03404nam 22006015 450 991025407070332120200817140133.03-319-48384-610.1007/978-3-319-48384-9(CKB)3710000001006488(DE-He213)978-3-319-48384-9(MiAaPQ)EBC6315123(MiAaPQ)EBC5577498(Au-PeEL)EBL5577498(OCoLC)1066197652(PPN)197140874(EXLCZ)99371000000100648820161125d2016 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierInverse Problems Basics, Theory and Applications in Geophysics /by Mathias Richter1st ed. 2016.Cham :Springer International Publishing :Imprint: Birkhäuser,2016.1 online resource (XII, 240 p. 52 illus., 32 illus. in color.) Lecture Notes in Geosystems Mathematics and Computing,2730-59963-319-48383-8 1.Characterization of Inverse Problems -- 2.Discretization of Inverse Problems -- 3.Regularization of Linear Inverse Problems -- 4.Regularization of Nonlinear Inverse Problems -- Appendix: A.Results from Linear Algebra -- B.Function Spaces -- C.The Fourier Transform -- D.Proofs of Theorems from Chapter 3.The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.Lecture Notes in Geosystems Mathematics and Computing,2730-5996Numerical analysisPhysicsGeophysicsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Numerical and Computational Physics, Simulationhttps://scigraph.springernature.com/ontologies/product-market-codes/P19021Geophysics/Geodesyhttps://scigraph.springernature.com/ontologies/product-market-codes/G18009Numerical analysis.Physics.Geophysics.Numerical Analysis.Numerical and Computational Physics, Simulation.Geophysics/Geodesy.515.357Richter Mathiasauthttp://id.loc.gov/vocabulary/relators/aut755956MiAaPQMiAaPQMiAaPQBOOK9910254070703321Inverse problems1523415UNINA