Multiscale Potential Theory

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.

New mathematical methods are developed enabling the gravitational potential of a planetary body (the Earth) to be modeled and analyzed using a continuous flow of observations from land or satellite devices Comprehensive coverage of topics which, thus far, are only scattered in journal articles and conference proceedings Important applications and developments for future satellite scenarios; new modelling techniques involving low-orbiting satellites Multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling Exercises at the end of each chapter and an appendix with hints to their solutions Accessible to a broad audience of grad students, geoscientists, applied mathematicians, and engineers Includes supplementary material: sn.pub/extras

Klappentext

This self-contained book provides a basic foundation for students, practitioners, and researchers interested in some of the diverse new areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled and analyzed using a continuous flow of observations from land or satellite devices. Harmonic wavelet methods are introduced, as well as fast computational schemes and various numerical test examples.

The work is divided into two main parts: Part I treats well-posed boundary-value problems of potential theory and elasticity; Part II examines ill-posed problems such as satellite-to-satellite tracking, satellite gravity gradiometry, and gravimetry. Both sections demonstrate how multiresolution representations yield RungeWalsh type solutions that are both accurate in approximation and tractable in computation.

Topic and key features:

• Comprehensive coverage of topics which, thus far, are only scattered in journal articles and conference proceedings

• Important applications and developments for future satellite scenarios; new modelling techniques involving low-orbiting satellites

• Multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling

• Multilevel stabilization procedures for regularization

• Treatment of the real Earth's shape as well as a spherical Earth model

• Modern methods of constructive approximation

• Exercises at the end of each chapter and an appendix with hints to their solutions

Models and methods presented show how various large- and small-scale processes may be addressed by a single geoscientific modelling framework for potential determination. Multiscale Potential Theory may be used as a textbook for graduate-level courses ingeomathematics, applied mathematics, and geophysics. The book is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.

Inhalt
1 Introduction.- 2 Preliminary Tools.- 2.1 Basic Settings.- 2.2 Spherical Nomenclature.- 2.3 Sphere Oriented Potential Theory.- 2.4 Exercises.- I Well-Posed Problems.- 3 Boundary-Value Problems of Potential Theory.- 4 Boundary-Value Problems of Elasticity.- II Ill-Posed Problems.- 5 Satellite Problems.- 6 The Gravimetry Problem.- 7 Conclusion.- 8 Hints for the Solution of the Exercises.- References.