斜面発達とくに断層崖発達に関する数学的モデル

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タイトル別名
  • A STUDY OF A MATHEMATICAL MODEL OF SLOPE DEVELOPMENT
  • シャメン ハッタツ トクニ ダンソウ ガイ ハッタツ ニ カンスル スウガクテキ モデル

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抄録

A mathematical model of slope development is summarized by the relation<br> _??_<br> where u: elevation, t: time, x: horrizontal distances, a: subdueing coefficient, b: recessional coefficient, c: denudational coefficient and f (x, t): arbitrary function of x and t, respectively. Effects of the coefficients are shown in figs. 1-(A), (B) and 2-(A).<br> In order to explain the structural reliefs, the spatial distribution of the rock-strength against erosion owing to geologic structure and lithology is introduced into the equation by putting each coefficient equal a function, in the broadest sence, of x, t and u. Two simple examples of this case are shown in fig. 5.<br> The effects of tectonic movements, for instance of faulting, are also introduced by the function f (x, t), which is, for many cases, considered to be separable into X (x) and T (t), where X (x) and T (t) are functions of x only and t only, respectively. An attempt to classify the types of T (t) has been made.<br> Generally speaking, provided the coefficients a, b and c are independent of u, the equation is linear and canbe solved easily. With suitable evaluation of the coefficients (as shown, for example, in fig. 4-(A)), this linear model can be used to supply a series of illustrations of humid cycle of erosion, especially of the cycle started from faulting.

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  • 地理学評論

    地理学評論 39 (5), 324-336, 1966

    公益社団法人 日本地理学会

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