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Forward and Inverse Modeling of Planetary Gravity and Topography
Pauer, Martin ; Čadek, Ondřej (advisor) ; Martinec, Zdeněk (referee) ; Novák, Pavel (referee)
Title: Forward and Inverse Modeling of Planetary Gravity and Topography Author: Martin Pauer Department/Institute: Department of Geophysics MFF UK Supervisor of the doctoral thesis: Doc. RNDr. Ondřej Čadek, CSc., Department of Geophysics MFF UK Abstract: The aim of this work was to investigate various mechanisms compensating the observed planetary topography - crustal isostasy, elastic support and dynamic support caused by mantle flow. The investigated models were applied to three different planetary problems. Firstly we applied dynamic compensation model to explain today large-scale gravity and topography fields of Venus and investigate its mantle viscosity structure. The results seem to support not only models with constant viscosity structure but also a model with a stiff lithosphere and a gradual increase of viscosity toward a core. In the second paper several crust compensation models were employed to estimate the density of the Martian southern highlands crust. Since the used methods depends differently on crustal density changes, we were able to provide some constraints on the maximum density of the studied region. In the third application, the strength of a possible ocean floor gravity signal of Jupiter's moon Europa was studied. It turned out that if the long wavelength topography reaches height at...
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Numerical Modeling of Ice Sheet Dynamics
Souček, Ondřej ; Martinec, Zdeněk (advisor) ; Málek, Josef (referee) ; Ivins, Erik R. (referee)
Title: Numerical modeling of ice sheet dynamics Author: Ondřej Souček Department: Department of Geophysics, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Prof. RNDr. Zdeněk Martinec, DrSc. Supervisor's e-mail address: zdenek@cp.dias.ie Abstract: The main topic of the presented thesis is the numerical modeling of large-scale ice-sheet evo- lution over several glacial cycles. For this purpose a "Shallow Ice Approximation" (SIA) is traditionally adopted, a scaling approximation utilizing the fact that the vertical-to-horizontal aspect ratio in ice sheets is typically a small parameter allowing for a perturbation expansion of the governing equations with respect to this parameter. We present a formulation of the boundary value problem for a polythermal ice sheet based on the rational thermodynamics of mixtures and derive its "shallow-ice" form. We then provide a novel SIA-I algorithm for iterative improvement of the SIA and thoroughly test its performance in a series of benchmarks including the ISMIP-HOM benchmark and a realistic simulation for the Dronning Maud Land region, Antarctica. The SIA-I algorithm is implemented to an evolutionary thermo-mechanical numerical ice-sheet model and this model is tested in the SIA regime in two EISMINT benchmarks, EISMINT - Effect of...
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Time-domain modelling of global barotropic ocean tides
Einšpigel, David ; Martinec, Zdeněk (advisor) ; Haagmans, Roger (referee) ; Matyska, Ctirad (referee)
Traditionally, ocean tides have been modelled in frequency domain with forcing of selected tidal constituents. It is a natural approach, however, non-linearities of ocean dynamics are implicitly neglected. An alternative approach is time-domain modelling with forcing given by the full lunisolar potential, i.e., all tidal constituents are included. This approach has been applied in several ocean tide models, however, a few challenging tasks still remain to solve, for example, the assimilation of satellite altimetry data. In this thesis, we present DEBOT, a global and time-domain barotropic ocean tide model with the full lunisolar forcing. DEBOT has been developed "from scratch". The model is based on the shallow water equations which are newly derived in geographical (spherical) coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a physically consistent form. The numerical model employs finite differences in space and a generalized forward-backward scheme in time. The validity of the code is demonstrated by the tests based on integral invariants. DEBOT has two modes for ocean tide modelling: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. We introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing...
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Numerical modeling of free oscillations applied to superconducting-gravimeter data in a low-frequency seismic range
Zábranová, Eliška ; Matyska, Ctirad (advisor) ; Martinec, Zdeněk (referee) ; Vavryčuk, Václav (referee)
Title: Numerical modeling of free oscillations applied to superconducting-gravimeter data in a low-frequency seismic range Author: Eliška Zábranová Department: Department of Geophysics Supervisor: Doc. RNDr. Ctirad Matyska, DrSc. Abstract: Deformations and changes of the gravitational potential of prestressed selfgravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spheri- cally symmetric bodies we transform the equations and boundary conditions into ordinary differential equations of the second order by the spherical harmonic de- composition and further discretize the equations by highly accurate pseudospectral difference schemes on Chebyshev grids. We thus receive a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Since elas- tic parameters are frequency dependent, we solve the problem for several fiducial frequencies and interpolate the results. Both the mode frequencies and the eigen- functions are benchmarked against the output from the Mineos software package based on Runge-Kutta integration techniques. Subsequently, we use our method to calculate low-frequency synthetic accelerograms of the recent megathrust events and compare them with the observed...
