Spatial correlation structure estimation using geophysical and hydrogeological data

The large spatial variability of hydraulic properties in natural geologic systems over a wide range of scales, and the difficulty of collecting representative and sufficient hydraulic property measurements using conventional sampling techniques, render estimation of spatial correlation parameters difficult. Further compounding the estimation problem is the observation that the integral scale estimate is a function of the measurement support scale. To mitigate these problems, we investigate the use of tomographic geophysical data in combination with hydrogeological data in the spatial correlation estimation procedure. Two synthetic case studies were investigated where the scale of the geophysical measurements were varied relative to the scale of the hydrogeological properties. The spatial correlation structure parameter estimation procedure was performed in the spectral domain, where analysis of data having different support scales and spatial sampling windows was facilitated. Comparison of the spatial correlation structure parameters estimated from measured data with those of the synthetic aquifers revealed which type of data (tomographic, hydrogeological, or a combination of both) was most effective for recovering spatial correlation statistics under different sampling/heterogeneity conditions. These synthetic case studies suggest that collection of a few tomographic profiles and interpretation of these profiles together with limited well bore data can yield correlation structure information that is otherwise obtainable only from extensive hydrological sampling.