MAGNETOTELLURIC AND DEEP GEOMAGNETIC SOUNDING
(30 hours)
Josef Pek
- Aim of the course
The course aims at explaining the physical principles of geoelectric
induction methods used in regional and global geoelectrical investigations.
- Introduction
Geoelectricity as a geophysical discipline, its subject.
Classification of geoelectrical methods.
- Electrical conductivity of the earth's material
Electrical conductivity of minerals, rocks and fluids. Principal factors
affecting the conductivity of the earth's materials
(temperature, pressure, saturation with fluids -- Archie's law,
structure, texture, time factor). Other electromagnetic parameters
-- electric permitivity, magnetic permeability, electrochemical
parameters.
- Primary sources of the magnetotelluric field
Frequency range of geoelectrical induction methods, sources
of the primary electromagnetic field in radio-, audio-
and helio-frequency bands, their structure in time and space.
- Theory of linear relationships in the magnetotelluric field
General physical principles of the magnetotelluric and deep
geomagnetic soundings. Maxwell's equations as linear differential relationships
in the magnetotelluric field, their general solution in terms
of Green's tensors. Schematic models of primary magnetotelluric
source fields -- excitation operators, characteristic field vectors.
Linear algebraic relationships between
the components of the magnetotelluric field -- fundamental characteristic
field operators, magnetotelluric operators and matrices (impedance,
admittance, telluric, magnetic), their relation to the source fields
and to the geoelectrical structure.
- Magnetotelluric field in horizontally homogeneous structures
-- Cagniard-Tikhonov model
Direct and inverse magnetotelluric problem. Plain wave impeding on the
layered earth's surface. Cagniard-Tikhonov fundamental model of the
magnetotelluric problem, impedance of a geoelectrical cross-section,
apparent resistivity and magnetotelluric phase. Long period asymptotics
of magnetotelluric curves. Analytical properties of the magnetotelluric impedances.
Techniques for solving 1-D magnetotelluric inverse problem.
- Electromagnetic induction in a layered Earth assuming
a non-homogeneous source field
Maxwell's equations in spatial-frequency domain. Impedance ratio,
magnetotelluric and magnetic spectral impedances of a layered structure.
Limitations of Cagniard-Tikhonov model in case of an inhomogeneous
source field. Generalization to spherical conductors --
global electromagnetic soundings into the mantle depths.
- Magnetotelluric field in horizontally inhomogeneous structures
Classification of lateral inhomogeneities (local, regional, 2-D, 3-D).
Modelling of electromagnetic fields in horizontally inhomogeneous
structures (laboratory models, numerical models).
Approximate long period asymptotic models, unimodal and bimodal
thin sheet induction. Distortions of the magnetotelluric curves
due to lateral inhomogeneities, their identification and elimination.
Deep geomagnetic soundings -- geomagnetic transfer functions and induction arrows.
- Interpretation of magnetotelluric and deep geomagnetic
soundings, geoelectrical models
Practical aspects of magnetotelluric and deep geomagnetic soundings
(instrumentation, data acquisition, data processing, interpretation).
Geoelectrical projects. Electrical anomalies within the Earth,
their explanation in terms of thermodynamic, structural and tectonic
conditions. Estimates of the electrical conductivity of the lower mantle
and the earth's core.
MODERN INSTRUMENTAL SEISMOLOGY
(30 hours)
Axel Plesinger
- Introduction
frequency and amplitude ranges of seismic signals at
teleseismic, regional, and local distances; generalized Earth noise models;
optimization of seismological observations; the concept of very-broad-band
seismometry.
- Mathematical fundamentals (review)
Laplace transform, concept of zeros and
poles; transfer functions, steady-state and transient responses; Hilbert
transform; bilinear transform; z-transform; frequency-domain vs. time-domain
digital filtering; IIR and FIR filters; causal and acausal filters.
- Instruments and data acquisition systems for digital observations in global,
regional, and local scales
standard instruments; conventional responses;
force-balance seismometers; gain ranging and high resolution (sigma-delta)
analog-to-digital converters; modern computer-aided calibration methods;
stabilized inversion of calibration responses.
- Digital seismological data formats
classes of formats; conventional formats
for data exchange and archiving; calibration headers and important relations
among different conventions.
- Routine processing of digital seismograms
basic editing and resampling;
simulation of standard and/or user defined seismograms; recovery of true
ground motion; component rotation and rectilinear motion detection; wavegroup
identification; determination of onset times and amplitudes; program
systems for interactive seismological analyses (review).
