## Abstract

Tectonomagnetic modeling based on the linear piezomagnetic effect is reviewed with special attention to dislocation models. Stacey's scheme was the prototype for such modeling, as proposed in his first seismomagnetic calculations in 1964. The linear piezomagnetic law is presented, in which the stress-induced magnetization is expressed as a linear combination of stress components. The Gauss law for magnetic field and the Cauchy-Navier equation for static elastic equilibrium are combined through linear piezomagnetism and the Hooke law to yield the basic equation for piezomagnetic potential. A representation theorem for its solution is given by surface integrals of the displacement and its normal derivative over the strained body.

A Green's function method is developed to compute the piezomagnetic field produced by a dislocation surface in an elastic half-space. Volterra's formula for piezomagnetic potential is derived by modifying Stacey's scheme for tectonomagnetic modeling. The Green's functions for the problem are called elementary piezomagnetic potentials, which are defined as potentials produced by elementary dislocations. Special consideration is required to construct the elementary piezomagnetic potentials, because the stress field around a point dislocation has a singularity of order*r*
^{−3}. The integral representing elementary piezomagnetic potentials is not uniformly convergent. Owing to inappropriate convergency, the Green's functions obtained in an earlier study led to a puzzling outcome. Revised Green's functions give consistent results with those obtained so far by numerical integrations. Generally the piezomagnetic field produced by dislocation sources is weak in the case of a homogeneous earth model. Two enhancement effects for piezomagnetic signals are suggested: one due to inhomogeneous magnetization and the other via bore-hole observations.

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## References

Banks, P. O., Stuart, W. D. and Liu, S. W.: 1991, Piezomagnetic fields of screw dislocation fault models,

*J. Geophys. Res.*,**96**, 21575–21582.Bonafede, M. and Sabadini, R.: 1980, A theoretical approach to the seismomagnetic effect,

*Boll. Geof. Teor. Appl.*,**22**, 105–116.Christoffel, D. A.: 1989, Variations in magnetic field intensity at White Island volcano related to the 1976-82 eruption sequence,

*N. Z. Geol. Surv. Bull.*,**103**, 109–118.Davis, P. M.: 1974, The piezomagnetic computation of magnetic anomalies due to ground loading by a man-made lake,

*Pageoph*,**112**, 811–818.Davis, P. M.: 1976, The computed piezomagnetic anomaly field for Kilauea Volcano, Hawaii,

*J. Geomag. Geoelectr.*,**28**, 113–122.Fitterman, D. V.: 1979, Theory of electrokinetic-magnetic anomalies in a faulted half-space,

*J. Geophys. Res.*,**84**, 6031–6040.Hao, J. Q., Hastie, L. M. and Stacey, F. D.: 1982, Theory of the seismomagnetic effect: a reassessment,

*Phys. Earth Planet. Int.*,**28**, 129–140.Hao, J., Huang, P., Zhang, T., Xu, M., Zhou, J. and Ma, X.: 1990, The effect of stress on remanent magnetization of rocks,

*Acta Seism. Sinica*,**3**, 465–475.Henyey, T. L., Pike, S. J. and Palmer, D. F.: 1978, On the measurement of stress sensitivity of NRM using a cryogenic magnetometer,

*J. Geomag. Geoelectr.*,**30**, 607–617.Hildenbrand, T. G.: 1975, Seismomagnetism,

*Ph. D. Thesis*, Univ. California, Berkeley, 158pp.Johnston, M. J. S.: 1978, Local magnetic field observations and stress changes near a slip discontinuity on the San Andreas fault,

*J. Geomag. Geoelectr.*,**30**, 607–617.Johnston, M. J. S.: 1989, Review of magnetic and electric field effects near active faults and volcanoes in the U.S.A.,

*Phys. Earth Planet. Interiors*,**57**, 47–63.Johnston, M. J. S., Mueller, R. J. and Keller, V.: 1981, Preseismic and coseismic magnetic field measurements near the Coyote Lake, California, earthquake of August 6, 1979,

