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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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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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Dynamic models of earthquake source and modeling of seismicity
Kostka, Filip ; Gallovič, František (advisor) ; Matyska, Ctirad (referee)
In the present thesis we perform modeling of earthquake source using laboratory derive rate-and-state laws of friction. We have developed a code in Fortran 90 for modeling a planar, two-dimensional fault with general dip and heterogeneous distribution of frictional parameters. We use a quasi-dynamic approximation and assume that the fault is submnerged in an infinite elastic half-space. We performed an extensive number of numerical experiments to study the effect of fricitonal parameters distribution on the spatio-temporal complexity of slip on fault. We also study the effect of the so called Coulomb stress changed on clock advance and clock delay of events. For this purpose we use both a homogeneous model and a model of random frictional parameteres which exhibits the Gutenberg-Richter frequency- size dependence in the range of two magnitudes. We find that the effect of Couloumb stress change is nontrivial and depends on factors such as the domain of stress load and the slip velocity on it. Powered by TCPDF (www.tcpdf.org)
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Vliv materiálových parametrů na stabilitu termální konvekce
Dostalík, Mark ; Matyska, Ctirad (advisor) ; Klika, Václav (referee)
The thesis is focused on the investigation of Rayleigh-Bénard problem in an extended setting approximating the conditions in the Earth's mantle. The aim is to evaluate the influence of depth- and temperature- dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on the qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection and characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly non-linear analysis. It has been found that the character of convection differ substantially from the standard case of Rayleigh-Bénard convection. Powered by TCPDF (www.tcpdf.org)
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Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics
Šustková, Hana ; Matyska, Ctirad (advisor) ; Čížková, Hana (referee)
Title: Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics Author: Hana Šustková Department: Department of Geophysics Supervisor: doc. RNDr. Ctirad Matyska, DrSc. Abstract: This thesis concerns the study of convection in Cartesian models in two and three dimensions. Specifically, it deals with the systematic monitoring of critical Rayleigh numbers based on the geometry model, on the functional dependence of the viscosity or of other parameters. Models has been created with layered viscosity and constant or temperature- and depth- dependent parameters (thermal expansion and conductivity). The system has been described by conventional dimensionless Boussinesq approximation. Part of the work is devoted to the application of matrix method for solving the appropriate Stokes flow and use of Euler's method for solving the thermal equation. The actual calculations were then performed in an environment of commercial software Comsol and thus by using the finite element method. It was shown that the dominant influence on the critical Rayleigh numbers has a viscosity model (with increasing viscosity the critical Rayleigh numbers increase), other important parameter is system's geometry (larger size and dimension of the geometry reduce the critical Rayleigh number). The...
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Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics
Šustková, Hana ; Matyska, Ctirad (advisor) ; Čížková, Hana (referee)
Aim of this work is a systematic investigation of the modes of thermal convection (onset of convection, stationary solutions, periodic solutions, chaotic states) in a material whose properties vary with depth like the material of Earth mantle; the problem was solved in Cartesian geometry. The Stokes equation set was consistently formulated in the spectral region not only horizontally but also vertically, and thus in the model consisting of layers with a constant viscosity but with general course of velocity and temperature in each layer. This equation set was solved with matrix method for each wave vector. Thermal equation was solved in the spatial domain and the transition of velocity and temperature between spectral and spatial domains was performed using the fast Fourier transform. This procedure allows a straightforward parallelization, thereby opening the possibility of not only two-dimensional but also three-dimensional modeling and modeling of chaotic regimes. On the basis of the numerical difficulties of method presented here an model investigated in finite elemens was used. The basic modes of thermal convection were then investigated using model assembled in the software Comsol. Powered by TCPDF (www.tcpdf.org)
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2D finite element formulation of elastic string vibrations with large displacements
Michálek, Jakub ; Horáček, Jaromír (advisor) ; Matyska, Ctirad (referee)
The thesis addresses the numerical solution of the oscillation of the vocal fold at finite strain, whereas the literature has so far been concerned with infinitesimal strain only. The geometry concerned corresponds to the easiest situation of falsetto, since we observe an isolated vocal fold. The vocal fold is treated as non-linear and non-isotropic continuum in 2D space. To demonstrate the function of the model, we simulate the behaviour of the vocal fold with the linear constitutive equation numerically. The vocal fold is modelled by the finite element method with quadratic elements for static and dynamic surface load. We show that a proper simulation of vocal fold tissue deformation requires the equations with finite strain term. Numerical simulation of the vocal fold can be used e.g. for the construction of artificial vocal folds, and for the optimization of their function. Understanding the phonatory mechanism is also essential for discovering the causes of the disorders such as the vocal nodules and for the scientific foundation of phoniatrics and education of singers. The thesis is interdisciplinary and synthesises the facts from mechanics of continuum, anatomy and education of singers.
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