Measurement and comparison of soil structures.

A model is established to describe the structures of tilled soils using Markov chain theory. The effectiveness of the model in describing soil structures, and its accuracy when the model parameters are determined from limited field data is investigated by a consideration of variances of the transition probabilities and Markov chain state occurances in finite length chains. Criteria for correlation of soil structures at small horizontal and vertical displacements are derived, in order to establish distances at which soil structures become effectively independent. In this, a mathematical analysis is made of limiting covariances, generally applicable to the type of Markov chain used in describing these structures, in order to drastically reduce computing time in processing field data. Similarity coefficients are defined from the theory to measure similarity in different soil structures, and are compared in practice.