Up and Down Through the Gravity Field
Die Kenntnis des Schwerefeldes hat weitreichende Anwendungen in den Geo- wissenschaften, insbesondere in Geodsie und Geophysik. Unser Anliegen in diesem Beitrag ist die Beschreibung von Eigenschaften zur Fortpflanzung des Potentials oder seiner relevanten
- PDF / 719,441 Bytes
- 54 Pages / 439.36 x 666.15 pts Page_size
- 92 Downloads / 208 Views
Contents 1 Gravity Field: Why and How . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Principles of Upward Continuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Geodetic Boundary Value Problems (GBVP’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Global Models as Approximate Solutions of the GBVP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Principles of Downward Continuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 The Constant Density Layer with Unknown Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Some Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 5 11 18 24 33 45 53
Abstract
The knowledge of the gravity field has widespread applications in geosciences, in particular in Geodesy and Geophysics. The point of view of the paper is to describe the properties of the propagation of the potential, or of its
This chapter is part of the series Handbuch der Geodäsie, volume “Mathematical Geodesy/Mathematische Geodäsie”, edited by Willi Freeden, Kaiserslautern. F. Sansó () Department of Civil and Environmental Engineering, Politecnico di Milano, Milan, Italy E-Mail: [email protected] M. Capponi Department of Civil, Constructional and Environmental Engineering, Università di Roma La Sapienza, Rome, Italy Department of Civil and Environmental Engineering, Politecnico di Milano, Milan, Italy E-Mail: [email protected] D. Sampietro Geomatics Research & Development s.r.l., Como, Italy E-Mail: [email protected] © Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018 W. Freeden, R. Rummel (Hrsg.), Handbuch der Geodäsie, Springer Reference Naturwissenschaften, https://doi.org/10.1007/978-3-662-46900-2_93-1
1
2
F. Sansó et al.
relevant functionals, while moving upward or downward. The upward propagation is always a properly posed problem, in fact a smoothing and somehow related to the Newton integral and to the solution of boundary value problems (BVP). The downward propagation is always improperly posed, not only due to its intrinsic numerical instability but also because of the nonuniqueness that is created as soon as we penetrate layers of unknown mass density. So the paper focuses on recent results on the Geodetic Boundary Value Problems on the one side and on the inverse gravimetric problem on the other, trying to highlight the significance of mathematical theory to numerical applications. Hence, on the one hand we examine the application of the BVP theory to the construction of global gravity models, on the other hand the inverse gravimetric problem is studied for layers together with proper regularization techniques. The level of the mathematics employ
Data Loading...
