Negative correlation between porosity and hydraulic conductivity in sand-and-gravel aquifers at Cape Cod, Massachusetts, USA

Although it may be intuitive to think of the hydraulic conductivity K of unconsolidated, coarse-grained sediments as increasing monotonically with increasing porosity Φ, studies have documented a negative correlation between these two parameters under certain grain-size distributions and packing arrangements. This is confirmed at two sites on Cape Cod, Massachusetts, USA, where groundwater investigations were conducted in sand-and-gravel aquifers specifically to examine the interdependency of several aquifer properties using measurements from four geophysical well logs. Along with K and Φ, the electrical resistivity R0 and the natural gamma activity γ of saturated deposits were determined as functions of depth. Qualitative examination of results from the first site implies a negative correlation between K and Φ that is substantiated by a rigorous multivariate analysis of log data collected from the second site. A principal components analysis describes an over-determined system of inversion equations, with approximately 92% of the cumulative proportion of the total variance being accounted for by only three of the four eigenvectors. A subsequent R-mode factor analysis projects directional trends among the four variables (K, Φ, R0 and γ), and a negative correlation between K and Φ emerges as the primary result.