Geomathematik

[no abstract available

Theory and application of the adjoint method in geodynamics and an extended review of analytical solution methods to the Stokes equation

The initial condition problem with respect to the temperature distribution in the Earth's mantle is Pandora's box of geodynamics. The heat transport inside the Earth follows the principles of advection and conduction. But since conduction is an irreversible process, this mechanism leads to a huge amount of information getting lost over time. Due to this reason, a recovery of a detailed state of the Earth's mantle some million years ago is an intrinsically unsolvable problem. In this work we present a novel mathematical method, the adjoint method in geodynamics, that is not capable of solving but of circumventing the presented initial condition problem by reformulating this task in terms of an optimisation problem. We are aiming at a past state of the Earth's mantle that approaches the current and thus, observable state over time in an optimal way. To this end, huge computational resources are needed since the 'optimal' solution can only be found in an iterative process. In this work, we developed a new general operator formulation in order to determine the adjoint version of the governing equations of mantle flow and applied this method to the high-resolution numerical mantle circulation code TERRA. For our models, we used a global grid spacing of approx. 30 km and more than 80 million mesh elements. We found a reconstruction of the Earth's mantle at 40 Ma that is, with respect to our modelling parameters, consistent with today's observations, gathered from seismic tomography. With this published fundamental work, we are opening the door to a variety of future applications, e.g. a possible incorporation of geological and geodetic data sets as further constraints for the model trajectory over geological time scales. Where high-resolution numerical models and even the implementation of inversion schemes have become feasible over the past decades due to increasing computational resources, in the community there is still a high demand for analytical solution methods. Restricting the physical parameter space in the governing equations, e.g. by only allowing for a radial varying viscosity, it can be shown that in some cases, the resulting simplified equations can even be solved in a (semi-)analytical way. In other words, in these simplified scenarios, no large scale computational resources or even high-performance clusters are needed but the solution for a global flow system can be determined in minutes even on a standard computer. Besides this apparent advantage, analytical and numerical solutions can even go hand-in-hand since numerical computer codes may be tested and benchmarked by means of these manufactured solutions. Here, we spend a large portion of this work with a detailed derivation of these analytical approaches. We basically start from scratch, having the intention to cover all possible traps and pitfalls on the way from the governing equations to their solutions and to provide a service to future scientists that are stuck somewhere in the middle of this road. Besides the derivation, we also present in detail how such an analytical approach can be used as a benchmark for a high-resolution mantle circulation code. We applied this theory to the prototype for a new high-performance mantle convection framework being developed in the Terra-Neo project and published the results along with a small portion of the derived theory. In an additional chapter of this work, we focus on a detailed analysis of the current state of the Earth's gravitational field that is measured in an unimaginably accurate way by the recent satellite missions CHAMP, GRACE and GOCE. The origin of the link of our work to the gravitational field also lies in the analytical solution methods. It can be shown that due to the effect of flow induced dynamic topography, the Earth's gravity field is highly sensitive to the viscosity profile in the Earth's mantle. We show that even without using any other external knowledge or data set, the gravitational field itself restricts the possible choices for the Earth's mantle viscosity to a well-defined parameter space. Furthermore, in the course of these examinations, we found that mantle processes are not capable of explaining the short wavelength signals in the observed gravity field at all, even with the best-fitting viscosity profile. To this end, we developed a simple crustal model that is only based on topographic data (ETOPO) and the principle of isostasy and showed that even with this very basic approach we can explain the majority of short length-scale features in the observed gravity signal. Finally, in combination with a (simple, static and analytic) mantle flow model based on a density field derived from seismic topography and mineralogy, we found a nearly perfect fit of modelled and observed gravitational data throughout all wavelengths under consideration (spherical harmonic degree and order up to l=100)

Wavelet-Mie-Representations for Solenoidal Vector Fields with Applications to Ionospheric Geomagnetic Data

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

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

Wavelet-Mie-Representations for Solenoidal Vector Fields with Applications to Ionospheric Geomagnetic Data

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

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

1995 BRAC Commission

Naval Research Lab: Military Value Data Call. Tabular data, memos, documents. Box 178, L-110