Synthetic Seismograms in Realistic Media : A Wave-theoretical Approach
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概要
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In order to interpret seismograms, we should separate the effects of source and medium, which are strongly coupled. The medium effect is usually estimated by computing synthetic seismograms for a model of the Earth. Of course, a three-dimensionally heterogeneous, arbitrarily anisotropic and attenuative medium is the most realistic model, but it requires a great deal of theoretical and numerical effort. At present one- or two-dimensionally layered, isotropic and attenuative media consisting of homogeneous layers are the most productive models for precise waveform analyses of seismograms. A new approach based on the reflectivity method is presented here to compute complete synthetic seismograms in these models. Following the standard derivation of the reflectivity method, displacement and stress components are doubly transformed into the frequency-wavenumber domain, and they are treated together in a motion-stress vector. In one-dimensionally layered media which have only flat interfaces, the boundary conditions at the interfaces are simply satisfied by the motion-stress vectors and propagator matrices for individual wavenumbers. Thus synthetic seismograms can be obtained by summing up displacement transforms computed individually. These seismograms include all multiple reflections and surface waves. The effect of Q-values can easily be introduced into them. In two-dimensionally layered media, on the other hand, scattering by irregular interfaces causes the coupling among different wavenumbers. The boundary conditions are not satisfied for individual wavenumbers, but only for a total wave-field. Then we introduce the Aki-Larner technique to solve the integral equations for these conditions and enlarge the propagator matrices to express the total wave-field. Numerical examples are presented for several one- and two-dimensionally layered media to confirm the validity of our approach. Some of them compare to the results of other methods, i.e. the finite element and difference methods, the asymptotic ray theory, and the Gaussian beam method. Our results agree well with those of the finite element and difference methods even in a later portion where the latter two methods break down. In the second half our approach is applied to investigate the effects of the details of crustal structures on synthetic seismograms. Computations for typical models reveal that layers thicker than /i/10 (λ: wavelength of input signal) cannot be ignored, and interface dents larger than λ/10 must affect seismograms. Seismograms are also synthesized for the crustal model of the Kanto plain obtained by refraction experiments. They show that the irregular interface strongly affects their waveform and amplitudes.地震記録を解析するためには,地震波を発生させた震源の影響と地震波を伝播させる媒質の影響を,記録から正しく分離しなければならない.媒質の影響は通常,理論地震記象を計算して評価される.従来この評価に際して,簡単な場合には無限媒質や半無限媒質,特に考慮される場合でも水平成層構造に対して地震記象を計算することで済まされてきた.ところが人工地震探査などの結果は,地球内部にいくつもの不規則な境界面があることを示しており,従来のやり方では正しく媒質の影響を評価できない.本研究ではより現実的な媒質モデルとして不規則成層構造を考え,波動論のアプローチで,それにおける完全な理論地震記象の計算方法を提案する.
- 東京大学地震研究所,Earthquake Research Institute, University of Tokyo,地震研究所の論文
- 1988-01-29
東京大学地震研究所,Earthquake Research Institute, University of Tokyo,地震研究所 | 論文
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