Multifractal Modeling of Heterogeneous Subsurface


The movement and dispersion of groundwater solutes is controlled, to a large extent, by the heterogeneity of the aquifer hydraulic conductivity (K) field. Therefore, a means of quantifying spatial variability of the hydraulic conductivity field is essential for the application of solute transport models to practical problems. However, for a typical groundwater modeling effort, K values must be assigned based on just a few point measurements (for example, an aquifer volume of 10 km3 described by, at best, a few hundred measurements) due to the high cost of obtaining accurate K data. Therefore, a great need exists for a means of accurately estimating the K field, which has been found to vary as much as 6 orders of magnitude at some sites.

We used statistical spatial analyses to analyze the variability of K. We found that K could be treated as a multifractal for some fields.

Logarithm of the vertical structure function for Borden. Scaling is observed from 0.05 m up to 0.5 m after which periodicity dominates.

Effect of the a parameter on generated multifractal fields for c1=0.1 and H=0.0. The field becomes sparse as a decreases.


 Because the measurements of K are costly, we explored analyzing surrogate quantities of K, such as the electrical conductivity and the K-40 gamma radiation.

Logarithm of the east-west structure functions for the electric conductivity data. Scaling is observed from 100 ft to 6000 ft, close to the maximum range.