Soil monitoring and inventory require a sampling strategy. One component of this strategy is the support of the basic soil observation: the size and shape of the volume of material that is collected and then analysed to return a single soil datum. Many, but not all, soil sampling schemes use aggregate supports in which material from a set of more than one soil cores, arranged in a given configuration, is aggregated and thoroughly mixed prior to analysis. In this paper, it is shown how the spatial statistics of soil information, collected on an aggregate support, can be computed from the covariance function of the soil variable on a core support (treated as point support). This is done via what is called here the discrete regularization of the core-support function. It is shown how discrete regularization can be used to compute the variance of soil sample means and to quantify the consistency of estimates made by sampling then re-sampling a monitoring network, given uncertainty in the precision with which sample sites are relocated. These methods are illustrated using data on soil organic carbon content from a transect in central England. Two aggregate supports, both based on a 20 m 20 m square, are compared with core support. It is shown that both the precision and the consistency of data collected on an aggregate support are better than data on a core support. This has implications for the design of sampling schemes for soil inventory and monitoring.