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Fri, 08 Jul 2011 07:18:26 +0200Fri, 08 Jul 2011 07:18:26 +0200Mathematical aspects of stress field simulations in deep geothermal reservoirs
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2671
This report gives an insight into basics of stress field simulations for geothermal reservoirs.
The quasistatic equations of poroelasticity are deduced from constitutive equations, balance
of mass and balance of momentum. Existence and uniqueness of a weak solution is shown.
In order of to find an approximate solution numerically, usage of the so–called method of
fundamental solutions is a promising way. The idea of this method as well as a sketch of
how convergence may be proven are given.Matthias Augustinreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2671Fri, 08 Jul 2011 07:18:26 +0200Locally Supported Wavelets for the Separation of Spherical Vector Fields with Respect to their Sources
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2284
We provide a space domain oriented separation of magnetic fields into parts generated by sources in the exterior and sources in the interior of a given sphere. The separation itself is well-known in geomagnetic modeling, usually in terms of a spherical harmonic analysis or a wavelet analysis that is spherical harmonic based. However, it can also be regarded as a modification of the Helmholtz decomposition for which we derive integral representations with explicitly known convolution kernels. Regularizing these singular kernels allows a multiscale representation of the magnetic field with locally supported wavelets. This representation is applied to a set of CHAMP data for crustal field modeling.Christian Gerhardsreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2284Tue, 08 Feb 2011 12:16:54 +0100Wärmetransportmodellierung in tiefen geothermischen Systemen
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2129
Gegenstand dieser Arbeit ist die Entwicklung eines Wärmetransportmodells für tiefe geothermische (hydrothermale) Reservoire. Existenz- und Eindeutigkeitsaussagen bezüglich einer schwachen Lösung des vorgestellten Modells werden getätigt. Weiterhin wird ein Verfahren zur Approximation dieser Lösung basierend auf einem linearen Galerkin-Schema dargelegt, wobei sowohl die Konvergenz nachgewiesen als auch eine Konvergenzrate erarbeitet werden.Isabel Ostermannreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2129Sat, 19 Sep 2009 16:50:42 +0200Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2040
Gegenstand dieser Arbeit ist die kanonische Verbindung klassischer globaler Schwerefeldmodellierung in der Konzeption von Stokes (1849) und Neumann (1887) und moderner lokaler Multiskalenberechnung mittels lokalkompakter adaptiver Wavelets. Besonderes Anliegen ist die "Zoom-in"-Ermittlung von Geoidhöhen aus lokal gegebenen Schwereanomalien bzw. Schwerestörungen.Willi Freeden; Kerstin Wolfreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2040Tue, 18 Nov 2008 13:50:49 +0100Classical Globally Reflected Gravity Field Determination in Modern Locally Oriented Multiscale Framework
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2031
The purpose of this paper is the canonical connection of classical global gravity field determination following the concept of Stokes (1849), Bruns (1878), and Neumann (1887) on the one hand and modern locally oriented multiscale computation by use of adaptive locally supported wavelets on the other hand. Essential tools are regularization methods of the Green, Neumann, and Stokes integral representations. The multiscale approximation is guaranteed simply as linear difference scheme by use of Green, Neumann, and Stokes wavelets, respectively. As an application, gravity anomalies caused by plumes are investigated for the Hawaiian and Iceland areas.W. Freeden; T. Fehlinger; M. Klug; D. Mathar; K. Wolfreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2031Tue, 14 Oct 2008 12:34:09 +0200Local Modelling of Sea Surface Topography from (Geostrophic) Ocean Flow
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1836
