23. 低速層が介在する場合の彈性波の傳播
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In the presence of a slow-speed-bed the time-distance curve becomes discontinuous, as shown in Fig.1. As is well known, it is impossible in such case to deduce from the travel-time curve unique values for seismic velocities at depth. In dealing with the theory of this case, the travel-time curve is, as usual, assumed to be completely known from fie'd data. However, from the experimental point of view, the required degree of completeness in a travel-time curve that contains a gap is not always certain, wherein lies the difficulty in actual practice. Let T be the discontinuity in time, and X in distance. Then, for a given discontinuity T, the maximum thickness of the slower bed h_n is h_m=1/2√<XL>, where L denotes VT-X, and is the distance marked in Fig.1. The velocity v_m, which insures this maximum thickness for the slower layer, becomes v_m=√<(XV)/T>, where V denotes the highest value of the velocity in the uppermost layer. The minimum thickness of a slow horizon is also easily found, in calculating which we may always fix a limiting value, below which the velocity cannot fall in any bed that may be present. Then, the minimum thickness becomes h_l=L/2 v_e/√<V^2-v_e-2> The interpretation of the travel-time curve beyond the discontinuity involves three parts ; (1) the interpretation gained from the initial segment of the travel-time curve in the normal way, (2) a maximum and minimum interpretation gained from the gap, and (3) the corresponding two interpretations gained from the second segment by using the two known, but artificial, velocity functions. In practic it will probably often be found that their mean may be used without risk of error that may be significant from the geological point of view. An actual example of the travel-time curve containing a gap is shown in Fig.3. The interpretation of the initial segment up to the gap was made under the assumption that the velocity increased linearly with depth, such as is expressible by the formula, v=v_0+ah. The maximum and minimum interpretations were gained from the gap, while the interpretations of the second segment were gained in the ordinary way. The results gave two velocity functions, such as shown in Fig.5. In Fig.6, the results of borings are shown for comparison with the results of our interpretations.
- 東京帝国大学地震研究所,Earthquake Research Institute, Tokyo Imperial University,地震研究所の論文
- 1942-06-30
東京帝国大学地震研究所,Earthquake Research Institute, Tokyo Imperial University,地震研究所 | 論文
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