Characterisation of the soil structure and microwave backscattering based on numerical three-dimensional surface representation: Analysis with a fractional Brownian model

In this paper, local structure of bare soil is analyzed from the fractal po int of view. Soil surface profiles were created from three dimensional (3-D ) stereoscopic images of soil surface leading to 3-D numerical reconstructi on of the soil topography with very fine resolution. Investigations are don e with a database (four soils) that includes three main soil classes accord ing to the way of tillage: smoothed field from rainfalls, ploughed, and sow ed fields. The fractional Brownian model developed by Mandelbrot is used to describe local structure of soil roughness. For the database soils, fracta l nature of the profiles is demonstrated over a finite range of scales show ing a good stability of fractal dimension for each one. This model also pro vides an excellent analytic fit to the experimental correlation function of the soil. Therefore, a new method to calculate its shape at the origin and a more stable correlation length is presented. To study the influence of t he band-limited fractal nature of the soil on radar signal, the Moment Meth od is used to evaluate the backscattered field and to obtain the radar cros s-section by statistical averaging. Surfaces used for this electromagnetic simulation are cylindrical and perfectly conducting. A method is developed to generate soil surface profiles that have the same statistical properties and the sam roughness parameters values (rms height, correlation length, a nd fractal dimension) as what has been found on our database soils. The gen eration method is based on an initially Gaussian correlated random profile, modified by the random mid-point displacement method to introduce the shor t-range disorder that depends on fractal dimension. The radar disorder that depends on fractal dimension. The radar signal level computed on these sur faces by the Moment Method shows the dependence of backscattering on fracta l dimension and new aspects in electromagnetic scattering behavior over soi ls. (C) Elsevier Science Inc., 2000.