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Geomagnetic Induction Studies This article was originally published in Treatise on Geophysics, Second Edition, published by Elsevier, and the attached copy is provided by Elsevier for the author's benefit and for the benefit of the author's institution, for non-commercial research and educational use including without limitation use in instruction at your institution, sending it to specific colleagues who you know, and providing a copy to your institution’s administrator. All other uses, reproduction and distribution, including without limitation commercial reprints, selling or licensing copies or access, or posting on open internet sites, your personal or institution’s website or repository, are prohibited. For exceptions, permission may be sought for such use through Elsevier's permissions site at: http://www.elsevier.com/locate/permissionusematerial Constable S Geomagnetic Induction Studies. In: Gerald Schubert (editor-in-chief) Treatise on Geophysics, 2nd edition, Vol 5. Oxford: Elsevier; 2015. p. 219-254. Author's personal copy 5.07 Geomagnetic Induction Studies S Constable, University of California San Diego, La Jolla, CA, USA ã 2015 Elsevier B.V. All rights reserved. 5.07.1 Geomagnetic Induction Studies 220 5.07.1.1 Historical Beginnings 220 5.07.1.2 The Earth’s Geomagnetic Environment 220 5.07.1.3 Earth/ionosphere cavity 221 5.07.1.4 Daily variation and Sq 222 5.07.1.5 The magnetospheric ring current 222 5.07.1.6 Pulsations 223 5.07.2 Geomagnetic Sounding 223 5.07.2.1 Introductory Theory 223 5.07.2.2 The MT Method 224 5.07.2.3 MT in Practice 225 5.07.2.4 Equipment 225 5.07.2.4.1 Electric field measurements 225 5.07.2.4.2 Magnetic field measurements 226 5.07.2.5 MT Data Processing 227 5.07.2.6 Global Conductivity Studies 228 5.07.2.7 Global Response Functions 228 5.07.2.7.1 Using magnetic satellites 229 5.07.3 Interpretation of GDS and MT Data 230 5.07.3.1 Forward Model Studies 230 5.07.3.2 Parameterized Inversion 230 5.07.3.3 Regularized Inversion 231 5.07.3.4 Analytic Least Squares Solutions 231 5.07.3.5 MT over a Layered Earth 231 5.07.3.5.1 Weidelt’s transformation 231 5.07.3.6 Forward Modeling in Higher Dimensions 231 5.07.3.7 Numerical Inversion of Geomagnetic Data 232 5.07.3.8 Analytic Inversion and Estimation of Bounds 233 5.07.4 Electric Conductivity of Earth Materials 234 5.07.4.1 Moving an Electric Charge 234 5.07.4.1.1 Conduction in native metals 234 5.07.4.1.2 Semiconduction 235 5.07.4.1.3 Ionic, or point defect, conduction 235 5.07.4.1.4 Pressure 236 5.07.4.1.5 Aqueous electrolytic conduction 237 5.07.4.1.6 Clay minerals 237 5.07.4.1.7 Magma 237 5.07.4.2 Binary Mixing Laws 237 5.07.4.3 Polarization 238 5.07.4.4 Anisotropy 238 5.07.4.4.1 Crystallographic anisotropy 238 5.07.4.4.2 Textural anisotropy 238 5.07.4.4.3 Structural anisotropy 238 5.07.4.5 Laboratory Measurement of Conductivity 238 5.07.4.6 High-Pressure Measurements 241 5.07.4.7 Thermopower Measurements 241 5.07.4.8 Conductivity of Mantle Minerals 242 5.07.4.9 Olivine Conductivity 242 5.07.5 Global Conductivity Structure 244 5.07.5.1 The Oceans and Crust 244 5.07.5.2 The Mantle 247 5.07.5.2.1 Melt 248 5.07.5.2.2 Carbon 248 5.07.5.2.3 Strain-induced defects 249 Treatise on Geophysics, Second Edition http://dx.doi.org/10.1016/B978-0-444-53802-4.00101-9 219 Treatise on Geophysics, 2nd edition, (2015), vol. 5, pp. 219-254 Author's personal copy 220 Geomagnetic Induction Studies 5.07.5.2.4 Water 249 5.07.5.2.5 Oxides and sulfides 249 5.07.5.3 The Core 250 5.07.6 Conclusions 251 5.07.6.1 3D Conductivity from Satellite Data 251 5.07.6.2 Water in the Mantle 251 5.07.6.3 Anisotropy Measurements 252 Acknowledgment 252 References 252 5.07.1 Geomagnetic Induction Studies Induction effects associated with magnetic storms were first seen in telegraph cables, the storm of 1838 being seen on The interaction of temporal fluctuations in the Earth’s external Norwegian telegraph cables; in telegraph lines in England, magnetic field with the electrically conductive rocks of the spontaneous currents reported by W.H. Barlow (1849); and planet generates internal secondary electric and magnetic fields. in an observation by Clement (1859) that the aurora of The measurements of the primary and secondary fields may 29 August disrupted telegraphy. The critical mathematical then be used to probe the conductivity structure over depths developments started in 1839 with Gauss’ spherical harmonic from a few meters to the lower mantle. Conductivity in turn may expansion of the main magnetic field, which allows the sepa- be used to infer physical and chemical properties, such as tem- ration of internal and external magnetic sources, and later perature, melt content, water and volatile content, mineral type, (1864) with Maxwell’s equations of electromagnetism. In and anisotropic fabric. There are three basic steps necessary to 1865, the Greenwich