HYDROLOGIC HETEROGENEITY: FAILURE OF THE GEOSTATISTICAL APPROACH

Outcrops offer a unique opportunity to characterize geologic and hydrologic heterogeneity that is inaccessible in the subsurface. A primary objective of many outcrop-based heterogeneity studies is to characterize the spatial statistics (mean, variance, and correlation length) of hydraulic properties. In principle spatial statistics derived from outcrops can then be used in probabilistic (stochastic) flow and transport models of analogous subsurface locations. Unfortunately small observation errors and inversion model errors may preclude this use of hydraulic property data, as these errors lead to spatially biased property estimates. This bias results in distortion of the distribution and variogram of the hydraulic property, increases variogram uncertainty, and can lead to order of magnitude errors in stochastic model predictions. Non-parametric indicator statistics are less sensitive to bias because spatial errors reflect only misclassification, and indicator approaches can accurately extract the true spatial pattern from even highly biased hydraulic property data. However, the spatial pattern of hydraulic properties often simply reflects the geology. Perhaps we should limit our efforts to characterize spatial statistics of hydraulic properties and focus instead on connecting measured hydraulic properties with quantifiable geologic metrics. This would allow us to develop geologically based approaches for simulating hydraulic heterogeneity.