Mathematical Methods in Geophysics (1)




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Master Study

Branch of Study: 4.1.1 Physics

Study programme: Geophysics

Guarantor: prof. RNDr. Peter Moczo, DrSc.

Obligatory Subjects


2-FGF-1012-FGF-1032-FGF-1042-FGF-1052-FGF-1082-FGF-1022-FGF-1102-FGF-1112-FGF-1122-FGF-1062-FMK-1082-FGF-9102-FGF-1072-FGF-2102-FGF-2022-FGF-2032-FGF-2042-FGF-2052-FGF-9112-FGF-2072-FGF-2082-FGF-2092-FGF-2062-FGF-9122-FGF-1312-FGF-1322-FGF-1332-FGF-1342-FGF-1352-FGF-1372-FGF-1382-FGF-1392-FGF-2322-FGF-2332-FGF-2342-FGF-2352-FGF-2362-FGF-2372-FGF-2382-FGF-2402-FGF-2392-FGF-1512-FGF-1532-FGF-1542-FGF-1552-FGF-1562-FGF-1572-FGF-1592-FGF-1522-FGF-1582-FGF-2312-FGF-9502-FGF-9512-FGF-9522-FGF-990

Mathematical Methods in Geophysics (1) - Guba P., Kováčová Mo. Physics of the Earth's Interior - Moczo P., Ševčík S. Physical Fields and Processes in Close Surroundings of the Earth - Ondrášková A., Ševčík S. Measurement and Processing of Geophysical Data (1) - Kostecký P., Kristeková M. Numerical Methods (1) - Kristek J., Gera Ma. Mathematical Methods in Geophysics (2) - Kováčová Mo., Guba P. Seismic Waves and Physics of Earthquakes (1) - Moczo P., Kristek J. Magnetic Field of the Earth - Ondrášková A. The Shape and Gravity Field of the Earth - Brimich L. Measurement and Processing of Geophysical Data (2) - Kristeková M., Kostecký P. Numerical Methods (2) - Gera Ma., Kristek J. Diploma Thesis (1) - Moczo P. Measurement and Processing of Geophysical Data (3) - Kristeková M., Kostecký P. Seismic Waves and Physics of Earthquakes (2) - Moczo P., Kristek J. Ionospheric and Magnetospheric Physics - Ondrášková A. Geodynamics - Boďa J. Inverse Problems in Geophysics - Gális M. Geophysical Diploma Thesis Seminar (1) - Moczo P., Ševčík S. Diploma Thesis (2) - Moczo P. Structure of the Earth - Ševčík S., Brestenský J. Physics of Planetary Bodies - Brestenský J. Regional Geophysical Model - Bielik M. Geophysical Diploma Thesis Seminar (2) - Moczo P., Ševčík S. Diploma Thesis (3) - Moczo P. Signal Analysis (1) - Kováčová Mo. Asymptotic Methods - Brestenský J. Computer Methods - Gális M. Magnetohydrodynamics - Ševčík S. Numerical Simulations of the Seismic Wavefields (1) - Kristek J. Seminar on Geomagnetism - Ševčík S., Ondrášková A., Brestenský J. Seminar on Seismology - Moczo P., Kristek J. Contribution to the Students' Science Conference (1) - Moczo P. Physics of the Earthquake Source - Moczo P. Geophysical Hydrodynamics and Convection in the Mantle - Brestenský J., Boďa J. Schumann Resonances - Kostecký P. Numerical Methods in Geodynamics - Kostecký P. Numerical Simulations of the Seismic Wavefields (2) - Moczo P. Electromagnetic Sounding of the Earth - Ševčík S. Temperature and Heat Flow Inside the Earth - Gális M. Introduction to Nuclear Geophysics - Masarik J. Contribution to the Students' Science Conference (2) - Moczo P. Hydrodynamics (1) - Brestenský J. Programming in Fortran and C - Gális M. Numerical Methods in Fluid Mechanics - Ševčík S. Fractals and Chaos in Geophysics - Guba P. Strong-Motion Seismology and Site Effects - Moczo P., Kristek J. Physics of the Middle and Upper Atmosphere - Ondrášková A. Electromagnetic Waves in Cavity Resonator - Ondrášková A., Kostecký P. Hydrodynamics (2) - Guba P. Earthquake Hazard Analysis - Labák P. (KAFZM) Signal Analysis (2) - Kristeková M. Physics of the Earth's Interior - KAFZM Physical Fields and Processes in the Close Cosmic Space of Earth - KAFZM Theoretical Methods in Geophysics - KAFZM Diploma Thesis Defense - KAFZM




