A Basic overview

Background

The first work done that contributed to the development of the electro-seismic effect was done in 1944 by Frenkel. He described the relative flow of fluid to the matrix brought about by the passage of a compression seismic wave through the medium. He investigated the induced electric fields generated by this relative motion of fluid, matrix interaction with Helmholtz-Smoluchowski equations. However, his investigations did not fully explain this relationship. In 1964, Biot made further progress by developing theories that predicted movement of a seismic wave through a saturated porous media. Various advances toward the development of a general equation describing the link between the relative fluid matrix interaction, and the electro-magnetic fields induced by this motion, were formulated between 1962 and 1994. These developments include irreversible thermodynamic coupling effects in porous media and averaging of fluid volume to determine the governing equations of the electro seismic effect. Then in 1995, Haartsen and Pride explained the electromagnetic field induced by the fluid motion relative to a porous matrix as being generated by dynamic current imbalances. These current imbalances are generated by plane sheer waves moving across and interface between rocks with different electro seismic properties. These net current imbalances induce an electromagnetic field which can be read at the surface as an interface response. However, if the plain sheer waves pass through a homogeneous saturated medium, with no interfaces of different electro kinetic properties, then the net currents induced will be balanced and cancel each other out. This essentially means there is no current flow induced by the relative motion of the fluid and matrix. This means no electromagnetic fields are induced that can be read at the surface. In 1997 Haartsen and Pride made use of their findings on electromagnetic interface response to investigate electro kinetic waves from single point sources in layered rock formations. They discovered saturated media interfaces produced a response equivalent to that of a dipole induced field on the interface directly under the seismic point source. In 1980, Chandler used a theoretical model and saturated core samples in laboratory experiments to relate the rise time of electro seismic signals to permeability. However, Haartsen in 1998 proved that the electro seismic response is a function of the salinity, porosity and permeability of a porous elastic media.

The electric double layer

Grains of rock display net electric charges on their surfaces due to unsatisfied chemical bonds. In an aquifer, water makes contact with these charged surfaces and an electric potential is produced, since water is also electrolytic in nature. This potential difference then draws the free ions in the water toward the surface of the grain of rock where an electric double layer is formed. An electric double layer consists of a layer of ions drawn into the solid surface by electrostatic Van der Waal forces.  This inner layer is called the Stern layer, while the outer layer consists of free ions in the water drawn in by the potential difference across the rock grain surface. This outer layer is called the Gouy layer. The Stern layer is only one ion thick and as shown in Figure 1, the electric potential drops sharply across this layer. Boltzmann distributions can be used to describe the concentrations of ions in the Gouy layer, provided that the electrolytic content in the water is lower than 0.1 moles per liter. The electric potential in this layer of diffused ions is described by the following equation:

Where:

k = inverse Debye radius

x = distance from the charged surface

The slipping plane is the area where relative movement between the solid and water allow for motion between the outer diffused layer of ions and the inner strongly bound ions. This slipping plane has an electric potential across it that is called the zeta (z) potential. This electric potential is produced by the shearing between the inner and outer ions of the Stern and Gouy Layers. The Zeta potential plays an important role in the electro kinetic effect and is part of the equation used to determine the electromagnetic coupling tensor, which in turn determines the magnitude of the electromagnetic field induced.

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The electro-seismic effect

The electro seismic effect can be observed when a fast traveling p wave intersects a water saturated interface of differing anelastic or electrical properties. The electro seismic effect is in effect a form of converted energy which is released as dissipated energy. This conversion of energy takes place when a fast moving P waves produce slower P waves as it passes through the interface. These slow P waves produce much more movement between the rock and water. This in turn leads to a high loss of energy in the form of heat due to friction and electro seismic effects, such as electromagnetic radiation due to ionic movement. Electro seismic signals are produced by the out of phase motion between all the ions in the water and those attached to the rock. The relationship between applied pressure P and electric potential response f for a porous rock is generally given by the following equation (Millar and Clarke 1997):

Where,

f = electrical potential response or streaming potential

C = electro-kinetic coefficient

P = applied pressure

ee0 = permittivity of the pore space

z = zeta potential

h = fluid viscosity

s = electrical conductivity

This equation relates the electrical potential response f developed in a porous rock to the stimulus of an incident pressure change P, allowing the rock to be characterized by C on a macroscopic scale when modelling such electro-kinetic responses. To see how the electro-seismic function is derived please refer to Fourie’s dissertation on electro-seismic field theory 2003[6].

