MAGNETOTELLURIC AND DEEP GEOMAGNETIC SOUNDING

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

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

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

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

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

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

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

Ludvik Urban

Rules for computer networks.

Basic introduction to UNIX.

Electronic mail. ELM. PINE.

Network services.

Telnet. Basic commands. Telnet client for DOS.

FTP.

Gopher.

Finger. Whois, UDS. Netfind. Ping. WWW. Lynx and Mosaic. Doslynx client. Harvest.

GENERATION OF SEISMIC WAVES BY EARTHQUAKE SOURCES

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

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

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

Jiri Zahradnik