Institute of Geophysics of the CAS, v. v. i.
MSc and PhD projects offered
Offered theses
Running theses
Defended theses
Comparison of two formulations of ray tracing for inhomogeneous anisotropic media, study of their behaviour in singular regions of S waves
[MSc. project]
Supervisor : RNDr. Ivan Pšenčík, CSc.
References:
Červený,V., 1972. Seismic rays and ray intensities in inhomogeneous anisotropic media. Geophys. J.R. astr. Soc. 28, 113.
Červený,V., 2001. Seismic Ray Theory. Cambridge University Press, Cambridge.
Gajewski,D. & Pšenčík,I., 1987. Computation of highfrequency seismic wavefileds in 3D laterally inhomogeneous anisotropic media. Geophys.J.R.astr.Soc., 91, 383411.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Vavryčuk, V., 2001. Ray tracing in anisotropic media with singularities. Geophys.J.Int. 145, 265276.
Construction of the complete propagator matrix of the dynamic ray tracing in the ANRAY package. Applications.
[MSc. project]
Supervisor : RNDr. Ivan Pšenčík, CSc.
References:
Červený,V., 2001. Seismic Ray Theory. Cambridge University Press, Cambridge.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Moser,T.J. & Červený, V.: Paraxial ray methods for anisotropic inhomogeneous media. Geophysical Prospecting, 2006, in press.
Construction of the code for the R/T coefficients in anisotropic media, using ANRAY package. Study of behaviour of R/T coefficients.
[MSc. project]
Supervisor : RNDr. Ivan Pšenčík, CSc.
References:
Červený,V., 2001. Seismic Ray Theory. Cambridge University Press, Cambridge.
Chapman,C.H., 1994. Reflection/transmission coefficient reciprocities in anisotropic media. Geophys.J.Int., 116, 498501.
Gajewski,D. & Pšenčík,I., 1987. Computation of highfrequency seismic wavefileds in 3D laterally inhomogeneous anisotropic media. Geophys.J.R.astr.Soc., 91, 383411.
Introduction of a weak attenuation into the ANRAY package, tests of its accuracy and study of its effects
[MSc. project]
Supervisor : RNDr. Ivan Pšenčík, CSc.
Present version of the program package ANRAY (Gajewski & Pšenčík, 1990) can be used for computation of seismic wavefields in elastic, layered, laterally inhomogeneous isotropic and/or anisotropic structures. The goal of this project is to generalize the considered model by allowing weak attenuation, see Gajewski & Pšenčík (1992). An approximate consideration of weak attenuation requires only an additional integration along a realvalued ray (attenuation is generally connected with complexvalued rays), see, e.g., Červený (2001). The resulting code can be then used to study effects of weak attenuation on seismic waves propagating in inhomogeneous, anisotropic, weakly attenuating media. Possible additional goal is to test the accuracy of the generalized package with respect to available codes based on more accurate methods. e.g., matrix methods (see Wang, 1999).
References:
Červený,V., 2001. Seismic Ray Theory. Cambridge University Press, Cambridge.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Gajewski,D. & Pšenčík,I.,1992. Vector wave fields for weakly attenuating anisotropic media by the ray method. Geophysics, 57, 2738.
Wang,R., 1999. A simple orthonormalization method for the stable and efficient computation of Green's functions, Bull.seismol.Soc.Am., 89, 733741.
Comparison of results of quasiisotropic ray approximation with results of more accurate methods
[MSc. project]
Supervisor : RNDr. Ivan Pšenčík, CSc.
Present version of the program package ANRAY (Gajewski & Pšenčík, 1990) allows approximate computation of coupled shear waves in inhomogeneous, weakly anisotropic media, which is based on the quasiisotropic (QI) approximation (Pšenčík, 1998) of the coupling ray theory, see Coates & Chapman (1990), Klimeš & Bulant (2006), Červený (2001) and references there. Principal goal of this project is to test accuracy of the QI approximation in various models of inhomogeneous, weakly anisotropic media by comparing the results obtained with ANRAY package with results of available codes based on more accurate methods like, e.g., Chebyshev spectral method, see Tessmer (1995).
References:
Červený,V., 2001. Seismic Ray Theory. Cambridge University Press, Cambridge.
Coates,R.T. & Chapman,C.H., 1990. Quasishear wave coupling in weakly anisotropic 3D media, Geophys.J.Int., 103, 301320.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Klimeš,L. & Bulant,P., 2006. Errors due to the anisotropiccommonray approximation of the coupling ray theory. Stud.Geophys.Geod., 50, 463477.
Pšenčík,I., 1998. Green's functions for inhomogeneous weakly anisotropic media. Geophys.J. Int., 135, 279288. Tessmer,E., 1995. 3D seismic modelling of general material anisotropy in the presence of the free surface by a Chebyshev spectral method. Geophys.J.Int., 121, 557575.
