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Motional electromagnetic induction in the subsurface ocean in Europa
Kureš, Ondřej ; Velímský, Jakub (advisor) ; Souček, Ondřej (referee)
Europa is one of the Jovian icy moons with confirmed subsurface ocean. Circulation of the ocean in presence of the Jovian ambient magnetic field leads to generation of the ocean-induced magnetic field (OIMF). On Earth, the OIMF has potential to provide us with informations about water flow and electrical conductivity. However, the OIMF in Europa has been addressed only briefly in the available literature. This thesis is focused on numerical modelling of motionally driven process of the electromagnetic induction (EMI) in the subsurface ocean of Europa. Firstly, the EMI equation is introduced with its corresponding weak formulation. Its solutions are obtained by the means of finite element method (FEM) in combination with spherical harmonic functions. I discuss the structure of the linear problem and subroutines applied in the numerical solver. The code is successfully tested against a set of independent semi-analytical solutions. Three models of flow in the Europa's ocean are explored, using simple analytical expressions of ocean velocities and Jovian magnetic field. 1
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Studium rovnováhy mezi klesajícími kapkami železa a roztavenými silikáty v magmatických oceánech
Ulvrová, Martina ; Velímský, Jakub (advisor) ; Šrámek, Ondřej (referee)
During the Earth's accretion process deep magma oceans were episodically formed. Differentiation of iron took place within the melted zone and small droplets of iron were sinking to the base of the magma ocean due to the density contrast. In the present work we study the process of equilibration between dispersed metal droplets and surrounding silicates that proceeds by the advection transport and diffusion at the rim. We allow for steady state ow of a spherical liquid blob falling in a host liquid and establish the numerical code in axisymmetric spherical coordinates computing the chemical evolution of such heterogeneous system. We focus on determining the time scales of equilibration for which we propose an analytical model based on the boundary layer analysis. The obtained characteristic times are especially for low silicate viscosities very short that supports the idea that the drops attained equilibrium while sinking.
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Stochastic simulations and modelling in the magnetotelluric method
Klanica, Radek ; Pek, Josef (advisor) ; Růžek, Bohuslav (referee) ; Velímský, Jakub (referee)
In the thesis I deal with the development of a stochastic inversion procedure for the magnetotelluric method in 1D/2D isotropic and anisotropic cases, and its application to both synthetic and real data. The magnetotelluric method is a geoelectric inductive technique that utilizes variations of naturally occurring electromagnetic fields as a source of the electromagnetic induction for estimating the Earth's subsurface resistivity to depths of several tens of kilometres. The purpose of the inversion procedure is to estimate a real distribution of the electrical resistivity in the Earth's subsurface from surface measurements. Common inversion procedures in magnetotellurics perform a model optimization by minimizing the misfit between the data and the model response. Stochastic methods are based on the exploration of the model parameter space, and they pick models according to their probability, which makes them effective for the solution of high-dimensional problems which do not show a single pronounced minimum of the target function. The effective ways of mapping the parameter space are sampling algorithms based on Monte Carlo simulations which allow to sort models according to their probability. Results of these methods are obtained in the form of a fully probabilistic description of the...
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Joule heating of Mercury
Peisar, Ondřej ; Velímský, Jakub (advisor) ; Čížková, Hana (referee)
In this paper we investigate influence of the interior and exterior magnetic fields on mantle heating of Mercury. Exterior field is induced by currents in the magnetosphere, interior field is generated by dynamo deep in the planetary core, whose outer layer is stably stratified. After summarization of basic facts about Mercury we derive a formula for magnetic field on the surface and on the inner boundary. Afterwards we investigate the influence of conductivity estimates and periods on heat production in the mantle. We found out that for expected conductivities (iron core, silicate mantle) magnetic field doesn't have any influence on mantle convection.