- Global digital seismological networks. European regional networks and arrays.
Principles of microearthquake networks.
RAY PERTURBATION THEORY FOR ANISOTROPIC MEDIA
(30 hours)
Ivan Psencik
- Basics of ray theory for anisotropic media.
- Perturbation theory.
Perturbation theory for eigenvalues and eigenvectors of the Christoffel
matrix: nondegenerate and degenerate cases.
- Perturbation theory for elastodynamic equation.
- Specification for hexagonal media.
Perturbations in terms of elastic parameters. Perturbations
in terms of Thomsen's parameters.
- Applications of perturbation theory.
Travel time computations, slight absorption computations, ray paths
computations, ray amplitude computations, use of perturbations
in R/T problems, perturbations of radiation patterns,
kinematic inversion, use of perturbation theory in problems
of coupling of shear waves.
INDUCED SEISMICITY
(30 hours)
Vladimir Rudajev
- Natural and induced seismicity
General and individual features of both kinds of seismic phenomena:
reasons and conditions of tectonic and induced events origin,
fundamental characteristics of natural and induced seismic sources
(focal mechanism, radiated seismic waves, range of seismic energies),
seismic active zones in Czech Republic.
- Multidimensional seismic space, part 1
Geometric coordinates -- location of near foci in media.
Focal time and distribution of events in time.
Energy of events.
- Multidimensional seismic space, part 2
Seismic moment tensor. Stress drop.
- Up-to date known mechanics of induced events
Field investigation of mining induced events.
Laboratory investigation of acoustic emission.
- Seismicity of source zones
Seismic energy flow. Energy -- frequency distribution.
Laboratory research.
- Discrete time series -- results of field and
laboratory research
N, E = f(t) -- description of the fundamental time series.
Stationarity (steady-state, trends, harmonic components).
Nonstationarity (clustering, aftershock sequences).
- The interoccurrence structure of time series
Autocorrelation functions (dependence of the energy low level).
Nonrandomness of occurrence as a tool for prediction of total
fracturing and extremal rockbursts.
- Time series exploration (seismic data)
Wiener extrapolation (classic, mowing, with memory).
Linear regression, Bayes conditional probability.
- Time series extrapolation using the complex geo-science data
- Application of results in mining practice and earthquake
research
APPLIED GEOPHYSICS
(60 hours)
Jiri Skopec
- Introduction
Principles of applied geophysics, interrelation between applied geophysics
and geophysics, geology and some industrial branches. Review of some rock types.
- Gravimetric methods
Physical and geological principles of gravimetric methods, gravity
anomalies, rock densities, gravity observations, data processing
and interpretation, use of gravimetric methods.
- Magnetometric methods
Magnetic properties of rocks and their determination, direct problem
of magnetometry, instruments for magnetic survey, field measurements
and data processing, interpretation in magnetometry, use of magnetometry.
- Radiometric methods and methods of nuclear geophysics
Physical basis of nuclear methods, measurements of nuclear radiation,
radiometric exploration methods, use of radiometric methods
in prospecting and exploration, methods of nuclear physics.
- Geothermal methods
Near-surface thermal field, instruments and methods of geothermal
measurements, application of geothermic method.
- Geoelectrical methods
Electric properties of rocks, fundamental division of geoelectrical
methods, electrochemical methods, D.\ C.\ methods, potential methods,
electromagnetic methods, use of geoelectrical methods.
- Seismic methods
Elastic properties of rocks, seismic travel-time curves,
reflection and refraction methods, seismic instruments and methods
of field prospecting, seismic data processing, use of seismic
methods in oil prospection and in solving near-surface problems.
- Geophysical well-logging
Logging equipment, electrical and nuclear logging methods,
other logging methods, methods for geometric parameters determination,
borehole fluids study, rational
complex of logging methods.
- Complex using of geophysical methods in solving geological
problems with practical examples.
SELECTED PARTS FROM PROGRAMMING
(45 hours)
Ludvik Urban
- Basic introduction to personal computers
PC inside. Installation and setup.
Starting and finishing work.
Memories, graphic adapters, floppy disks.
Harddisks, logical and physical partitions.
Printers, plotters, scanners.
- Operation systems for PCs
DOS. Basic commands and programs.
Formatting floppy disks and harddisks.
Work with directory tree.
Managing files.
System testing and information.
- Basic software tools
File managers. Recovery and backup.
