A STUDY OF A MATHEMATICAL MODEL OF SLOPE DEVELOPMENT
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- HIRANO Masashige
- 大阪市立大学大学院地質学専攻
Bibliographic Information
- Other Title
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- 斜面発達とくに断層崖発達に関する数学的モデル
- 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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Abstract
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.
Journal
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- Geographical Review of Japan
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Geographical Review of Japan 39 (5), 324-336, 1966
The Association of Japanese Geographers
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Details 詳細情報について
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- CRID
- 1390282679309542400
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- NII Article ID
- 130003567176
- 10003194841
- 10003665852
- 10003515794
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- NII Book ID
- AN00148053
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- ISSN
- 21851719
- 00167444
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- NDL BIB ID
- 8676170
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed