LEADER 04486nam 22006375 450 001 9910574863403321 005 20251113193708.0 010 $a9783030743536 024 7 $a10.1007/978-3-030-74353-6 035 $a(CKB)23689207100041 035 $a(DE-He213)978-3-030-74353-6 035 $a(BIP)84541427 035 $a(EXLCZ)9923689207100041 100 $a20220609d2022 u| 0 101 0 $aeng 135 $aurun|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis of the Gravity Field $eDirect and Inverse Problems /$fby Fernando Sanṣ, Daniele Sampietro 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2022. 215 $a1 recurso en línea 225 1 $aLecture Notes in Geosystems Mathematics and Computing,$x2512-3211 311 08$aPrint version: Sanṣ, Fernando Analysis of the Gravity Field Cham : Springer International Publishing AG,c2022 9783030743529 327 $aIntroduction -- Part I: Forward Modelling of the Gravity Field -- The Vertical Gravitational Signal of Homogeneous Bodies, Bounded in the Horizon Plane -- Fourier Methods -- Part II: The Preprocessing and Processing of Gravity Data: From Observations to a Gravity Map on a Local Horizontal Plane -- The Gravity Field of Earth -- Gravity Surveying and Preprocessing -- Gravity Processing -- Part III: Inverse Theory and Applications -- Elementary Inverse Theory -- On the Mathematical Characterization of the Inverse Gravity Problem -- General Inversion Approaches -- Some Conclusions -- Part IV: Appendices -- Mathematical Auxillia -- The Theory of Random Fields and the Wiener-Kolmogorov Prediction Method -- The Tikhonov Regularization and Morozov's Discrepancy Principle. 330 $aThis 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. . 345 $aProquest Ebook Central 410 0$aLecture Notes in Geosystems Mathematics and Computing,$x2512-3211 606 $aMathematics$xData processing 606 $aGeophysics 606 $aStochastic processes 606 $aFourier analysis 606 $aComputational Mathematics and Numerical Analysis 606 $aGeophysics 606 $aStochastic Processes 606 $aFourier Analysis 615 0$aMathematics$xData processing. 615 0$aGeophysics. 615 0$aStochastic processes. 615 0$aFourier analysis. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aGeophysics. 615 24$aStochastic Processes. 615 24$aFourier Analysis. 676 $a518 700 $aSanso?$b F$g(Fernando),$f1945-$0422254 702 $aSampietro$b Daniele 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 801 2$bUJAEN 906 $aBOOK 912 $a9910574863403321 996 $aAnalysis of the Gravity Field$92880523 997 $aUNINA