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This textbook presents a comprehensive treatment of the theory and implementation of inverse methods in the analysis and interpretation of Earth's gravity field. By restricting their consideration to a local rather than global level, the authors focus on the use of observations and data that are more sensitive to local mass anomalies. All necessary theoretical aspects are reformulated in terms of a Euclidean framework so that less complex tools from mathematical analysis can be utilized.Divided into three parts, the text begins with a review of basic mathematical properties of gravitation, computing gravity from mass distributions, and relevant methods from Fourier analysis. In the second part of the text, the Earth's gravity field and its properties are introduced, and the preprocessing and processing of gravity data are explored. Finally, elementary inverse theory is discussed, after which the general inversion problem is considered via application of both the Tikhonov deterministic approach and a stochastic MCMC model. Throughout, examples and exercises are provided to both clarify material and to illustrate real-word applications for readers. Analysis of the Gravity Field: Direct and Inverse Problems is carefully written to be accessible to both mathematicians and geophysicists without sacrificing mathematical rigor. Readers should have a familiarity with the basics of mathematical analysis, as well as some knowledge of statistics and probability theory. Detailed proofs of more advanced results are relegated to appendices so that readers can concentrate on solution algorithms.

This volume presents a collection of contributions that were published in'Pure and Applied Geophysics - pageoph'and which deals with the major earthquake that hit Illapel, Chile on September 16, 2015 with magnitude 8.3, and associated trans-oceanic tsunami. The subducting Nazca plate beneath the Andes caused this major earthquake, generating strong shaking, permanent deformation, free oscillations of the Earth, and tsunamis. This event occurred in the flat-angle subducting segment of the plate.The generated tsunami spread throughout the entire Pacific Ocean and was recorded by numerous coastal tide gauges and open-ocean DART stations.All articles give an up-to-date account of research in one of the most active seismic zones worldwide. An introductory article by Kenji Satake rounds this collection off.