*J. Geophys. Res.*,**86**, 921–926.Johnston, M. J. S. and Mueller, R. J.: 1987, Seismomagnetic observation during the 8 July 1986 magnitude 5.9 North Palm Springs earthquake,

*Science*,**237**, 1201–1203.Martin, III, R. J., Habermann, R. E. and Wyss, M.: 1978, The effect of stress cycling and inelastic volumetric strain on remanent magnetization,

*J. Geomag. Geoelectr.*,**83**, 3485–3496.Maruyama, T.: 1964, Statical elastic dislocations in an infinite and semi-infinite medium,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**42**, 289–368.Mizutani, H. and Ishido, T.: 1976, A new interpretation of magnetic field variation associated with the Matsushiro earthquakes,

*J. Geomag. Geoelectr.*,**28**, 179–188.Mogi, K.: 1958, Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**36**, 99–134.Murakami, H.: 1989, Geomagnetic fields produced by electrokinetic sources,

*J. Geomag. Geoelectr.*,**41**, 221–247.Nagata, T.: 1943, The natural remanent magnetism of volcanic rocks and its relation to geomagnetic phenomena,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**21**, 1–196.Nagata, T.: 1969, Tectonomagnetism,

*I. A. G. A. Bull.*,**27**, 12–43.Nagata, T.: 1970, Basic magnetic properties of rocks under the effect of mechanical stresses,

*Tectonophysics*,**9**, 167–195.Ohshiman, N.: 1980, Local magnetic changes associated with fault activity,

*M. Sc. Thesis*, Tokyo Inst. Tech., 178pp.Okada, Y. and Yamamoto, E.: 1991, A model for the 1989 seismo-volcanic activity off Ito, central Japan, derived from crustal movement data,

*J. Phys. Earth*,**39**, 177–195.Okubo, S.: 1991, Potential and gravity changes raised by a point dislocation,

*Geophys. J. Int.*,**105**, 573–586.Oshiman, N.: 1990, Enhancement of tectonomagnetic change due to non-uniform magnetization in the Earth's crust - two dimensional case studies,

*J. Geomag. Geoelectr.*,**42**, 607–619.Oshiman, N., Honkura, Y., Sasai, Y., Ishikawa, Y., Utada, H., Koyama, S., Tanaka, Y. and Yukutake, Y.: 1991, Magnetometer array observation in the north-eastern Izu region after the Teisi Knoll seafloor eruption in 1989,

*J. Phys. Earth*,**39**, 321–328.Pozzi, J. P., Barthes, V., Thibal, J., Pocachard, J., Lim, M., Thomas, T., and Pages, G.: 1993, Downhole magnetostratigraphy in sediments: comparison with the paleomagnetism of a core,

*J. Geophys. Res.*,**98**, 7939–7957.Sasai, Y.: 1979, The piezomagnetic field associated with the Mogi model,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**54**, 1–29.Sasai, Y.: 1980, Application of the elasticity theory of dislocations to tectonomagnetic modelling,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**55**, 387–447.Sasai, Y.: 1983, A surface integral representation of the tectonomagnetic field based on the linear piezomagnetic effect,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**58**, 763–785.Sasai, Y.: 1986a, A Green's function for tectonomagnetic problems in an elastic half-space,

*J. Geomag. Geoelectr.*,**38**, 949–969.Sasai, Y.: 1986b, Multiple tension-crack model for dilatancy: surface displacement, gravity and magnetic changes,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**61**, 429–473.Sasai, Y.: 1991a, Piezomagnetic field associated with the Mogi model revisited: analytic solution for finite spherical source,

*J. Geomag. Geoelectr.*,**43**, 21–64.Sasai, Y.: 1991b, Tectonomagnetic modeling on the basis of the linear piezomagnetic effect,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**66**, 585–722.Sasai, Y.: 1994, Resolution of contradiction between seismomagnetic models,

