Relation of certain geometrical features to the dielectric anomaly of rocks

Abstract

We show that the real part of the dielectric constant ε′ of rocks at low frequencies can be anomalously high due to the presence of a small concentration η of high aspect ratio particles. For oblate spheroidal grains [Formula: see text] with depolarization factor along symmetry [Formula: see text] axis, [Formula: see text] [Formula: see text] the static value of the dielectric constant of rock [Formula: see text] and dc conductivity [Formula: see text] are given for [Formula: see text] by [Formula: see text] [Formula: see text] and for (2) [Formula: see text] [Formula: see text] Here [Formula: see text] is the dielectric constant of the grain; [Formula: see text] is the dc conductivity of the host rock. Case (1) corresponds to the well known Maxwell‐Wagner effect with [Formula: see text] diverging as η → 0, and [Formula: see text] Case (2) gives a novel result that [Formula: see text] may diverge for [Formula: see text], with a nonvanishing σ(0). Case (2) is applied to explain frequency and salinity dependences and the giant values [Formula: see text] of the dielectric constant of conducting sedimentary rocks. For [Formula: see text], [Formula: see text], [Formula: see text], we find [Formula: see text], which is large compared to [Formula: see text] or the dielectric constant of water [Formula: see text].