Theoretical Study on Earth Tides by Assuming the Earth as a Visco-elastic Body
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概要
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Forced oscillations of the earth by tide generating potential are investigated by assuming the earth as a visco-elastic body. First, the Kelvin-Voigt type visco-elastic model is adopted for the earth and equations of motion are deduced. By solving the equations numerically, phase retardations of earth tides are calculated where viscosity within the mantle is assumed to be uniform. As a result, it is noticed that the retardations become marked when the viscosity is over 1015 poises. Second, the retardations are calculated for real earth models where radial distribution of viscosity is converted from Q model by Anderson and Hart (1978). Obtained retardations are too small to be detected by actual observations. It is concluded that the effect of mantle viscosity to the phase retardations is negligibly small. Through the calculations, Love's numbers, diminishing factor, gravimetric factor, etc. are also calculated for several principal components of tide potential. The results are nearly equal to the values obtained from the solutions of static deformation of the earth. There is, however, slight frequency dependence of Love's numbers. Finally, relations between the visco-elastic model of the Kelvin-Voigt type and the Maxwell type are studied. From the results, it may be said that even if any kind of vibrating motion of the Kelvin-Voigt type earth is considered, the same vibration is possible for the Maxwell type earth only by taking new appropriate values of viscosity. For example, 2×1O10 poises of viscosity for the Kelvin-Voigt model corresponds to about 1022 poises for the Maxwell model in the frequencies of earth tides.ここでは,地殻,マントルを粘弾性体と考えた場合,地球潮汐の状態がどのようになるか,特にその場合の位相遅れがどのぐらいになるかを理論的に考察している.地球潮汐の位相遅れは,高さ方向の変位に対するもの,水平方向の変位に対するもの,およびポテンシャルの変化に対するものの3種が定義できる.
- 1979-12-25
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