Editors. Editing large files.
Interpreters and compilators.
Computer languages.
Graphic editors. Scientific packages.
Databases. Spreadsheets. Antivirus programs.
- FORTRAN
Description and programming. The simplest fortran program.
Input and output data management.
Loops, switches, jumps. Mathematical functions.
Procedures and functions.
- TURBO PASCAL
Description and programming. The simplest pascal program.
Modules and units. Variables and types.
Input and output data management.
Loops, switches, jumps. Procedures and functions.
Units Crt, Dos, Graph.
Debugging program, watches. Linking external units.
SEMINAR ON COMPUTER GRAPHICS
(30 hours)
Ludvik Urban
(Basic skills in TURBO PASCAL programming are necessary.)
- Graphic adapters for personal computers
Description and testing.
Graphic drivers and modes.
CGA, EGA, VGA, SVGA.
- TURBO PASCAL
Basic graphic procedures and functions.
Basic algorithms.
Initialization of graphic mode.
Plotting dots, lines, rectangles, rings. Filling objects.
BIOS video services. Interrupts and ports.
- Colors a palettes
16colors mode. EGA bitplanes.
256colors mode. VGA and SVGA video memory mapping.
Color and palette editors.
- Mouse
Getting information on mouse cursor position.
Getting mouse buttons status.
Programming. Simple mouse driver.
- Graphic drivers
Simple graphic driver.
- Speed of graphic operations. Fast access to video memory.
- Simple graphic interface
Drawing objects. Redrawing and moving objects around screen.
Work with videopages.
Introduction to animation.
WORLDWIDE COMPUTER NETWORK
(30 hours)
Ludvik Urban
(Devoted for network beginners.)
Rules for computer networks.
Short description of BITNET. Short description of INTERNET.
Basic introduction to UNIX.
Login and logout. Terminal specifications. Users area.
Basic commands: pwd, ls, mkdir, rmdir, cp, mv.
Editors: vi and Pico.
Manuals and helps.
Electronic mail. ELM. PINE.
Pine: sending mail, receiving, replying, archiving mail.
Postponed mail and canceled mail.
Address books.
E-mail lists. Listprocessors and listservers.
Netnews and netnews servers.
Network services.
Telnet. Basic commands. Telnet client for DOS.
FTP.
Basic commands. Receiving files, sending files.
Transfer modes. Commands prompt, hash.
FTP to/from public anonymous servers.
Archie. Connecting to archie servers. BAsic commands.
Trickle.
Gopher.
Gopher servers and services. Veronica.
Gopher clients.
Communication with other users. Talk.
Getting information on remote hosts.
Multiuser communication.
Finger. Whois, UDS. Netfind. Ping.
WWW. Lynx and Mosaic. Doslynx client. Harvest.
GENERATION OF SEISMIC WAVES BY EARTHQUAKE SOURCES
(30 hours)
Jiri Zahradnik
- Motivations and objectives
Tectonic earthquakes. Earthquakes and plate motions. Faults and
rupture processes. Earthquake preparation and prediction. Strong
ground motions.
- Continuum mechanics
Prestressed media. Displacements, strain, stresses. Equilibrium
equation. Equation of motion. Displacement discontinuity at the
fault surface. Strains, stresses and tractions at the fault
surface.
- Earthquake-generated displacement fields
Green's tensor. Integral representation of the displacement field
(representation theorem). Body-force equivalents of ruptures.
Scalar seismic moment. Moment tensor. Moment-tensor eigenvalues
and eigenvectors. Displacement field for tangential slip.
Displacement field for non-tangential slip. Higher-order moment
tensors.
- Far-field source time function
First-order (Fraunhofer's) approximation. Zero-order
approximation; directivity neglected. Rectangular fault model.
Haskell's model. Surface and time integrations; a comparison.
Circular fault models and generalizations. Low-frequency band and
seismic moment. High frequency band and stopping phases.
Intermediate-frequency band and source dimension.
- Source-dimension determination
Corner frequency. Determination of the source dimension in the
frequency and time domain.
- Moment-tensor determination
First-onset polarities. Fault-plane solutions. Normal faults.
Reverse faults. Strike-slip faults. P-T axes. Composite
solutions. Scalar seismic moment. Moment determination in the
frequency and time domain. Moment-tensor inversion.
Moment-tensor interpretation. Moment time functions.
- Stress-drop determination
Static stress drop. Dynamic stress drop. Stress drop and seismic
energy. Scaling laws.
