TECHNICAL PAPERS
Sep 1, 2005

Electroseismic Wave Theory of Frenkel and More Recent Developments

Publication: Journal of Engineering Mechanics
Volume 131, Issue 9

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.

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References

Berge, P. A., Wang, H. F., and Bonner, B. P. (1993). “Pore-pressure buildup coefficient in synthetic and natural sandstones.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30, 1135–1141.
Biot, M. A. (1956a). “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range.” J. Acoust. Soc. Am., 28, 168–178.
Biot, M. A. (1956b). “Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range.” J. Acoust. Soc. Am., 28, 179–191.
Biot, M. A., and Willis, D. G. (1957). “The elastic coefficients of the theory of consolidation.” J. Appl. Mech., 24, 594–601.
Brown, R. J. S. (1980). “Connection between formation factor for electrical resistivity and fluid-solid coupling factor in Biot’s equations for acoustic wave in fluid-filled porous media.” Geophysics, 45, 1269–1275.
Frenkel, J. (1944). “On the theory of seismic and seismoelectric phenomena in a moist soil.” J. Phys. (USSR), 8, 230–241.
Garambois, S., and Dietrich, M. (2001). “Seismoelectric wave conversions in porous media: field measurements and transfer function analysis.” Geophysics, 66, 1417–1430.
Garambois, S., and Dietrich, M. (2002). “Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid-saturated stratified porous media.” J. Geophys. Res., 107, 40–58.
Gassmann, F. (1951). “Über die Elastizität poröser Medien.” Vierteljahrsschrift Naturforschenden Gesellschaft Zürich, 96, 1–23.
Haartsen, M. W., and Pride, S. R. (1997). “Electroseismic waves from point sources in layered media.” J. Geophys. Res., 102, 24745–24769.
Ivanov, A. G. (1939). “Effect of electrization of earth layers by by elastic waves passing through them.” Dokl. Akad. Nauk SSSR, 24, 42–45.
Johnson, D. L., Koplik, J., and Dashen, R. (1987). “Theory of dynamic permeability and tortuosity in fluid-saturated porous media.” J. Fluid Mech., 176, 379–402.
Kosten, C. W., and Zwikker, C. (1941). “Extended theory of the absorption of sound by compressible wall coverings.” Physica (Amsterdam), 8, 968–978.
Martner, S. T., and Sparks, N. R. (1959). “The electroseismic effect.” Geophysics, 24, 297–308.
Okada, Y. (1992). “Internal deformation due to shear and tensile faults in a half-space.” Bull. Seismol. Soc. Am., 82, 1018–1040.
Pride, S. R. (1994). “Governing equations for the coupled electromagnetics and acoustics of porous media.” Phys. Rev. B, 50, 15678–15696.
Pride, S. R., and Berryman, J. G. (1998). “Connecting theory to experiment in poroelasticity.” J. Mech. Phys. Solids, 46, 719–747.
Pride, S. R., and Haartsen, M. W. (1996). “Electroseismic wave properties.” J. Acoust. Soc. Am., 100, 1301–1315.
Pride, S. R., Moreau, F., and Gavrilenko, P. (2004). “Mechanical and electrical response due to fluid-pressure equilibration following an earthquake.” J. Geophys. Res., 109, B03302.
Skempton, A. W. (1954). “The pore-pressure coefficients A and B.” Geotechnique, 4, 143–147.
Thompson, A. H., and Gist, G. A. (1993). “Geophysical applications of electrokinetic conversion.” The Leading Edge, 12, 1160–1173.
von Smoluchowski, M. (1903). “Contribution à la théorie de l’endosmose électrique et de quelques phenomènes corrélatifs.” Bull. Int. Acad. Sci. Cracovie, 8, 182–200.

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Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 131Issue 9September 2005
Pages: 898 - 907

History

Received: Nov 11, 2003
Accepted: Jul 29, 2004
Published online: Sep 1, 2005
Published in print: Sep 2005

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Notes

Note. Associate Editor: Alexander H.-D. Cheng

Authors

Affiliations

Steven R. Pride [email protected].
Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (corresponding author). E-mail: [email protected].
Stephane Garambois [email protected]
LIRIGM, Maison des Geosciences, Univ. Joseph Fourier, 38041 Grenoble Cedex 9, France. E-mail: [email protected]

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