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Study of the dynamic processes in the Earth is one the most important problems of geophysics today.
The results of these studies are of a huge practical importance because they provide a basis for taking measures for people security.
Investigation of physical processes in seismic zones and related phenomena resulting in earthquakes is the subject of seismology.
These studies are based on interpretation of seismic waves generated by seismic sources.
Therefore the theoretical basis for any seismological studies are the theory of wave propagation in the models of elastic media adequate to the real Earth, and the methods for solving the inverse problems — determination of source characteristics and the Earth's structure from seismic wave observations. Since seismic waves generated by earthquakes spread over the whole Earth, they provide invaluable information on the Earth interior. Our knowledge on the Earth structure is based mainly on seismological data.
Principles of the geophysical inverse problem solution
The mathematical grounds for solution of the inverse problems of geophysics are given. The
methods of regularization for incorrectly stated problems are considered. Statistical methods of
estimation of searching parameters for geophysical objects are presented. The algorithms for rayed
and diffractional geophysical tomography are considered.
Data analysis and processing of geophysical information
The modern methods of geophysical data processing are considered: Fourier transform, Laplace
transform, correlation analysis, estimate of the power spectrum, mutual spectral analysis,
maximum entropy spectral analysis, cepstrum analysis, deconvolution (inverse) filtering, bondpass
filtering, Batteruorte filtering, wave propagation in the layed media as filtering process, velocity
filtering, gomomorphic filtering.
The asymptotic methods in the theory of seismic wave propagation
The asymptotic methods in the theory of seismic wave propagation such as ray theory, local and
uniform asymptotic expansions are outlined. In the ray theory considered are:
constructing the ray series in continious inhomogeneous media, reflection and refraction of the
waves at discontinuities, kinematic and dynamic ray tracing, paraxial approximation, Gaussian
beams. Local and uniform asymptotics are demonstrated on the examples of caustic and vicinity of
the critical ray.
Inverse problems of seismology
The inverse problem for the travel–time curve is considered for the case of existence of the low–velocity zones in the medium.
All other inverse problems are solved using linearization.
The least–square method, Backus–Gilbert method and the generalized linear inversion are considered for solving the
linearized problems. The methods are applied for the inverse problems of seismic source and of the Earth's structure using the data
on body waves, surface waves and free oscillations of the Earth.
Geothermics and radiometry
Heat flow, temperature evaluation by heat flow data. Estimation of the Earth's interior uppermost and lowermost temperature starting from elastic properties of rocks: temperature of melting and adiabatic compression. Temperature assessment on the base of the Earth's electrical conductivity data. Thermal history of the Earth. Main contributors of the heat inside the Earth. The problem of the Earth's heating as a consequence of radioactive elements decomposition.
The subject of geology, its branches. Endogenous, exogenous and metamorphic processes in Earth
crust. Introduction to minerology and petrology. Geophysical methoads in geology. Geotectonic
zoning of Russia, its mineral resources and possibility to increase it.
Lectures are followed by geological practice in Crimea.
Disciplines (Lectures) for choice
Theory of surface waves and free oscillations of the Earth
Exact solution of the elastodynamic equations for a layer on a half–space is analysed in a framework of the generalized ray theory and the normal mode theory. Rayleigh and Love waves in a layered half-space are analysed with the matrix method and as a solution of the boundary problem. Free oscillations of homogeneous and radially inhomegeneous sphere, including the effect of gravity, are considered. The relationship between eigenfrequencies and surface wave phase velocity is derived.
Ray seismic tomography
Time–delay tomography based on the ray approximation is considered. The problem is non–linear, and it is solved by iterative procedure using linearization at each step. The solution is represented as a series in some basis functions, and the problem is reduced to solving of a system of linear equations. Different approaches for selection of the basis functions are discussed. It is shown how resolving power and standard error of the solution are estimated. Methods for solving large linear systems are outlined.
Physics of the earthquake source
Representation theorem is presented for representation of seismic source as a slip over a fault area and for determination of the equivalent force source. Seismic moment tensor is introduced. Seismic source kinematics and the related problems are discussed. The source spectrum and the source parameters are considered. Different magnitude scales and the relationships between magnitudes and seismic energy are presented.