- Energy determination
Energy flux. Strain energy. Prestressed medium with fault.
Mechanical and seismic energy. Earthquake energy. Seismic energy
and magnitude. Integration at the focal sphere. Energy
determination from a single station. Neglecting or considering
directivity effects. Seismic energy and moment tensor.
NUMERICAL METHODS
(45 hours)
Jiri Zahradnik
- Typical problems in geophysical data processing.
Typical problems
in geophysical modelling. Computer requirements. Visualization.
Verification.
- Interpolation and approximation
Review of different approaches. The Lagrange interpolation. The
Newton interpolation. Spectral interpolation by FFT.
Interpolation splines. Least-square approximation. Smoothing
(running average) formulas. Approximation splines in 1D and 2D.
- Integration
The Newton-Cotes integration. Simple and composite formulas.
Error estimation. The Richardson extrapolation. The Romberg
integration. The Gauss-Legendre integration. Other Gauss'
methods. Spectral integration by FFT.
- Differentiation
Differentiation of the Newton polynomial. Error estimation for
grid points. First derivative by
1st-, 2nd, and 4th-order formulas. Taylor-expansion methods.
Second derivative by 2nd and 4th-order formulas. Mixed second
derivatives. Spectral differentiation by FFT.
- Ordinary differential equations
Taylor-expansion methods. The Runge-Kutta methods of 2nd and 4th
order. Error estimation. Predictor-corrector methods. Error
estimation.
- Partial differential equations
Classification of finite-difference methods. Regular and
irregular grids. Explicit and implicit methods. Constant and
variable (discontinuous) coefficients. Second spatial derivatives
with non-constant coefficients (local approximations and several
approximations with geometrical averages). Consistency,
convergency and stability. Stability conditions. 1D and 2D
problems. Smoothed source terms. Alternating-direction method.
The higher-order schemes. Principles of the multigrid methods.
- Elastodynamic equations
Numerical dispersion and anisotropy. Dispersion analysis.
Comparing explicit and implicit schemes. Homogeneous and
heterogeneous schemes. The 2nd- and 4th-order methods. Spectral
methods. The Fourier-Chebyshev method. Schemes consistent with
the traction-continuity condition. Free-surface approximations.
The vacuum formalism. The body-force sources. The incident plane
waves. The Alterman-Karal excitation. The integration-approach
schemes. The non-reflecting conditions.
NUMERICAL PREDICTION OF THE EARTHQUAKE GROUND MOTIONS
(30 hours)
Jiri Zahradnik
- Strong ground motions.
Damaging effects of earthquakes. Source, path and site effects.
Instrumental effects. Soil-structure interaction. Ground motion
records. Peak values. Root-mean-square values. Fourier spectra.
Response spectra. Husid plots. Duration. Spectral intensity.
Differential motions. Examples from world-wide data bases. Reach
of data by Internet. Empirical relations between the strong
motions, earthquake size, distance and soil type.
- Basic elements of wave propagation.
Green's tensor. Near- and far-field approximations. Body and
surface waves. Attenuation and material dispersion. Q-factor.
Matrix method for plane waves in layered media.
Discrete-wavenumber method for point source and finite-extent
sources in layered media. Finite-difference method for 2-D media.
Hybrid methods.
- Basic elements of source physics.
Magnitude. Moment. Energy. Stress drop. Fault length. Focal
mechanism. Simple dynamic models. Kinematic models. Source
directivity. Scaling relations (moment-length-stress drop).
'Fmax' phenomenon. Source inversions. Rupture history at real
faults. Deterministic and stochastic features of strong motions.
- Artificial accelerograms.
Purely stochastic methods. White noise and its modulation. Random
time series. Combined deterministic-stochastic methods. Amplitude
spectra from deterministic source models. Random phases.
Amplitude spectra from empirical models. Empirical envelopes.
Application to real data of the West Bohemia earthquake swarm.
Uncertainties.
- Accelerograms from empirical Green functions.
Weak earthquakes as Green functions. Effects of different focal
mechanisms. Effects of finite fault lengths. Inversion for Green
tensor. Artificial source time functions.
- Synthetic accelerograms by discrete-wavenumber method.
Continuous and discrete wavenumber representation. Source
periodicity. Singularities. Complex frequency and artificial
attenuation. Analytical solutions. Numerical solutions in
combination with matrix method. Fortran Power Station for Windows
and Grapher for Windows. Computer program. Input, output,
graphics. Practical training.
