Simple Graphical Descriptions of Natural Land Profiles and the Application of Fractal and Sub-Fractal Models to Them.

摘要

Terrain profiles from four widely different areas of Britain are obtained from Ordnance Survey maps and shown to be well modelled as either fractal or as a hierarchy of different fractals. The profiles are then smoothed using a crude small-scale smoothing method to allow them to be modelled as sub-fractal surfaces. Rays are drawn from these surfaces to simulate the scattering of incoherent radiation. The resulting ray density statistics are analysed and shown to be approximately Gamma-distributed. Based on the findings suggestions are made regarding possible methods of remotely determining surface texture for metrology purposes. The overall aim of this Memorandum is not mathematical rigour, but rather the use of simple pictorial methods as an aid to gaining a physical insight into rough surface scattering and how such information might be used in describing and measuring surface texture. Great Britain. (rrh)