Dielectric anomaly in inhomogeneous materials with application to sedimentary rocks

A small concentration of thin plate-like insulating material in a conducting host can give rise to anomalously high values of dielectric constant. For a small concentration η of oblate spheroidal grains (a ≪ b = c) with depolarization factor along symmetry (a) axis Ls = 1−δ,δ = πa/2b, the static value of the dielectric constant of rock εs and dc conductivity σ(0) are given for (a) δ<η as σ(0) = δσR/η, εs≅εm/η, and for (b) δ≳η as σ(0)≅σR(1−η/δ), εs≅ηεm/δ2. Case (a) corresponds to the well-known Maxwell–Wagner effect with εs diverging as η→0, and σ(0)→0. Case (b) gives a novel result that εs may diverge for δ≳η≫δ2, with a nonvanishing σ(0). Case (b) is applied to explain frequency and salinity dependences and the large values (∼103, observed at MHz frequencies) of the dielectric constant of conducting sedimentary rocks. Possible reasons for the larger values (∼106) observed experimentally at lower (khz) frequencies are discussed.