Tessmer,E., 1995. 3D seismic modelling of general material anisotropy in the presence of the free surface by a Chebyshev spectral method. Geophys.J.Int., 121, 557575.
Generalization of the quasiisotropic approach for the reference rays computed in the studied anisotropic medium
[PhD. project]
Supervisor: RNDr. Ivan Pšenčík, CSc.
Present version of the program package ANRAY (Gajewski & Pšenčík, 1990) allows approximate computation of coupled shear waves in inhomogeneous, weakly anisotropic media, which is based on the quasiisotropic (QI) approximation of the coupling ray theory, see Coates & Chapman (1990), Klimeš & Bulant (2006), Červený (2001) and references there. The amplitude contribution of the two coupled shear waves is calculated by integrating two coupled ordinary differential equations along a reference ray in a reference isotropic medium, see Kravtsov & Orlov (1980), Pšenčík (1998), Pšenčík & Delinger (2001). As shown, e.g., by Bulant & Klimeš (2004), the choice of the reference ray in a reference isotropic medium may have a substantial effect on accuracy of the QI approximation. The goal of this project is to substitute the presently used reference ray in an isotropic medium by a reference ray in the anisotropic medium, in which the QI computations are to be performed. The corresponding coupling equations should be modified accordingly, then coded and resulting code should be tested by comparing its results with results of available codes based on more accurate methods like, e.g., Chebyshev spectral method, see Tessmer (1995).
References:
Červený,V., 2001. Seismic Ray Theory: Cambridge University Press, Cambridge.
Bulant & Klimeš, 2004. Comparison of quasiisotropic approximations of the coupling ray theory with the exact solution in the 1D anisotropic "oblique twisted crystal" model. Stud.Geophys.Geod., 48, 97116.
Coates,R.T. & Chapman,C.H., 1990. Quasishear wave coupling in weakly anisotropic 3D media, Geophys.J.Int., 103, 301320.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Klimeš,L. & Bulant,P., 2006. Errors due to the anisotropiccommonray approximation of the coupling ray theory. Stud.Geophys.Geod., 50, 463477.
Kravtsov, Yu.A. & Orlov,Yu.I., 1980. Geometrical optics of inhomogeneous media, Nauka, Moscow (in Russian).
Pšenčík,I., 1998. Green's functions for inhomogeneous weakly anisotropic media. Geophys.J. Int., 135, 279288.
Pšenčík,I. & Dellinger.J., 2001. Quasishear waves in inhomogeneous weakly anisotropic media by the quasiisotropic approach: a model study. Geophysics, 66, 308319.
Tessmer,E., 1995. 3D seismic modelling of general material anisotropy in the presence of the free surface by a Chebyshev spectral method. Geophys.J.Int., 121, 557575.
Generalization of the quasiisotropic approach for layered media
[PhD. project]
Supervisor: RNDr. Ivan Pšenčík, CSc.
Present version of the program package ANRAY (Gajewski & Pšenčík, 1990) allows approximate computation of coupled shear waves in smooth inhomogeneous, weakly anisotropic media, which is based on the quasiisotropic (QI) approximation (Kravtsov & Orlov 1980, Pšenčík, 1998) of the coupling ray theory, see Coates & Chapman (1990), Klimeš & Bulant (2006), Červený (2001) and references there. The amplitude contribution of the two coupled shear waves is calculated by integrating two coupled ordinary differential equations along a reference ray in a reference isotropic medium, see Kravtsov & Orlov (1980), Pšenčík (1998), Pšenčík & Delinger (2001). The principal goal of this project is to generalize the QI approximation, which works, at present, in smooth media without interfaces, to layered media. This requires derivation of the transformation relations at interfaces for the two coupled differential equations, their coding and testing the resulting code by comparing its results with results of available codes based on more accurate methods like, e.g., Chebyshev spectral method, see Tessmer (1995).
References:
Červený,V., 2001. Seismic Ray Theory: Cambridge University Press, Cambridge.
Coates,R.T. & Chapman,C.H., 1990. Quasishear wave coupling in weakly anisotropic 3D media, Geophys.J.Int., 103, 301320.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Klimeš,L. & Bulant,P., 2006. Errors due to the anisotropiccommonray approximation of the coupling ray theory. Stud.Geophys.Geod., 50, 463477.
Kravtsov, Yu.A. & Orlov,Yu.I., 1980. Geometrical optics of inhomogeneous media, Nauka, Moscow (in Russian).
Pšenčík,I., 1998. Green's functions for inhomogeneous weakly anisotropic media. Geophys.J. Int., 135, 279288.
Pšenčík,I. & Dellinger.J., 2001. Quasishear waves in inhomogeneous weakly anisotropic media by the quasiisotropic approach: a model study. Geophysics, 66, 308319.