- Site-modified accelerograms by matrix method.
Impulse response. Transfer function. Incidence wave. Bedrock
motion. Deconvolution of surface records. SH and P-SV case.
Computer program. Input, output, graphics. Practical training.
- Site-modified accelerograms by finite-difference method.
Block structures. Excitations by line sources and plane waves.
Free-surface approximations. Non-planar free surface. Vacuum
formalism. Internal discontinuities. Heterogeneous differential
equations and schemes. Absorption treatment. Nonreflecting
boundaries. Accuracy, stability, and grid steps. Alterman-Karal
excitation. Hybrid methods. Computer program. Input, output,
graphics. Practical training.
- Blind-prediction experiments.
Parkfield (California) and Ashigara (Japan) sites. Given data and
required predictions. Prediction methods. Prediction results and
comparison with real ground (blibded) ground motions.
SEISMOLOGY
(75 hours)
Jiri Zahradnik
- Objectives and methods
Seismic sources and seismic waves. Structural studies. Hazard
assessment. Macroseismic and instrumental data. Direct and
inverse problems. Numerical modelling. Laboratory modelling.
- Earthquakes and related phenomena
Volcanic, tectonic and man-made (induced) earthquakes. Nuclear
explosions. Microtremors (seismic noise). Aseismic and coseismic
fault motions. Vibratory ground motions. Liquefaction. Earth
slides. Tsunamis. Earthquake damage. Intensity. Macroseismic
scales. Large earthquakes of the world. Frequency and dynamic
range of seismic motions.
- Instrumental observations
Seismoscope. Seismometer. Seismograph. Transfer function.
Displacement, velocity and acceleration records. Classical
instruments (SP, MP, LP). Broad-band instruments. Strong-motion
instruments. Seismic networks (global, regional, local).
Interpretation of seismograms (seismic phases, arrival times,
amplitudes, polarities). Hypocentre location by travel-time
curves. Magnitudes. Magnitude calibration curves. Seismic
bulletins. Data centres. Catalogues.
- Seismicity
World geographic distribution of earthquakes. Inter- and
intraplate earthquakes. Aseismic gaps and quiescence. Foreshocks,
aftershocks, swarms. Magnitude-frequency relations. Benioff
graphs. Seismicity of subduction zones (Vadati-Benioff zones).
Seismicity of oceanic ridges. Seismicity of the Mediterranean and
adjacent regions. Seismicity of Czech territory.
- Body waves
Longitudinal (P) and transverse (S) waves. Particle motion.
Reflection and refraction. Head waves. P-S conversion.
Free-surface reflection and conversion. Diffraction. Attenuation.
Scattering. Anisotropy effects. Seismic body phases (crustal,
mantle, and core phases). Global and regional travel-time curves
and tables. Residuals. Numerical modelling by the ray method.
Travel-time inversion. Wiechert-Herglotz method. Tomography.
Amplitude variations around epicentral distances of 20 and 140
degrees. Spherically symmetrical models of the velocity
structure of the Earth.
- Seismic and interference waves
Love and Rayleigh waves. Particle motion. Dispersion curves.
Normal and leaky modes. Airy phase. Mantle waves. Lg waves. PL
waves. Numerical modelling by the discrete-wavenumber method.
- Free oscillations of the Earth
Spheroidal and toroidal modes. Line spectra. Line splitting.
- Earth structure
Oceanic and continental crust. MOHO. Crustal waveguide.
Anisotropy of the lithosphere. Low-velocity channel
(asthenosphere). Upper-mantle discontinuities. Core-mantle
boundary (CMB). Core transition zone. Three-dimensional
tomographic models of the Earth.
- Focal processes
Earthquake preparation and prediction. Fault plane. Rupture and
its propagation at the fault. Barriers and asperities. Slip and
its time variation. Moment. Focal mechanism. Pressure and tension
(P and T) axes. Moment tensor. Scaling laws. Stress drop. Energy.
Seismotectonic studies.
- Seismic hazard
Source and path effects. Source zones and their statistics.
Maximum possible earthquake. Probabilities and recurrence
periods. Seismic zoning. Site effects. Effects of sediments.
Effects of the ground water. Effects of topography. Nonlinear
effects. Numerical modelling of the site effects by the
finite-difference method. Seismic microzoning. Numerical
modelling of strong-ground motions (artificial accelerograms,
synthetic accelerograms, accelerograms from empirical Green
functions). Building codes. Antiseismic design.
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