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Electrical conductivity of the mantle and its thermochemical and mineralogical state: Forward problem
Knopp, Ondřej ; Velímský, Jakub (advisor) ; Šrámek, Ondřej (referee)
With the increased availability of new geomagnetic data, mainly from the Swarm mission satellites, it is possible to obtain global mantle conductivity models. A subse- quent task is to interpret such models in terms of the thermal and chemical structure of the Earth's mantle. It can be done using the experimental conductivity data for major mantle minerals combined with the Gibbs energy minimization. Here I describe these methods and present a forward problem calculating the electrical conductivity of the Earth's mantle, from its temperature and chemical composition. I also present the modelling results for a-priori temperature and compositional settings. This software com- ponent will become part of the existing tools used for global inversion of electromagnetic data to constrain the thermochemical and mineralogical structure of the mantle. 1
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Impact crater relaxation throughout the Solar System
Kihoulou, Martin ; Kalousová, Klára (advisor) ; Velímský, Jakub (referee)
Title: Impact crater relaxation throughout the Solar System Author: Martin Kihoulou Department: Department of Geophysics Supervisor: RNDr. Klára Kalousová, Ph.D., Department of Geophysics Abstract: In this thesis, we study the viscous relaxation of an impact-deformed icy shell of a dwarf planet Pluto. Motivation for this work is the position of Sputnik Planitia, a 1000 km wide, nitrogen-filled elliptic basin, which is located very close to Pluto-Charon tidal axis. Given this unlikely position on Pluto's sur- face, it was suggested that the basin was formed elsewhere and the whole body reoriented afterwards. For the reorientation to occur, the basin has to generate a positive gravity anomaly for which a combination of impact-related subsurface ocean uplift, ejecta blanket and accumulation of nitrogen ice was suggested. How- ever, to maintain the orientation towards the minimum principal axis of inertia until today, the ocean uplift must be present on timescales of billions of years, which may be achieved due to an insulating layer of high viscosity clathrates at the ice/ocean interface. We solve Pluto's ice shell evolution by the finite element method in 2D spherical axisymmetric geometry with an evolving free surface and assuming a viscous rheology. Our results show that the thermal effect of the im- pact...
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Stochastic simulations and modelling in the magnetotelluric method
Klanica, Radek ; Pek, Josef (advisor) ; Růžek, Bohuslav (referee) ; Velímský, Jakub (referee)
In the thesis I deal with the development of a stochastic inversion procedure for the magnetotelluric method in 1D/2D isotropic and anisotropic cases, and its application to both synthetic and real data. The magnetotelluric method is a geoelectric inductive technique that utilizes variations of naturally occurring electromagnetic fields as a source of the electromagnetic induction for estimating the Earth's subsurface resistivity to depths of several tens of kilometres. The purpose of the inversion procedure is to estimate a real distribution of the electrical resistivity in the Earth's subsurface from surface measurements. Common inversion procedures in magnetotellurics perform a model optimization by minimizing the misfit between the data and the model response. Stochastic methods are based on the exploration of the model parameter space, and they pick models according to their probability, which makes them effective for the solution of high-dimensional problems which do not show a single pronounced minimum of the target function. The effective ways of mapping the parameter space are sampling algorithms based on Monte Carlo simulations which allow to sort models according to their probability. Results of these methods are obtained in the form of a fully probabilistic description of the...
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Surface manifestation of melting within the ice shell of Europa
Vach, Dominik ; Kalousová, Klára (advisor) ; Velímský, Jakub (referee)
One of the most interesting extraterrestrial bodies in the Solar System is Europa, the icy satellite of Jupiter. This icy moon might have a sufficiently hospitable environment which could be harbouring life in the subsurface ocean deep under its icy crust. The thesis thoroughly examines the generation process of one of the surface formations called chaotic terrains. These huge areas of ice disruptions which uniquely characterize Europa's surface might play a significant role in the understanding of the inner structure of the moon. The latest research assumes the chaotic terrains form above liquid water lenses perched relatively shallow in the ice shell, however, no numerical simulations have been performed to confirm this theory. The goal of the thesis is to create a model which would validate the theory and explain the formation process of the chaotic terrains. The thesis runs several simulations, and our results suggest these water lenses and the process in the mantle might play a key role in the chaotic terrains formation.
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