Tessmer,E., 1995. 3D seismic modelling of general material anisotropy in the presence of the free surface by a Chebyshev spectral method. Geophys.J.Int., 121, 557575.
Coding and testing the firstorder ray tracing
[PhD. project]
Supervisor: RNDr. Ivan Pšenčík, CSc.
Pšenčík & Farra (2005) proposed an approximate Pwave ray tracing for smooth, inhomogeneous, weakly anisotropic media. It is of the first order with respect to deviations of anisotropy from isotropy. In contrast to standard ray tracing, which depends on 21 elastic parameters, the approximate Pwave ray tracing depends on only 15 weakanisotropy parameters (nondimensional parameters obtained by normalization of differences of elastic parameters or their combinations and squares of velocity of a reference isotropic medium). The equations are considerably simpler than the exact raytracing equations. For highersymmetry anisotropic media the approximate ray tracing equations differ only slightly from those for isotropic media. The first goal is to reformulate the raytracing equations of Pšenčík & Farra (2005) specified for transversely isotropic (TI) and orthorhombic (OR) media according to Iversen & Pšenčík (2006) so that the resulting ray tracer allows consideration of TI and/or OR media with varying orientation of symmetry axes. The next step of this project is to substitute the standard raytracing equations in the present version of the program package ANRAY (Gajewski & Pšenčík, 1990) by the newly developed Pwave raytracing equations. The resulting code should be tested on accuracy and speed with the standard version of ANRAY. The final, but not necessary, step is the corresponding modification of the dynamicraytracing equations (Červený, 2001) and generalization of the procedure for layered media.
References:
Červený,V., 2001. Seismic Ray Theory: Cambridge University Press, Cambridge.
Gajewski,D. & Pšenčík,I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures. J.geophys.Res., 95, 1130111315.
Iversen,E. & Pšenčík,I., 2006. Ray tracing for continuously rotated local coordinates belonging to a specified anisotropy. In: Seismic Waves in Complex 3D Structures, Report 16, pp.4776, Dept.of Geophysics, Charles University Prague, online at http://sw3d.mff.cuni.cz.
Pšenčík,I., Farra,V., 2005. Firstorder ray tracing for qP waves in inhomogeneous weakly anisotropic media. Geophysics, 70, D65D75.
Thermal regime of soil and bedrock in relation to the surface air temperature and other meteorological variables
[MSc. project]
Supervisor: RNDr.Jan Šafanda, CSc.
Description of the problem
One of the new methods of the past climate reconstruction is based on analysis of a transient component of temperature  depth profiles measured in boreholes. It provides information about longterm changes of the ground surface temperature. For the climatic interpretation of these results it is necessary to know a relationship between the ground surface temperature and the surface air temperature. To explore the relationship, the Department of Geothermics of the Geophysical Institute has established a “borehole climate” station, which has been monitoring temperature in a 40 m deep borehole, in soil and in the air together with some other meteorological variables since 1994.
Aim of the thesis
Comparison of annual temperature signals in air, soil and bedrock observed at the station.
Analysis of sources of a difference between mean annual temperatures of air and soil and sources of an interannual variability of this difference.
Thermal regime of soil and bedrock in relation to the surface air temperature and other meteorological variables
[PhD. project]
Supervisor: RNDr.Jan Šafanda, CSc.
Description of the problem
One of the new methods of the past climate reconstruction is based on analysis of a transient component of temperature  depth profiles measured in boreholes. It provides information about longterm changes of the ground surface temperature. For the climatic interpretation of these results it is necessary to know a relationship between the ground surface temperature and the surface air temperature. To explore the relationship, the Department of Geothermics of the Geophysical Institute has established a “borehole climate” station, which has been monitoring temperature in a 40 m deep borehole, in soil and in the air together with some other meteorological variables since 1994.
Aim of the thesis
Running theses
Name of the student 
Beginning of study 
University 
Supervisor/consultant 
Title  
Mgr. Radka Matějková 
2008 
Geofyzika F7/MFF UK 
RNDr. Aleš Špičák, CSc. 
Doctoral thesis: Interpretation of tectonic structure and evolution of plate margins by an analysis of earthquake foci distribution and mechanisms. 

