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Time dependent piezomagnetic fields in viscoelastic medium
Language
English
Obiettivo Specifico
3.6. Fisica del vulcanismo
Status
Published
JCR Journal
JCR Journal
Title of the book
Issue/vol(year)
2/172 (2008)
Publisher
Blakwell Publishing
Pages (printed)
536-548
Issued date
February 2008
Last version
http://hdl.handle.net/2122/3080
Keywords
Abstract
We investigated time dependent piezomagnetic fields due to volcanic sources embedded in a
viscoelastic, homogeneous half-space. Especially in volcanic areas, the presence of inhomogeneous
materials and high temperatures produce a lower effective viscosity of the Earth’s
crust that calls for considering anelastic properties of the medium. Piezomagnetic properties
are carried by grains of titano-magnetite, which occupy only a small fraction of ordinary rock
volume and are supposed to be elastic, while the non-magnetic surrounding matrix is assumed
to be viscoelastic. From all the possible rheological models, we investigated two cases in which
the bulk modulus is purely elastic and the shear modulus relaxes as: (i) a Maxwell solid and
(ii) a standard linear solid (SLS). We applied the Correspondence Principle to the analytical
elastic solutions for pressurized spherical sources and dislocation sources in order to determine
the time dependent piezomagnetic fields in a viscoelastic medium. The piezomagnetic field
completely vanishes after the relaxation process for a Maxwell rheology, whereas it is found
to decrease over time and reach some finite offset value for a SLS rheology. These different
behaviours provide helpful hints in understanding the temporal evolution of piezomagnetic
anomalies in volcanic regions.
viscoelastic, homogeneous half-space. Especially in volcanic areas, the presence of inhomogeneous
materials and high temperatures produce a lower effective viscosity of the Earth’s
crust that calls for considering anelastic properties of the medium. Piezomagnetic properties
are carried by grains of titano-magnetite, which occupy only a small fraction of ordinary rock
volume and are supposed to be elastic, while the non-magnetic surrounding matrix is assumed
to be viscoelastic. From all the possible rheological models, we investigated two cases in which
the bulk modulus is purely elastic and the shear modulus relaxes as: (i) a Maxwell solid and
(ii) a standard linear solid (SLS). We applied the Correspondence Principle to the analytical
elastic solutions for pressurized spherical sources and dislocation sources in order to determine
the time dependent piezomagnetic fields in a viscoelastic medium. The piezomagnetic field
completely vanishes after the relaxation process for a Maxwell rheology, whereas it is found
to decrease over time and reach some finite offset value for a SLS rheology. These different
behaviours provide helpful hints in understanding the temporal evolution of piezomagnetic
anomalies in volcanic regions.
References
Bonafede, M., Dragoni, M. & Quareni, F., 1986. Displacement and stress
fields produced by a pressure source in a viscoelastic half-space: application
to the study of ground deformation and seismic activity at Campi
Flegrei, Italy, Geophys. J. R. astr. Soc., 87, 455–485.
Christensen, R.M., 1971. Theory of Viscoelasticity: An Introduction, Academic
Press, New York.
Christensen, R.M., 1982. Theory of Viscoelasticity: An Introduction, 2nd
edn, 364 pp., Academy Press, New York.
Currenti, G., Del Negro, C. & Ganci, G., 2007a. Modelling of ground deformation
and gravity fields using finite element method: an application to
Etna volcano, Geophys. J. Int., doi:10.1111/j.1365-246X.2007.03380.x.
Currenti, G., Del Negro, C., Johnston, M.&Sasai,Y., 2007b. Close temporal
correspondence between geomagnetic anomalies and earthquakes during
the 2002–2003 eruption of Etna volcano, J. geophys. Res., 112, B09103,
doi:10.1029/2007JB005029.
Del Negro, C. & Currenti, G., 2003. Volcanomagnetic signals associated
with the 2001 flank eruption of Mt. Etna (Italy), Geophys. Res. Lett.,
30(7), 1357.
Del Negro, C. & Napoli, R., 2004. Magnetic field monitoring at Mt. Etna
during the last 20 years, in Etna Volcano Laboratory pp. 241–262, eds
Calvari, S., Bonaccorso, A., Del Negro, C. L. & Falsaperla, S., AGU,
Geophysical monograph series.
Del Negro, C., Currenti, G., Napoli, R. & Vicari, A., 2004. Volcanomagnetic
changes accompanying the onset of the 2002–2003
Eruption of Mt. Etna (Italy), Earth Planet. Sci. Lett., 229, 1–14,
doi:10.1016/j.epsl.2004.10.033.
