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

澄清固体地球的介质非均质性对研究地球演化过程具有重要意义。速度非均匀性谱可以认为是非常广泛的；因此，对具有相同震波波长尺度的非均匀性进行研究，需要对散射过程进行测量。重点研究了波在随机介质中传播的数学基础，以及利用观测到的地震波短周期特征测量地球介质非均质性的方法。得到的结果如下：(1)根据马尔可夫近似，成功地建立了层状随机介质表面短周期矢量波包络的合成。(2)利用小地震s波包络分析估计了日本本州东北地区的随机速度不均匀性，其中第四纪火山下的速度不均匀性较强。(3)基于多重各向同性散射模式对Hi-net记录的局地地震s震包线进行了分析，阐明了日本地区s波散射损失和本征吸收的区域变化。(4)根据辐射传递理论对爆炸地震记录进行分析，估计在10 Hz下，Asamo火山下的平均自由径小至1 km，比岩石圈内的自由径强2个数量级。(5)利用Born近似证明了散射介质噪声互相关函数的格林函数检索。在此基础上，证明了噪声源在空间上均匀随机分布时散射介质的格林函数反演和广义光学定理的等价性。(6)编撰了地震波短周期观测特征和随机非均质地球介质中地震波散射数学理论的教材。少

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