土砂移動の確率モデルと地形変化のグリーン関数

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Any kind of down-slope movement of earth material brings landform change, and transportation from the source and diffusion (scattering) of the debris are essential features of the movement. Debris thickness is often approximated by a normal distribution with σ and μ. It is possible to introduce Green's function with the transport distance μ = bt and with the degree of scattering given by σ = √<2at> for unit mass from the point source at x = ξ. The function is a singular solution of the landform equation with subduing coefficient a and recessional coefficient b. Normal distribution is an approximation by continuous function to binomial distribution resulted from n-trials with the probability p to move over unit distance 〓x of dislocation. Binomial distribution as a probability model shows accumulation range over finite distance unlike the normal distribution extending infinitely. The parameters included in the probability model were determined for debris distributions by the gigantic landslides at Mt. Ontake in 1984 and Mt. St. Helens in 1980 where debris thicknesses are known, assuming reasonably that p = 0.5 . Unit dislocation 〓x is larger at Mt. St. Helens than in Mt. Ontake presumably affected by the length of straight channel segment in which debris flowed down. Statistical point of view on frequency and magnitude of landslides is necessary to evaluate the coefficients in geologic time scale. Dependence of the coefficient of equivalent friction on debris volume concerns the parameters contained in the probability model. It is possible to explain the dependence under the assumption that terminal point of debris is situated at μ + k σ , and that the angle referring the head from the center of debris is constant. Investigation on more cases is appreciated to overcome some problems which are still open in the present investigation.
日本地形学連合の論文
2003-10-25

著者

平野昌繁
大阪市立大

土砂移動の確率モデルと地形変化のグリーン関数

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