Dragoni, M. & Magnanensi, C., 1989. Displacement and stress produced
by a pressurized, spherical magma chamber, surrounded by a viscoelastic
shell, Phys. Earth Planet. Inter, 56, 316–328.
Fernandez, J., Tiampo, K.F. & Rundle, J.B., 2001. Viscoelastic displacement
and gravity changes due to point magmatic intrusions in a gravitational
layered solid earth, Geophys. J. Int., 146, 155–170.
Folch, A., Fernandez, J., Rundle, J.B. & Marti, J., 2000. Ground deformation
in a viscoelastic medium composed of a layer overlying a half-space: a
comparison between point and extended sources, Geophys. J. Int., 140,
37–50.
Fung, Y.C., 1965. Foundations of Solid Mechanics, Prentice-Hall, Englewood
Cliffs. Japanese traslation by Y. Ohashi, S. Murakami and N.
Kamiya, 1970, Baifukan, 524 pp.
Johnston, M.S., 2002. Electromagnetic fields generated by earthquakes, International
Handbook of Earthquake and Engineering Seismology, 81,
621–635.
Lee, E., 1955. Stress analysis in viscoelastic bodies, Quart. J. Appl. Math.,
13, 183–190.
Nagata, T., 1970. Basic magnetic properties of rocks under mechanical
stresses, Tectonophysics, 9, 167–195.
Newman, A.V., Dixon,T.H., Ofoegbu, G.I.&Dixon, J.E., 2001. Geodetic and
seismic constraints on recent activity at Long Valley Caldera, California:
evidence for viscoelastic rheology, Jour. Volcan. Geother. Res., 105, 183–
206.
Peltier,W.R., 1974. The impulse response of a Maxwell earth, Rev. Geophys.
Space Phys., 12, 649–669.
Piombo, A., Tallarico, A. & Dragoni, M., 2007. Displacement, strain and
stress fields due to shear and tensile dislocations in a viscoelastic halfspace,
Geophys. J. Int., doi:10.1111/j.1365-246X.2007.03283.x
Pozzi, J.P., 1977. Effects of stresses on magnetic properties of volcanic rocks,
Phys. Earth Planet. Int., 14, 77–85.
Okubo, A. & Oshiman, N., 2004. Piezomagnetic field associated with a
numerical solution of the Mogi model in a non-uniform elastic medium,
Geophys. J. Int., 159, 509–520.
Rundle, J.B., 1978. Viscoelastic crustal deformation by finite quasi-static
sources, J. geophys. Res., 83, 5939–5945.
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., 1986. A Green’s function for tectonomagnetic problems in an
elastic half-space, J. Geomag. Geoelectr., 38, 949–969.
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, 65, 585–
722.
Sasai, Y., Uyeshima, M., Zlotnicki, J., Utada, H., Kagiyama, T., Hashimoto,
T. & Takahashi, T., 2002. Magnetic and electric eld observations durino
the 2000 activity of Miyake-jima volcano, Central Japan, Earth Planet.
Sci. Lett., 203, 769–777.
Trasatti, E., Giunchi, C. & Bonafede, M., 2003. Effects of elastic and rheological
layering on ground deformation in volcanic regions, J. Volcan.
Geotherm. Res., 122, 89–110.
Utsugi, M., Nishida, Y. & Sasai, Y., 2000. Piezomagnetic potentials due to
an inclined rectangular fault in a semi-infinite medium, Geophys. J. Int.,
140, 479–492.
fields produced by a pressure source in a viscoelastic half-space: application
to the study of ground deformation and seismic activity at Campi
Flegrei, Italy, Geophys. J. R. astr. Soc., 87, 455–485.
Christensen, R.M., 1971. Theory of Viscoelasticity: An Introduction, Academic
Press, New York.
Christensen, R.M., 1982. Theory of Viscoelasticity: An Introduction, 2nd
edn, 364 pp., Academy Press, New York.
Currenti, G., Del Negro, C. & Ganci, G., 2007a. Modelling of ground deformation
and gravity fields using finite element method: an application to
Etna volcano, Geophys. J. Int., doi:10.1111/j.1365-246X.2007.03380.x.
