55,5 Mb
Release : 2007-11-15
Category : Science
ISBN : 9783540723349

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Potential Theory in Applied Geophysics by Kalyan Kumar Roy Pdf

This book introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.

Author : Willi Freeden,Volker Michel
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220480

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Multiscale Potential Theory by Willi Freeden,Volker Michel Pdf

This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.

Author : Bengt Fornberg,Natasha Flyer
Publisher : SIAM
Page : 221 pages
File Size : 49,7 Mb
Release : 2015-09-30
Category : Science
ISBN : 9781611974041

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A Primer on Radial Basis Functions with Applications to the Geosciences by Bengt Fornberg,Natasha Flyer Pdf

Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work. The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others. This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.