Non-linear Langevin model of geomorphic erosion processes
Non-linear Langevin model of geomorphic erosion processes
复制标题
地貌侵蚀过程的非线性朗之万模型
DOI：
10.1111/j.1365-246x.1993.tb00894.x
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发表时间：
1993
影响因子：
2.8
通讯作者：
Yi
中科院分区：
文献类型：
--
作者：
D. Sornette;Yi
最近对地貌和山脉垂直剖面的光谱研究表明，它们是自仿射分形，即在距离L尺度上平均的均方根高度波动Ah（L）为Ah（L）- Lx，x = 0.5 f 0.1，与水平等高线的分维Df = 2 - x = 1.5有关。我们建议，自仿射粗糙景观的非线性和噪声的相互作用。为了说明这个想法和模型的形成，这样的结构，我们建议一个非线性随机方程ahla？= DV*h + A（Vh）' + ~（r，t），它是确定性Culling线性方程的推广。非线性项h（Vh）* 来自侵蚀与景观暴露面积成比例的要求;噪声项~（r，t）说明了由于土壤的不均匀性和风暴的分布，侵蚀在局部是不规则的。使用这个一般框架，我们恢复的标度律Ah（L）- Lx与x 2 0.4。从这种分析中出现了几种新的研究途径，以进一步量化地质数据。
SUMMARY Recent spectral studies of vertical transect profiles of landscapes and mountains have shown them to be self-affine fractals, i.e. the rms height fluctuation Ah(L) averaged over a distance L scales as Ah(L) - Lx with x = 0.5 f 0.1, related to the fractal dimension Df = 2 - x = 1.5 of the horizontal contours. We propose that self-affine rough landscapes are created by the interplay of non-linearity and noise. To illustrate this idea and model the formation of such structures, we suggest a non-linear stochastic equation ahla? = DV*h + A(Vh)' + ~(r, t), which is the generalization of the deterministic Culling's linear equation. The non-linear term h(Vh)* comes from the requirement that erosion is proportional to the exposed area of the landscape; the noise term ~(r, t) accounts for the fact that erosion is locally irregular, as a result of the heterogeneity of soils and distribution of storms. Using this general framework, we recover the scaling law Ah(L) - Lx with x 2 0.4. Several novel avenues of research emerge from this analysis to further quantify geological data.