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WAVES IN ELASTIC MEDIA
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.
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
Numerical methods of wave field modeling for anisotropic elastic media
Equations of motion in linear elastic theory. Tensor of elastic constants. Hooke's law in
anisotropic elastic theory. Law of conservation of energy, vector of flux of energy. Reciprocity
theorems in anisotropic elastic media. Plane (homogeneous and inhomogeneous) waves. Ray
method for anisotropic elastic media, methods of calculations of spreading of rays. Matrix method
for layered anisotropic media.
Asymptotic methods in the theory of seismic waves 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: principles for
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.