Compressing soil structural information into parameterized correlation functions

Soil structure is highly interconnected to all of its properties and functions. The structure for most soils is very complex and hierarchical in nature. Considering the fact that a truly multiscale digital 3D soil structure model for a single genetic horizon, even with the resolution not finer than 1 μm, will contain an enormous amount (approx. up to 10¹⁵ voxels or even more) of data, it is an appealing idea to compress this structural information. Effective management and pore‐scale simulations based on such datasets do not seem feasible at the moment. Another approach would be to reduce the complexity to a limited but meaningful set of characteristics/parameters, for example using universal correlation functions (CFs). In this study, we successfully compressed the soil structural information in the form of 3D binary images into a set of correlation functions, each of which is described using only six parameters. We used four different correlation functions (two‐point probability, lineal, cluster and surface‐surface functions) computed in three orthogonal directions for the pores. The methodology was applied to 16 different soil 3D images obtained using X‐ray microtomography (XCT) and segmented into pores and solids. All computed CFs were fitted using a superposition of three basis functions. In other words, we reduced 900–1300³ voxel images into sets of 72 parameters. Fitting of computed correlation functions and reducing them to a number of parameters is a powerful way of compressing soil structural information. However, the analysis based on parameters alone is different from the one where correlation functions are used. This problem can be negated by uncompressing the correlation functions back from these parameters before any application. This way, correlation functions are not only a way to compress the soil structural information with minimal loss, but also may be used to solve a number of additional problems, including the comparison and differentiation of soil samples, location of elementary volumes, effective physical property prediction using machine learning, and fusion of hierarchical soil structures.