外营力地貌作用随机特性和分形布朗地貌的稳定性

ON THE STOCHASTIC NATURE OF EXOGENIC PROCESSES AND THE STABILITY OF FRACTIONAL BROWNIAN LANDSCAPE

通过建立外营力地貌作用的分形模型，揭示了外营力在微观上塑造地表不平的动力机制。外营力在宏观和微观上具有各自的表现，可能预示地貌空间尺度的差异，使演化具有不同的独特规律。

According to Scheidegger's “Instability Principle”, the development of landforms, controlled by exogenic processes which are essentially random, is unstable. But the instabilities cannot grow indefinetely, there is a certain size limitation present. To discover the behaviour of the exogenic processes, a fractional Brownian model of exogenic morphological evolution is proposed. There are two kinds of landform evalution. The first one isH(x,t) t=K 1[C 0+C(x,α)], H(x,0)=H 0(1)The right item in equation (1) is a random force , where C(x,a) is a fractional Brownian motion with α as its Hurst index and K 1 is a constant coefficient interpreting the strength of the force. The equation will draw a self similar geomorphological profiles H(x,t) . Its fractal dimension is D 1(α,t)=2-a that don't vary with t. Equation (2) is:H(x,t) t=K 212[H′(x+0,t)-H′(x-0,t)](2)that interpretes a hight moving to the equation (1), a new equation H(x,t) t=K 1[C 0+C(x,α)]+K 212(x+0,t)-H′(x-0,t), H(x,0)=H 0 (3)is obtained, the fractal dimension of which is written as D 2=(α,t) . Equation (3) describes the second one of landform evolution which posses one item describing planation process more than the equation (1), so we suspect equation (3) will draw more smooth geomorphological profiles than (1). It is surprising that a result of D 2(α,t)≡D 1(α,t)=2-a is calculated. From the stability of the fractal dimensions of the two processes, a conclusion should be obtained: in the instability of the exogenic acting there is a stability nucleus.