Number:

Mech 29/91

Author(s):

ISICHENKO, M.B., KALDA, J.

Title:

Statistical topography I. Fractal dimension of coastline and number-area rule for islands. 39 p.

Language:

English ABSTRACT.Statistical topography involves the geometrical properties of the iso -sets (contour lines or surfaces) of a random potential (r). Previously /1,2/ such a problem has been addressed for coastlines on a random relief (x,y) possessing a single characteristic spatial scale whose topography belongs to the universality class of the random percolation problem. In the present paper the previous analytical approach is extended to the case of a multiscale random function with a power spectrum of scales, , in a wide range of wavelengths, < < .It is found that the coastlines pattern differs significantly from a monoscale landscape provided that -3/4 < H < I, with the case -3/4 < H < 0 corresponding to the long-range correlated percolation and 0 < H < 1 to the fractional Brownian relief. The expression for the fractal dimension of an individual coastline is derived, Dh = (10 - 3H)/7, whose maximum value, Dh = 7/4, corresponds to the monoscale relief. The distributed function F(a) of level lines over their size is calculated: F. A comparison of the theoretical results with geographical data is presented.