Study on scattering and seismic-wave envelopes in short-periods in the heterogeneous medium

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It is important to clarify the medium heterogeneity of the solid earth for the study of the evolution process of the earth. The spectra of the velocity inhomogeneity can be considered to be very broad ; therefore, measurements of scattering process is necessary for the study of inhomogeneity having the same scale of the wavelength of seismic waves. We put a focus on the mathematical bases of the wave propagation through random media and the measurement of the earth medium heterogeneity from the characteristics of observed seismic waves in short periods. We enumerate the obtained results as follows :(1)We successfully formulated the synthesis of vector-wave envelopes in short periods on the surface of layered random media according to the Markov approximation.(2)We estimated random velocity inhomogeneities beneath Tohoku, Honshu, Japan from the envelope analysis of S-waves of small earthquakes, where the velocity inhomogeneity is strong especially beneath Quaternary volcanoes.(3)From th … More e analysis of S-seismogram envelopes of local earthquakes registered by Hi-net on the basis of the multiple isotropic scattering model, we clarified the regional variation of scattering loss and intrinsic absorption of S-waves in Japan.(4)From the analysis of explosion seismograms according to the radiative transfer theory, we estimated the mean free path beneath Asamo volcano to be as small as 1 km at 10 Hz, which is two order stronger than that in the lithosphere.(5)By using the Born approximation, we proved the Green function retrieval from the noise cross correlation function for a scattering medium. Then we proved the equivalence of the Green function retrieval and the generalized optical theorem for a scattering medium when the distribution of noise sources is random and uniform in space.(6)We published a textbook which compiles the characteristics of observed seismic waves in short periods and mathematical theories on scattering of waves in the randomly heterogeneous earth medium. Less