Wave Behavior

A seismic wave propagating in a medium can induce an electrical field or cause radiation of an electromagnetic wave. There are two electro-seismic effects that are considered in this report. The first effect is caused when a seismic wave crosses an interface between two media. When the spherical P-wave crosses the interface, it creates a dipole charge separation due to the imbalance of the streaming as shown in Figure 2. The second effect is caused when a seismic head wave travels along an interface between two media. It creates a charge separation across the interface, which induces an electrical field. This electric field moves along the interface with the head wave and can be detected by antennas when the head wave passes underneath as shown in Figure 3. Currents induced by the seismic wave on opposite sides of the interface. The electrical dipole radiates an EM wave which can be detected by remote antennas

Seismic wave crossing an interface generating an electromagnetic wave

Seismic wave crossing an interface generating an electromagnetic wave

Head wave traveling along an interface generating an electric field

Head wave traveling along an interface generating an electric field


References

1. Biot, M. A. (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. Journal of the Acoustical Society of America.

2. Biot, M. A. (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. Journal of the Acoustical Society of America.

3. Biot, M. A. (1962) Generalized theory of acoustic propagation in porous dissipative media. Journal of the Acoustical Society of America.

4. Botha, J. F., Verwey, J. P., Van der Voort, I., Vivier, J. J. P., Colliston, W. P. and Loock, J. C. (1998) Karoo Aquifers. Their Geology, Geometry and Physical Behaviour. Water Research Commission.

5. Butler, K. E., Russell, R. D. and Kepic, A. W. (1996) Measurement of the seismoelectric response from a shallow boundary. Geophysics.

6. Fourie, F. D. (2000) An Introduction to Geophysics for Geohydrologists. Unpublished lecture notes. Institute for Groundwater Studies, University of the Orange Free State.

7. Garambois, S. and Dietrich, M. (2001) Seismo-electric wave conversion in porous media: Field measurements and transfer function analysis. Geophysics.

8. Haartsen, M. W. and Pride, S. R. (1997) Electroseismic waves from point sources in layered media. Journal of Geophysical Research.

9. Haartsen, M. W., Dong, W. and Toksöz, M. N. (1998) Dynamic streaming currents from seismic point sources in homogeneous poroelastic media. Geophysical Journal International.

10. Ishido, T. (1981) Experimental and theoretical basis of electrokinetic phenomena in rockwater systems and its application to Geophysics. Journal of Geophysical Research.

11. Kepic, A. W., Maxwell, M. and Russell, R. D. (1995) Field trials of a seismoelectric method for detecting massive sulphides. Geopysics.

12. Martner, S. T. and Sparks, N. R. (1959) The electroseismic effect. Geophysics.

13. Maxwell, M., Russell, R. D., Kepic, A. W. and Butler, K. E. (1992) Electromagnetic responses from seismically excited targets B: Non-piezoelectric phenomena. Exploration geophysics.

14. Mikhailov, O. V., Haartsen, M. W. and Toksöz, M. N. (1997) Electroseismic investigation of the shallow subsurface: Field measurements and numerical modelling. Geophysics.

15. Millar, J. W. A. and Clarke, R. H. (1997) Electrokinetic techniques for hydrogeological site investigations. Groundflow

16. Pride, S. R. (1994) Governing equations for the coupled electromagnetics and acoustics of porous media.

17. Pride, S. R. and Haartsen, M. W. (1996) Electroseismic wave properties. Journal of the Acoustical Society of America.

18. Pride, S. R. and Morgan, F. D. (1991) Electrokinetic dissipation induced by seismic waves. Geophysics.

19. Ranada Shaw, A., Denneman, A. I. M. and Wapenaar, C. P. A. (2000) Porosity and permeability effects on seismo-electric reflection. In: Proceedings of the EAGE conference.

20. Russell, R. D., Butler, K. E., Kepic, A. W. and Maxwell, M. (1997) Seismoelectric exploration. The Leading Edge.

21. Rosenberg, M., Wallin, E., Bannister, S., Bourguigon, S., Jolly, G., Mroczek, E., Milicich, S., Graham, D., Bromley, C., Reeves, R., Bixley, P., Clothworthy, A., Carey, B., Climo, M. (2010) Tauhara Stage || Geothermal Project: Geoscience Report, GNS Science Consultancy Report 2010/138.

22. Du Preez, M. (2005) Accuracy of Electro-Seismic Techniques Applied to Groundwater Investigations in Karoo Formations. Master Thesis: University of the Free State