This paper deals with the problem of determining the sea surface topography from geostrophic flow of ocean currents on local domains of the spherical Earth. In mathematical context the problem amounts to the solution of a spherical differential equation relating the surface curl gradient of a scalar field (sea surface topography) to a surface divergence-free vector field(geostrophic ocean flow). At first, a continuous solution theory is presented in the framework of an integral formula involving Green’s function of the spherical Beltrami operator. Different criteria derived from spherical vector analysis are given to investigate uniqueness. Second, for practical applications Green’s function is replaced by a regularized counterpart. The solution is obtained by a convolution of the flow field with a scaled version of the regularized Green function. Calculating locally without boundary correction would lead to errors near the boundary. To avoid these Gibbs phenomenona we additionally consider the boundary integral of the corresponding region on the sphere which occurs in the integral formula of the solution. For reasons of simplicity we discuss a spherical cap first, that means we consider a continuously differentiable (regular) boundary curve. In a second step we concentrate on a more complicated domain with a non continuously differentiable boundary curve, namely a rectangular region. It will turn out that the boundary integral provides a major part for stabilizing and reconstructing the approximation of the solution in our multiscale procedure.Thomas Fehlinger; Willi Freeden; Simone Gramsch; Carsten Mayer; Dominik Michel; Michael Schreinerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1836Sun, 11 Feb 2007 15:03:15 +0100Regularized Multiresolution Recovery of the Mass Density Distribution From Satellite Data of the Earth´s Gravitational Field
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1586
The inverse problem of recovering the Earth's density distribution from data of the first or second derivative of the gravitational potential at satellite orbit height is discussed for a ball-shaped Earth. This problem is exponentially ill-posed. In this paper a multiscale regularization technique using scaling functions and wavelets constructed for the corresponding integro-differential equations is introduced and its numerical applications are discussed. In the numerical part the second radial derivative of the gravitational potential at 200 km orbitheight is calculated on a point grid out of the NASA/GSFC/NIMA Earth Geopotential Model (EGM96). Those simulated derived data out of SGG (satellite gravity gradiometry) satellite measurements are taken for convolutions with the introduced scaling functions yielding a multiresolution analysis of harmonic density variations in the Earth's crust. Moreover, the noise sensitivity of the regularization technique is analyzed numerically.Volker Michelreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1586Tue, 16 Nov 2004 14:25:33 +0100Wavelet-Mie-Representations for Solenoidal Vector Fields with Applications to Ionospheric Geomagnetic Data
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1494
A wavelet technique, the wavelet-Mie-representation, is introduced for the analysis and modelling of the Earth's magnetic field and corresponding electric current distributions from geomagnetic data obtained within the ionosphere. The considerations are essentially based on two well-known geomathematical keystones, (i) the Helmholtz-decomposition of spherical vector fields and (ii) the Mie-representation of solenoidal vector fields in terms of poloidal and toroidal parts. The wavelet-Mie-representation is shown to provide an adequate tool for geomagnetic modelling in the case of ionospheric magnetic contributions and currents which exhibit spatially localized features. An important example are ionospheric currents flowing radially onto or away from the Earth. To demonstrate the functionality of the approach, such radial currents are calculated from vectorial data of the MAGSAT and CHAMP satellite missions.Thorsten Maierreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1494Thu, 05 Feb 2004 16:17:08 +0100Wavelet Modelling of the Spherical Inverse Source Problem with Application to Geomagnetism
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1468
The article is concerned with the modelling of ionospheric current systems from induced magnetic fields measured by satellites in a multiscale framework. Scaling functions and wavelets are used to realize a multiscale analysis of the function spaces under consideration and to establish a multiscale regularization procedure for the inversion of the considered vectorial operator equation. Based on the knowledge of the singular system a regularization technique in terms of certain product kernels and corresponding convolutions can be formed. In order to reconstruct ionospheric current systems from satellite magnetic field data, an inversion of the Biot-Savart's law in terms of multiscale regularization is derived. The corresponding operator is formulated and the singular values are calculated. The method is tested on real magnetic field data of the satellite CHAMP and the proposed satellite mission SWARM.Carsten Mayerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1468Thu, 22 Jan 2004 18:15:36 +0100