Currenti, G., Del Negro, C., Johnston, M.&Sasai,Y., 2007b. Close temporal
correspondence between geomagnetic anomalies and earthquakes during
the 2002–2003 eruption of Etna volcano, J. geophys. Res., 112, B09103,
doi:10.1029/2007JB005029.
Del Negro, C. & Currenti, G., 2003. Volcanomagnetic signals associated
with the 2001 flank eruption of Mt. Etna (Italy), Geophys. Res. Lett.,
30(7), 1357.
Del Negro, C. & Napoli, R., 2004. Magnetic field monitoring at Mt. Etna
during the last 20 years, in Etna Volcano Laboratory pp. 241–262, eds
Calvari, S., Bonaccorso, A., Del Negro, C. L. & Falsaperla, S., AGU,
Geophysical monograph series.
Del Negro, C., Currenti, G., Napoli, R. & Vicari, A., 2004. Volcanomagnetic
changes accompanying the onset of the 2002–2003
Eruption of Mt. Etna (Italy), Earth Planet. Sci. Lett., 229, 1–14,
doi:10.1016/j.epsl.2004.10.033.
Dragoni, M. & Magnanensi, C., 1989. Displacement and stress produced
by a pressurized, spherical magma chamber, surrounded by a viscoelastic
shell, Phys. Earth Planet. Inter, 56, 316–328.
Fernandez, J., Tiampo, K.F. & Rundle, J.B., 2001. Viscoelastic displacement
and gravity changes due to point magmatic intrusions in a gravitational
layered solid earth, Geophys. J. Int., 146, 155–170.
Folch, A., Fernandez, J., Rundle, J.B. & Marti, J., 2000. Ground deformation
in a viscoelastic medium composed of a layer overlying a half-space: a
comparison between point and extended sources, Geophys. J. Int., 140,
37–50.
Fung, Y.C., 1965. Foundations of Solid Mechanics, Prentice-Hall, Englewood
Cliffs. Japanese traslation by Y. Ohashi, S. Murakami and N.
Kamiya, 1970, Baifukan, 524 pp.
Johnston, M.S., 2002. Electromagnetic fields generated by earthquakes, International
Handbook of Earthquake and Engineering Seismology, 81,
621–635.
Lee, E., 1955. Stress analysis in viscoelastic bodies, Quart. J. Appl. Math.,
13, 183–190.
Nagata, T., 1970. Basic magnetic properties of rocks under mechanical
stresses, Tectonophysics, 9, 167–195.
Newman, A.V., Dixon,T.H., Ofoegbu, G.I.&Dixon, J.E., 2001. Geodetic and
seismic constraints on recent activity at Long Valley Caldera, California:
evidence for viscoelastic rheology, Jour. Volcan. Geother. Res., 105, 183–
206.
Peltier,W.R., 1974. The impulse response of a Maxwell earth, Rev. Geophys.
Space Phys., 12, 649–669.
Piombo, A., Tallarico, A. & Dragoni, M., 2007. Displacement, strain and
stress fields due to shear and tensile dislocations in a viscoelastic halfspace,
Geophys. J. Int., doi:10.1111/j.1365-246X.2007.03283.x
Pozzi, J.P., 1977. Effects of stresses on magnetic properties of volcanic rocks,
Phys. Earth Planet. Int., 14, 77–85.
Okubo, A. & Oshiman, N., 2004. Piezomagnetic field associated with a
numerical solution of the Mogi model in a non-uniform elastic medium,
Geophys. J. Int., 159, 509–520.
Rundle, J.B., 1978. Viscoelastic crustal deformation by finite quasi-static
sources, J. geophys. Res., 83, 5939–5945.
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., 1986. A Green’s function for tectonomagnetic problems in an
elastic half-space, J. Geomag. Geoelectr., 38, 949–969.
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, 65, 585–
722.
Sasai, Y., Uyeshima, M., Zlotnicki, J., Utada, H., Kagiyama, T., Hashimoto,
T. & Takahashi, T., 2002. Magnetic and electric eld observations durino
the 2000 activity of Miyake-jima volcano, Central Japan, Earth Planet.
Sci. Lett., 203, 769–777.
Trasatti, E., Giunchi, C. & Bonafede, M., 2003. Effects of elastic and rheological
layering on ground deformation in volcanic regions, J. Volcan.
Geotherm. Res., 122, 89–110.
Utsugi, M., Nishida, Y. & Sasai, Y., 2000. Piezomagnetic potentials due to
an inclined rectangular fault in a semi-infinite medium, Geophys. J. Int.,
140, 479–492.
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