1/W1/W1/W1/W1/W1/S1/S1/S1/S1/S1/S1/S1/S2/W2/W2/W2/W2/W2/W2/S2/S2/S2/S2/S1/W1/W1/W1/S1/S1/S1/S1/S2/W2/W2/W2/W2/W2/S2/S2/S2/S1/W1/W1/S1/S1/S1/S1/S1/S2/W2/W

L3,P1L4L4L2,P1L2,P1L2,P1L2,P1L2,P1L2L2,P1L2,P1D2X2wL2L2L2L2S2D4L3L1L1S2D10L2,P1L2L1,P1L2L2S2S2LL2L2L2L2L2L2L2L2LL2L1,P1L2L2L2L2L2L2L2L2

4553433323412222222311210422223322322322233333333333

30/7020/8020/8050/5040/6030/7070/3020/8020/8030/7040/60100/0100/0100/010/9030/70100/0100/0100/020/8050/5030/70100/0100/0100/0100/0100/030/70100/0100/0100/0100/0100/030/7040/60100/050/5020/8020/80100/0100/020/80100/0100/0100/050/5020/80100/020/8070/3070/30

Obligatory-Optional Subjects obligatory choice: 20 credits


Electives


ssState Examination Subjects


2-FGF-132 Asymptotic Methods

doc. RNDr. Jozef Brestenský, CSc.

Form and extent of the course: lecture - L2

Evaluation during the course: 100 % test, solving problems

Concluding evaluation: 0 %

2 credits; obligatory-optional in 1/W

Subject aim: To explain fundamentals of asymptotic methods and to develop the abilities of students to make estimations and approximations in solving theoretical and practical problems of physics.

Brief curriculum of the subject:

Approximations on the basis of asymptotic methods are irreplaceably important in recent period of prevailing numerical solutions. Contrary to numerics they give more wealthy information on physical nature of the solved problem.

The introduction to asymptotic methods. The origin of asymptotic expansions. The symbols ~, O, o. The operations with asymptotic and order relations (…, integrations, derivations…). Asymptotic solution of transcendental equations. Asymptotic estimations of integrals. Watson lemma, Riemann-Lebesque lemma. Asymptotic expansions on the basis of Laplace, stationary phase and saddle points methods. Solving of non-linear problems. The methods – straightforward , Poincare-Lindstedt, multiple scale method. The problems of boundary layers. Solvability conditions. Weakly non-linear analysis. Examples of asymptotic methods’ applications in physics, mainly in hydrodynamics.

Literature:

A.H.Nayfeh: Introduction to Perturbation Techniques, John Wiley&Sons NY, 1981

F.W.J.Olver: Introduction toAsymptotics andSpecial Functions, AcademicPressNY,1974;

A.H. Nayfeh, Perturbation Methods, John Wiley & Sons New York, 1973;

E. J. Hinch, Perturbation Methods, Cambridge University Press, New York, 1991

J. A. Murdock, Perturbations - Theory and Methods, John Wiley & Sons, New York, 1991

Language in which the subject is taught: Slovak

2-FGF-133 Computer Methods

Mgr. Martin Gális, PhD.

Form and extent of the course: lecture, practicals - L1,P1

Evaluation during the course: 100 % preparation of the codes, their testing and debugging, test

Concluding evaluation: 0 %

2 credits; obligatory-optional in 1/W

Subject aim: To provide basics of visualization methods, to explain how to use selected software tools for visualization and software tools for symbolic calculations.

Brief curriculum of the subject:

2D visualization with Mathematica, gnuplot. 3D visualization with Mathematica. Interpolation and approximation methods of 2D, 3D data (Inverse distance, Kriging, minimum curvature). Symbolic calculations with Mathematica.

Basic calculations, internal functions, creating own modules, using external modules in Mathematica. Technique for using external program and procedures in Mathematica. Mathematica and Linux operating system.

Literature:

web manual pages of GNU sw,

Show, N.T., Jason, T.: Applied Mathematica, 1994

Language in which the subject is taught: Slovak

2-FGF-139 Contribution to the Students' Science Conference (1)

prof. RNDr. Peter Moczo, DrSc.

Form and extent of the course: lecture - L

Evaluation during the course: 100 % student’s active participation in the conference

Concluding evaluation: 0 %

2 credits; obligatory-optional in 1/S

Subject aim: Supervise student’s work on a selected topic and preparation of the conference presentation.

