Electrokinetic Effect in Fractal Pore Media as Seismoelectric Phenomena

Summary

In this chapter the theory of electrokinetic effect on fractal is developed. Inhomogeneous water-saturated medium with fractal structure of pore space is a subject of investigation. The fluid migration along the percolation clusters is accompanied by the electrokinetic effect caused by contact potential difference at phase bounds. The electrokinetic current density is found to depend on both the transport critical exponent and correlation length critical exponent. Two different models of the inhomogeneity embedded in rock are considered. In the first model a fractal core with high pore fluid pressure is surrounded by weak permeable rock. In the second one a non-fractal core composed of high permeable broken rock is surrounded by a fractal periphery. The electrokinetic current in the fractal regions results in the appearance of electric currents in conductive layers under the ground. Amplitude of the electric signal versus the size of fractal structure and distance from the source is estimated. This dependence is applied for seismic electric signals (SES) occasionally observed prior to great crustal earthquakes. Interestingly enough the empirical dependence of the SES amplitude on earthquake magnitude can be explained solely by accounting for the scaling arguments. A special credit is paid to study the duration of the SES. The fluid migration is described by a generalized diffusion type equation in Euclidean spaces to fractal spaces. The use of this equation makes it possible to consider the envelope of the fluid pressure, which is, in fact, a non-analytic function. The SES duration is found to be the same order of magnitude as the time of fluid diffusion on fractal that is much greater than the duration of the electric current propagation in conductive medium.