Hydrogeophysical Approach for Identification of Layered Structures of the Vadose Zone from Electrical Resistivity Data

1 Heterogeneity and lack of sufficient site characterization render accurate and reliable predictions of subsurface flow and transport in the vadose zone notoriously elusive. It is now widely recognized that for quantitative descriptions of subsurface phenomena to be scientifically defensible, they have to be accompanied by some measure of predictive uncertainty. In other words, a major goal of subsurface modeling is to translate uncertainty about soil properties (e.g., hydraulic conductivity and dispersivity) and driving forces (e.g., infiltration rates and the location and amount of a spill) into uncertainty about system states (e.g., soil moisture and contaminant concentration) (Tartakovsky and Winter, 2008). This task can be accomplished by treating soil properties and other input parameters as random fields whose statistics are inferred from available data; the resulting flow and transport equations become stochastic (e.g., Rubin, 2003, and references therein). In general, solving these equations either analytically or numerically requires a closure approximation, which limits the applicability of such solutions. For example, perturbation closures of stochastic unsaturated flow equations (e.g., Tartakovsky and Guadagnini, 2001; Tartakovsky et al., 2003), which are often used in stochastic hydrology, are based on the assumption that the subsurface environment is only mildly heterogeneous. Twopoint closures, also known as Corrsin’s conjecture, (e.g., Neuman, 1993) and four-point closures (Dentz and Tartakovsky, 2008) of stochastic transport impose distributional assumptions (e.g., stationarity and Gaussianity) on the advective velocity, which might or might not hold true. The random domain decomposition (Winter and Tartakovsky, 2000, 2002; Winter et al., 2002) provides a general framework that allows these limitations to be overcome by explicitly accounting for both the geologic structure of a subsurface environment and the uncertainty associated with its delineation. The approach relies on a tacit assumption that available data allow reconstruction (albeit probabilistically) of major geologic units, e.g., layers comprising the vadose zone. This task can be accomplished by geostatistical (e.g., Ritzi et al., 1994; Guadagnini et al., 2004) or other (e.g., Wohlberg et al., 2006; Tartakovsky et al., 2007) analyses of material properties data, including hydraulic conductivity and soil texture, etc.—the so-called forward facies delineation problem. Such data are hard to come by and expensive to collect. They often have to be supplemented with measurements of hydraulic system states (e.g., soil moisture and pressure head) or their geophysical counterparts (e.g., electrical resistivity or permittivity), giving rise to the so-called inverse Hydrogeophysical Approach for Identification of Layered Structures of the Vadose Zone from Electrical Resistivity Data