Brief curriculum of the subject:

Intensive student’s study of selected literature and work on the selected topic. Logical structuring of the elaborated material and achieved results. Analysis, interpretation and evaluation of the achieved results. Comparison of the achieved results with the goals. Formulation of the conclusions based on the achieved results.

The final preparation of the conference contribution - structuring and writing the text, preparation of figures, tables, appendices, and list of references. Editing and checking the text, language check.

Preparation of the conference presentation.

Literature:

Literature recommended by the supervisor.

Language in which the subject is taught: Slovak

2-FGF-239 Contribution to the Students' Science Conference (2)

prof. RNDr. Peter Moczo, DrSc.

Form and extent of the course: lecture - L

Evaluation during the course: 100 % student’s active participation in the conference

Concluding evaluation: 0 %

3 credits; obligatory-optional in 2/S

Subject aim: Supervise student’s work on a selected topic and preparation of the conference presentation

Brief curriculum of the subject:

Intensive student’s study of selected literature and work on the selected topic. Logical structuring of the elaborated material and achieved results. Analysis, interpretation and evaluation of the achieved results. Comparison of the achieved results with the goals. Formulation of the conclusions based on the achieved results.

The final preparation of the conference contribution - structuring and writing the text, preparation of figures, tables, appendices, and list of references. Editing and checking the text, language check.

Preparation of the conference presentation.

Literature:

Literature recommended by the supervisor.

Language in which the subject is taught: Slovak

2-FGF-910 Diploma Thesis (1)

prof. RNDr. Peter Moczo, DrSc.

Form and extent of the course: diploma thesis - D2

Evaluation during the course: 100 % activity of student, student’s response to tasks

Concluding evaluation: 0 %

1 credit; obligatory in 1/S

Subject aim: Theoretical preparation for solving tasks of diploma thesis. Studying relevant literature.

Brief curriculum of the subject:

Introduction to the topic of diploma thesis. Study of journal articles and monographs. Formulation of detailed tasks and goals of the diploma thesis. Selection of methods. Outline of the structure of the diploma thesis.

Literature:

Literature recommended by the supervisor and lecturer.

Language in which the subject is taught: Slovak

2-FGF-911 Diploma Thesis (2)

prof. RNDr. Peter Moczo, DrSc.

Form and extent of the course: diploma thesis - D4

Evaluation during the course: 100 % activity of student, student’s progress in work

Concluding evaluation: 0 %

2 credits; obligatory in 2/W

Subject aim: Supervise student’s reading and studying selected journal articles, supervise student’s work on the diploma thesis tasks.

Brief curriculum of the subject:

Reading and studying selected journal articles relevant to the diploma thesis.

Elaboration of the specified tasks.

Reporting the achieved progress.

Discussions.

Refining the tasks and goals.

Literature:

Literature recommended by the supervisor and lecturer.

Language in which the subject is taught: Slovak

2-FGF-912 Diploma Thesis (3)

prof. RNDr. Peter Moczo, DrSc.

Form and extent of the course: diploma thesis - D10

Evaluation during the course: 100 % student’s activity, progress in work, and achieved results

Concluding evaluation: 0 %

10 credits; obligatory in 2/S

Subject aim: Supervise student’s work and finalization of the diploma thesis.

Brief curriculum of the subject:

Intensive student’s work. Logical structuring of the elaborated material and achieved results. Analysis, interpretation and evaluation of the achieved results. Comparison of the achieved results with the goals of the diploma thesis. Formulation of the conclusions based on the achieved results.

The final preparation of the diploma thesis – structuring and writing the text, preparation of figures, tables, appendices, and list of references. Editing and checking the text, language check.

Preparation of the presentation of the diploma thesis. Preparation of the response to reviewer’s comments.

Literature:

Literature recommended by the supervisor and lecturer.

Language in which the subject is taught: Slovak

2-FGF-158 Earthquake Hazard Analysis

RNDr. Peter Labák, PhD. (KAFZM)

Form and extent of the course: lecture - L2

Evaluation during the course: 70 % test

Concluding evaluation: 30 % examination

3 credits; elective in 2/W (suspended)

Subject aim: Explain mathematical and physical models of time-space occurrence of earthquakes, seismological database, seismotectonic model, and methods of computation of seismic hazard characteristics.

Brief curriculum of the subject:

Earthquake as a random process, time space regime of earthquake occurrence and magnitude-frequency relationships, Poissonian and non-Poissonian processess, seismotectonic model, near and far regions, locality, attenuation relationships, characteristics of seismic hazard, deterministic and probabilistic computations, aleatoric and epictemic uncertainties, logic tree, de-aggregation of seismic hazard computation.

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