Two Generalizations of the Theory of Seismoelectric Effect: Parameterization Providing Suitability of Frenkel’s Theory for Any Geometry of Soil’s Pore Space. The Role of Thermoosmosis in Seismoelectric Effect

Abstract

Seismic vibrations of water-saturated soils and rocks cause the fluid motion relative to the charged interface and thus to the flow potential. Thus a seismoelectrical wave is formed, in which the ratio of its sound and electrical components carries diverse information about water in soils and rocks. As a result electroseismic method is of importance for the problem of water resources and is widely used in hydrogeology. However, at present it is possible to explain only a small part of the information carried by the electroseismic signal. Empowering the method depends on the improvement of equipment and measurement as well as by means of the further development of the theory of seismoelectric effect. This paper makes two steps in the development of theory. First, it manages to express the seismoelectric field strength through the ζ-potential and through only the macroscopic parameters of Frenkel’s classic theory, which makes it suitable for any geometry of soil’s pore space. Second, for the first time the influence on the seismoelectric effect is considered of thermoosmotic flow arising under the action of temperature gradients which always accompany the sound wave.

Appendix

It should be noted that here we consider the case of a weakly damped plane longitudinal sound wave propagating along the x-axis. Respectively, the time and space dependence of every sound-induced value may be represented by a multiplayer e ^{i(ωt − qx)}, where ω and q = 2πλ are the cyclic frequency and wave number; the sound speed is w = ω/q. All the vector quantities are represented by their x-components. Operators ∇ and grad denote differentiation by x, which, in turn, reduces to multiplication by − iq and the differentiation with respect to t reduces to multiplication by iω.