*J. Geomag. Geoelectr.*,**46**,*in print.*Sasai, Y., Shimomura, T., Hamano, Y., Utada, H., Yoshino, T., Koyama, S., Ishikawa, Y., Nakagawa, I., Yokoyama, Y., Ohno, M., Watanabe, H., Yukutake, T., Tanaka, Y., Yamamoto, T., Nakaya, K., Tsunomura, S., Muromatsu, F. and Murakami, R.: 1989, Volcanomagnetic effect observed during the 1986 eruption of Izu-Oshima volcano,

*J. Geomag. Geoelectr.*,**42**, 291–317.Sasai, Y. and Ishikawa, Y.: 1991, Tectonomagnetic signals related to the seismo-volcanic activity in the Izu Peninsula,

*J. Phys. Earth*,**39**, 299–319.Shamsi, S. and Stacey, F. D.: 1969, Dislocation models and seismomagnetic calculations for California 1906 and Alaska 1964 earthquakes,

*Bull. Seism. Soc. Amer.*,**59**, 1435–1448.Shapiro, V. A., Pushkov, A. N., Abdulabekov, K. N., Berdaliev, E. B. and Miminov, M. Yu.: 1978, Geomagnetic investigation in the seismoactive regions of middle Asia,

*J. Geomag. Geoelectr.*,**30**, 503–509.Shapiro, V. A. and Abdulabekov, K. N.: 1982, Anomalous variations of the geomagnetic field in East Fergana - magnetic precursor of the Alay earthquake with M7.0 (1978 November 21),

*Geophys. J. R. astr. Soc.*,**68**, 1–5.Stacey, F. D.: 1964, The seismomagnetic effect,

*Pageoph*,**58**, 5–22.Stacey, F. D., Barr, K. G. and Robson, G. R.: 1965, The volcanomagnetic effect,

*Pageoph.*,**62**, 96–104.Stacey, F. D. and Johnston, M. J. S.: 1972, Theory of the piezomagnetic effect in titanomagnetite-bearing rocks,

*Pageoph*,**97**, 146–155.Steketee, J. A.: 1958, Some geophysical applications of the elasticity theory of dislocations,

*Can. J. Phys.*,**36**, 1168–1198.Suzuki, Y. and Oshiman, N.: 1990, A paradox in volcanomagnetism: Disagreement between analytical and numerical estimates of geomagnetic changes due to an underground pressure nucleus,

*J. Geomag. Geoelectr.*,**42**, 1291–1308.Talwani, P. and Kovach, R. L.: 1972, Geomagnetic observations and fault creep in California,

*Tectonophysics*,**14**, 245–256.Tanaka, Y.: 1993, Eruption mechanism as inferred from geomagnetic changes with special attention to the 1989–1990 activity of Aso volcano,

*J. Volc. Geotherm. Res.*,**56**, 319–338.Yukutake, T. and Tachinaka, H.: 1967, Geomagnetic variation assocated with stress change within a semi-infinite elastic earth caused by a cylindrical force source,

*Bull. Earthq. Res. Inst., Univ. Tokyo*,**45**, 785–798.Zhan, Z.: 1989, Investigation of tectonomagnetic phenomena in China,

*Phys. Earth Planet. Interiors*,**57**, 11–22.Zlotnicki, J., Pozzi, J. P. and Cornet, F. H.: 1981, Investigation of induced magnetization variations caused by triaxial stresses,

*J. Geophys. Res.*,**86**, 11899–11909.Zlotnicki, J. and Cornet, F. H.: 1986, A numerical model of earthquake-induced piezomagnetic anomalies,

*J. Geophys. Res.*,**91**, 709–718.Zlotnicki, J. and Le Mouel, J. L.: 1990, Possible electrokinetic origin of large magnetic variations at la Fournaise volcano,

*Nature*,**343**, 633–636.

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Sasai, Y. Piezomagnetic fields produced by dislocation sources.
*Surv Geophys* **15, **363–382 (1994). https://doi.org/10.1007/BF00665998

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### Key words

- Linear piezomagnetic effect
- Tectonomagnetism
- Seismomagnetic effect
- Elasticity theory of dislocations
- Representation theorem
- Volterra's formula
- Elementary piezomagnetic potentials