Mgr. Petr Brož 
2011 
Geologie se zaměřeními/PřF UK 

Doctoral thesis: Pyroclastic cones on Mars: analogue experiments and comparison with terrestrial analogues. 

Mgr. Petr Dědeček 
2002 
Aplikovaná geologie/PřF UK 
RNDr. Jan Šafanda, CSc. 
Doctoral thesis: Factors determining temperature of soils and heat transfer from the ground surface to the rock basement. 

Mgr. Hana Karousová 
2008 
Geofyzika/MFF UK 
RNDr. Jaroslava Plomerová, DrSc. 
Doctoral thesis: Seismic tomography of the upper mantle beneath the Bohemian Massif. 

Mgr. Hana Davídkovová 
2007 
Geologie se zaměřeními PřF UK 
RNDr. Josef Bochníček, CSc. 
Doctoral thesis: Vliv sluneční aktivity, geomagnetické aktivity a povětrnostních změn na lidský organizmus. 

Mgr. Helena Munzarová 
2011 
Geofyzika F7/MFF UK 
RNDr. Jaroslava Plomerová, DrSc. 
Doctoral thesis: Anizotropní tomografie svrchního pláště pod Evropou. 

Ing. Jana Doubravová 
2011 
Geofyzika/MFF UK 
Ing. Josef Horálek, CSc. 
Doctoral thesis: Automated processing of seismic observational data from the local network WEBNET, with application on the West Bohemia earthquake swarm of 2011. 

Mgr. Jan Michálek 
2006 
Geofyzika/MFF UK 
RNDr. Tomáš Fischer, PhD. 
Doctoral thesis: Exact automatic location and determination of source parameters of microearthquakes. 

Mgr. Hana Čermáková 
2009 
Geofyzika F7/MFF UK 
Ing. Josef Horálek, CSc. 
Doctoral thesis: Earthquake swarms in diverse tectonic enviroments (triggering mechanism and driving forces). 

Mgr. Vojtěch Lávička 
2012 
Aplikovaná geologie/PřF UK 
RNDr. Václav Vavryčuk DrSc. 
Doctoral thesis: Modelling of seismic waves and sources in realistic structures. 
Name of the student 
Study period 
University 
Supervisor/consultant 
Title  
Bc. A. Zárubová 
20102013 
PřF UK 
RNDr. Eduard Petrovský, CSc. 
Bachelor's thesis: Měření magnetických vlastností environmentálních vzorků. 

Ing. Šárka Dlouhá, PhD. 
20082013 
Využití a ochrana přírodních zdrojů/ČZU 
prof. Dr. Ing. Luboš Borůvka / RNDr. Eduard Petrovský, CSc. 
Doctoral thesis: Study of risk elements distribution in alluvial soils using magnetic methods. 

Mgr. Martin Staněk PhD. 
20082013 
Geol. se zaměřeními/PřF UK 
RNDr. Stanislav Ulrich, PhD. 
Doctoral thesis: Structural and petrophysical characterisation of granites intended for nuclear waste repository site. 

Mgr. Václav Kuna 
20112013 
Aplik. geologie/PřF UK 
RNDr. Aleš Špičák CSc. 
Master thesis: Teleseismic earthquake occurrence and subductioninduced volcanic activity along island arcs. 

Mgr. Magdaléna Hrnková 
20112013 
Geologie/PřF UK 
Mgr. Jiří Laurin, PhD. 
Master thesis: The record of sealevel changes, water circulation and sediment dispersal in Upper Turonian hemipelagic stata of the Bohemian Cretaceous Basin. 

Mgr. Roland Nádaskay 
20112013 
Geologie/PřF UK 
RNDr. David Uličný, CSc. 
Master thesis: Depositional regime and genetic stratigraphy of Coniacian clastics in the Bohemian Cretaceous Basin: a response to changing tectonic regime during the Mesozoic. 

Mgr. Vladimír Kusbach, PhD. 
20072011 
PřF UK 
RNDr. Stanislav Ulrich, PhD. 
Doctoral thesis: Strain coupling versus decoupling of mantle and crust during orogenesis. 

Mgr. Matěj Machek, PhD. 
20032011 
PřF UK 
RNDr. Stanislav Ulrich, PhD. 
Doctoral thesis: Evolution of microporosity and permeability of rocks with different microstructure and mineral composition. 

Mgr. Petr Brož 
20082010 
Geologie/PřF UK 
Mgr. Prokop Závada, PhD. 
Master thesis: Plains volcanism in Tharsis region on Mars: Ages and rheology of eruption products. 

Mgr. Petra Adamová, PhD. 
20062013 
Geofyzika/MFF UK 
RNDr. Jan Šílený, CSc. 
Doctoral thesis: Models of eathquake focus and their tectonic interpretations. 