What Have we Learned from Deterministic Geostatistics at Highly Resolved Field Sites, as Relevant to Mass Transport Processes in Sedimentary Aquifers?

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In the method of deterministic geostatistics (sensu Isaaks and Srivastava, 1988), highly-resolved data sets are used to compute sample spatial-bivariate statistics within a deterministic framework. The general goal is to observe what real, highly resolved, sample spatial-bivariate correlation looks like when it is well-quantified in naturally-occurring sedimentary aquifers. Furthermore, it is to understand how this correlation structure, (i.e. shape and correlation range) is related to independent and physically quantifiable attributes of the sedimentary architecture. The approach has evolved among work by Rubin (1995, 2003), Barrash and Clemo (2002), Ritzi et al. (2004, 2007, 2013), Dai et al. (2005), and Ramanathan et al. (2010). In this evolution, equations for sample statistics have been developed which allow tracking the facies types at the heads and tails of lag vectors. The goal is to observe and thereby understand how aspects of the sedimentary architecture affect the well-supported sample statistics. The approach has been used to study heterogeneity at a number of sites, representing a variety of depositional environments, with highly resolved data sets. What have we learned? We offer and support an opinion that the single most important insight derived from these studies is that the structure of spatial-bivariate correlation is essentially the cross-transition probability structure, determined by the sedimentary architecture. More than one scale of hierarchical sedimentary architecture has been represented in these studies, and a hierarchy of cross-transition probability structures was found to define the correlation structure in all cases. This insight allows decomposing contributions from different scales of the sedimentary architecture, and has led to a more fundamental understanding of mass transport processes including mechanical dispersion of solutes within aquifers, and the time-dependent retardation of reactive solutes. These processes can now be described in terms of quantifiable physical attributes of the sedimentary architecture. In addition to discussing the benefits to basic scientific understanding, we also discuss some of the practical benefits derived from this insight.