斜面発達とくに断層崖発達に関する数学的モデル

抄録

A mathematical model of slope development is summarized by the relation
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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).
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.
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.
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.