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Gravitational signal of Earth's crustal models
Jaroš, Jaroslav ; Šrámek, Ondřej (advisor) ; Martinec, Zdeněk (referee)
Global models of the Earth's crust, such as CRUST1.0, describe the 3-D distribution of seismic speeds and of material density in the crust. They are widely used in the geophysical community as reference models in local and regional seismic studies and are also the basis of current prediction models of geoneutrino flux from Earth's lithosphere. In this study we attempt to validate the seismology-based CRUST1.0 model using GOCE-derived gravity data. We calculate the anomalous gravitational potential and its first and second radial derivatives, induced at altitude of 250 km by the density distribution in the uppermost ~80 km thick shell of the Earth as described by CRUST1.0. We then compare the prediction with the GOCE model datasets inferred from the GOCE mission satallite gravity measurements. We find that the predicted signal is a factor of ~4 stronger than the measurement in terms of its root-mean-square value. The signal overestimation is consistent across the spherical harmonic spectrum and the spectral correlation of prediction vs. measurement is weak. Our findings motivate the need for improvement of CRUST1.0 and similar models by incorporating gravity data in the model inversion.
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Modelling of global ocean circulation and ocean-induced magnetic field
Šachl, Libor ; Martinec, Zdeněk (advisor) ; Schindelegger, Michael (referee) ; Toh, Hiroaki (referee)
Title: Modelling of global ocean circulation and ocean-induced magnetic field Author: Libor Šachl Department: Department of geophysics Supervisor: prof. RNDr. Zdeněk Martinec, DrSc., Department of geophysics Abstract: The ocean modelling community commonly use several renown ocean general circulation models (OGCMs) such as NEMO, MOM and FESOM. These models have been developed by research groups for many years, which resulted in complex mathematical and numerical algorithms. There are geophysically rele- vant problems, such as the glacial isostatic adjustment, in which the global ocean plays an important role. Ocean circulation does not need to be modeled extremely complex, but other phenomena such as time changing geometry of ocean domain needs to be considered. Geophysical applications motivated us to develop a new OGCM called LSOMG. The LSOMG model is not meant to substitute the ex- isting OGCMs but to provide a modelling framework for geophysical rather than purely oceanographic applications. LSOMG is a 3-D baroclinic ocean model fully parallelized using the MPI standard. It is forced by atmospheric fluxes (wind stresses, heat fluxes, etc.) but also by tides. The model can be run in a simplified 2-D barotropic version if 3-D effects can be neglected. LSOMG was tested in a series of simplified...
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Magnus force acting upon a rotating sphere passing in an incompressible viscous flow
Beck, Dominik ; Martinec, Zdeněk (advisor) ; Čadek, Ondřej (referee)
Classical results of hydrodynamics such as Stokes' force law and Kirchhoff's mo- ment (torque) law are re-derived for laminar viscous flow in the framework of modern compact simplified vector calculus notation. First perturbations of these laws are found and compared visually with experiments. The Magnus drag force on a rotating and moving sphere surrounded by an incompressible viscous New- tonian fluid is derived from the perturbation series of the Navier-Stokes equations in low speed regimes with a small Reynolds number.
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Time-domain modelling of global barotropic ocean tides
Einšpigel, David ; Martinec, Zdeněk (advisor) ; Haagmans, Roger (referee) ; Matyska, Ctirad (referee)
Traditionally, ocean tides have been modelled in frequency domain with forcing of selected tidal constituents. It is a natural approach, however, non-linearities of ocean dynamics are implicitly neglected. An alternative approach is time-domain modelling with forcing given by the full lunisolar potential, i.e., all tidal constituents are included. This approach has been applied in several ocean tide models, however, a few challenging tasks still remain to solve, for example, the assimilation of satellite altimetry data. In this thesis, we present DEBOT, a global and time-domain barotropic ocean tide model with the full lunisolar forcing. DEBOT has been developed "from scratch". The model is based on the shallow water equations which are newly derived in geographical (spherical) coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a physically consistent form. The numerical model employs finite differences in space and a generalized forward-backward scheme in time. The validity of the code is demonstrated by the tests based on integral invariants. DEBOT has two modes for ocean tide modelling: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. We introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing...
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Numerical modeling of free oscillations applied to superconducting-gravimeter data in a low-frequency seismic range
Zábranová, Eliška ; Matyska, Ctirad (advisor) ; Martinec, Zdeněk (referee) ; Vavryčuk, Václav (referee)
Title: Numerical modeling of free oscillations applied to superconducting-gravimeter data in a low-frequency seismic range Author: Eliška Zábranová Department: Department of Geophysics Supervisor: Doc. RNDr. Ctirad Matyska, DrSc. Abstract: Deformations and changes of the gravitational potential of prestressed selfgravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spheri- cally symmetric bodies we transform the equations and boundary conditions into ordinary differential equations of the second order by the spherical harmonic de- composition and further discretize the equations by highly accurate pseudospectral difference schemes on Chebyshev grids. We thus receive a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Since elas- tic parameters are frequency dependent, we solve the problem for several fiducial frequencies and interpolate the results. Both the mode frequencies and the eigen- functions are benchmarked against the output from the Mineos software package based on Runge-Kutta integration techniques. Subsequently, we use our method to calculate low-frequency synthetic accelerograms of the recent megathrust events and compare them with the observed...
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