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 Runge-Walsh 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.