Electroseismic Wave Theory of Frenkel and More Recent Developments

Abstract

Frenkel’s 1944 theory of porous media acoustics is carefully scrutinized. After some manipulation, Frenkel’s equations are seen to have nearly identical form to Biot’s 1962 equations. The only difference is that Frenkel includes an extraneous fluid-pressure gradient in his bulk force balance. Frenkel also makes a slight error in the development of his effective poroelastic moduli that prevents him from being the first to obtain the so-called “fluid-substitution” relations. Outside of these two small problems, Frenkel’s analysis can be considered correct. He limits his treatment of electroseismic phenomena to explain the electric field that accompanies a compressional seismic wave in a homogeneous material. He predicts that the electric field in a compressional wave is directly proportional to the particle acceleration and this has been verified by the recent field measurements of Garambois and Dietrich. However, such electric fields are only a small part of the total electroseismic response of the earth. Accordingly, some of the additional phenomena not discussed by Frenkel are also presented and discussed.