著者

平野 昌繁

出版者

公益社団法人 日本地理学会

雑誌

地理学評論 (ISSN:00167444)

巻号頁・発行日

vol.39, no.5, pp.324-336, 1966

被引用文献数

8 4

---

A mathematical model of slope development is summarized by the relation<br> _??_<br> where <i>u</i>: elevation, <i>t</i>: time, <i>x</i>: horrizontal distances, <i>a</i>: subdueing coefficient, <i>b</i>: recessional coefficient, <i>c</i>: denudational coefficient and <i>f</i> (<i>x</i>, <i>t</i>): arbitrary function of <i>x</i> and <i>t</i>, 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 <i>x</i>, <i>t</i> and <i>u.</i> 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 <i>f</i> (<i>x</i>, <i>t</i>), which is, for many cases, considered to be separable into <i>X</i> (<i>x</i>) and <i>T</i> (<i>t</i>), where <i>X</i> (<i>x</i>) and <i>T</i> (<i>t</i>) are functions of <i>x</i> only and <i>t</i> only, respectively. An attempt to classify the types of <i>T</i> (<i>t</i>) has been made.<br> Generally speaking, provided the coefficients <i>a</i>, <i>b</i> and <i>c</i> are independent of <i>u</i>, 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.