Observatory started to observe Earth obtain useful information from geomagnetic induction studies: potentials on 15 km grounded lines. the estimation of electromagnetic impedances from observa- By early in the twentieth century, the relationship between tions of the electric and magnetic fields, the modeling of these magnetic activity and Earth currents was well known. Schuster impedances in both forward (conductivity to impedance) and and Lamb (1889) observed the relationship between the diur- inverse (impedance to conductivity) directions, and, finally, the nal magnetic variation and Earth potentials, and Chapman use of laboratory studies to relate conductivity to the relevant (1919) inferred that the Earth’s interior must be more conduc- physical and chemical properties. Each of these steps represents tive than crustal rocks and modeled the daily variation with a significant scientific challenges, and all of them are the subject of conductive sphere of smaller radius than the Earth’s. Although current research and recent progress. Clearly, the results of each Chapman and Bartels (1940) lamented that a more quantita- of these components depend on the quality of the preceding tive relationship between electric conductivity and magnetic step, and conclusions about the state of the Earth’s interior field variation was not yet available, progress in this direction depend on the reliability of all three parts of the process. was being made. Lahiri and Price (1939) modeled the internal Electromagnetic induction covers a very broad field that and external parts of the magnetic field using a radial conduc- includes applications in exploration, environmental and min- tivity profile to a depth of nearly 1000 km. Later, Banks (1969) ing geophysics, and studies of the Earth’s deep interior. proposed that the harmonics of the 27-day solar rotation were 0 Although many of the underlying principles span the entire dominantly of P1 spherical harmonic geometry, associated range of applications, in the context of Treatise on Geophysics, with the ring of current in the magnetosphere above the geo- we will concentrate on the ‘whole-Earth’ aspects of geomag- magnetic equator, and produced a conductivity profile down netic induction. For a good discussion of exploration and to nearly 2000 km. In order to get an estimate of the electric crustal applications, the reader is referred to the book by conductivity of the lowermost mantle, McDonald (1957) Simpson and Bahr (2005). modeled the outward propagation of an inferred geomagnetic secular variation signal originating in the core. Figure 1 sum- marizes the results of this early work. 5.07.1.1 Historical Beginnings These observations represent the beginnings of the geomag- netic depth-sounding (GDS) method, in which magnetic fields The history of geophysical electromagnetic induction is alone are used to probe the Earth’s conductivity. Another highly entwined with the development of the fundamental physics important method, magnetotelluric (MT) sounding, began in of electromagnetic energy, closely following Oersted’s 1820 the early 1950s when Tikhonov (1950) and Cagniard (1953) observation that an electric current deflected a magnet and quantified the relationship between induced electric currents Ampere’s quantification of this phenomenon in the 1820s. and the magnetic field. Both the GDS and MT methods are in Ampere also noted that an electric current exerts a force on a extensive use today, and we will discuss them in this chapter. second electric current and that a coil behaved like a magnetic dipole. In 1831, Faraday observed that moving a magnet through a coil produces an electric current, and in 1832, he 5.07.1.2 The Earth’s Geomagnetic Environment predicted that water moving through a magnetic field should produce an electric field, an effect that was observed by the Temporal variations in the Earth’s magnetic field exist on all British Admiralty much later in 1918. timescales from radio frequencies to the reversal record Treatise on Geophysics, 2nd edition, (2015), vol. 5, pp. 219-254 Author's personal copy Geomagnetic Induction Studies 221 (Figure 2). Electromagnetic induction methods can exploit become smaller as period increases, periods of a few weeks or only those fields that are externally generated, which in prin- shorter for MT methods. As mentioned in Section 5.07.1, the ciple means periods shorter than about 1 year for GDS propagation of internally generated fields of the secular varia- methods (with the possible exception of the 11-year sunspot tion upward through the mantle may be used to estimate cycle) and, because the induced electric field components conductivity (Alexandrescu et al., 1999; McDonald, 1957; Pinheiro and Jackson, 2008), but the lack of an independent estimate of the source-field timing limits this approach (Backus, 1983).
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