Electromagnetic Induction by Ocean Currents and the Conductivity of the Oceanic Lithosphere

Transcription

1 J. Geomag. Geoelectr., 35, , 1983 Electromagnetic Induction by Ocean Currents and the Conductivity of the Oceanic Lithosphere Alan D. CHAVE* and Charles. S. Cox** *Institute of Geophysics and Planetary Physicș University of California at San Diego, La Jolla, CA 92093, U.S.A. **Scripps Institution Oceanography, University of California at San Diego, La Jolla, CA 92093, U. S. A. (Received August 15, 1983) The principles of electromagnetic induction in the earth by ocean currents are reviewed with an emphasis on their interaction with the conducting earth and their modal structure. This is illustrated theoretically by examining a Kelvin wave off of the California coast and experimentally by separating seafloor measurements into ionospheric and oceanic parts. An attempt is made to estimate the electrical conductivity of the oceanic lithosphere from the polarization of the magnetotelluric fields near coastlines, yielding an upper limit of 0.001S/m. Possible interpretations of this value in terms of local current channeling are discussed. 1. Introduction Electromagnetic fields are induced in the earth by external, ionospheric and magnetospheric, current systems and have long been used to investigate the electrical conductivity of the earth by the magnetotelluric or geomagnetic depth sounding methods. In the world oceans an additional, internal electromagnetic source, the dynamo interaction of the water velocity field with the ambient geomagnetic field, can produce electromagnetic fields that are as large as their ionospheric counterparts through most of the frequency spectrum. Since the flow structure of the oceans is known only in a coarse sense, the spatial morphology and modal structure of these ocean-induced electromagnetic fields is poorly determined, and they are usually neglected in oceanic electromagnetic studies. In this paper, we will review the major principles of electromagnetic induction by fluid motion as they apply to the ocean. Emphasis will be placed on the modal form of the electromagnetic fields and on the very different sensitivity the two modes have to the electrical conductivity of the lithosphere underlying the ocean. A feature of motional electromagnetic processes is the limited effect of the pronounced conductivity difference between the ocean and its terrestrial 491

2 492 A. D. CURVE and C. S. Cox boundaries, since the source electric currents are confined to the water, which is in marked contrast to the ionospheric situation. Since very little is known about the conductivity beneath the oceans, we conclude by examining the polarization of magnetotelluric fields at the continent-ocean boundary and estimate an upper limit for the lithospheric conductivity to about 30 km depth. 2. Theory The theory of electromagnetic induction by ocean currents is discussed in SANFORD (1971) and CRAVE (1983). We write the Maxwell equations in the quasistatic limit as (1) (2) (3) where the symbols have their usual meanings and J0 is the source electric current. For induction by water flow, it is given by (4) static geomagnetic induction. Using the Helmholtz decomposition and (1), we may represent the magnetic induction as (5) magnetic (PM) modes respectively. The former has no vertical magnetic component, and the electric current flows in loops containing the vertical, while the latter has no vertical electric component, and the electric current is horizontal everywhere. it can be shown that the TM and PM modes are independent and governed by the differential equations (6) (7) where the source current is written as (8)

3 Electromagnetic Induction by Ocean Currents 493 and the electric field is given by (9) and appropriate boundary conditions in the presence of lateral discontinuities in J0, as occur at coastlines. Equations (6)-(7) and (10)-(11) are most easily solved by taking horizontal Fourier transforms, and have been applied to controlled source problems by CHAVE and Cox (1982) and oceanic problems by CHAVE (1983). They reduce to the familiar problem of ionospheric induction by taking appropriate limits. For induction by ocean water currents, the source decomposition (8) and (10)-(11) with (4) can be written (10) (11) (12) (13) (14) An interesting case develops for large scale, barotropic flows, such as the open currents are associated with the horizontally divergent part of the velocity field and lateral changes in the vertical magnetic field, while TM mode source currents ae produced by fluid vorticity and vertical source currents. This means that TM mode sources are intimately associated with the Coriolis deflection of the water velocity field on the rotating earth and may be appreciable at periods comparable to that of the earth's rotation. At shorter periods, where wave-like disturbances with large horizontal divergence occur, the PM sources are expected to dominate, while at sub-inertial periods the water flow is quasigeostrophic and nearly horizontally nondivergent, so that TM mode currents are important. For near-inertial tides, both sources are large. The actual electromagnetic field structure in the oceans is controlled both by the source behavior and by the inductive response of the conducting ocean and earth. Except in the vicinity of boundaries like the seafloor and sea surface, the field behavior is similar to that of the source electric currents producing them (CHAVE, 1983). CRAVE (1983) derived Green function solution of (6) and (7) and discussed the different influence that sub-oceanic conductive structure has on the modes.

4 494 A. D. CRAVE and C. S. Cox The PM mode is like that of magnetotellurics and is relatively insensitive to low conductivity regions, since horizontal electric currents couple across them by mutual induction. TM modes resemble DC currents, and are deflected by low conductivity regions. In general, the effect that lithospheric conductivity has on ocean-induced electromagnetic fields is controlled by the frequency (and hence the modal structure) and the spatial scale of the water velocity field (or its wavenumber structure). Broader horizontal scales for the ocaean flow lead to greater coupling with the earth, as the induced current loops close within the earth rather than within the ocean. 3. Ocean Induced Electromagnetic Fields Due both to their analytic simplicity and to their consistency with coastal observations of sea level, Kelvin waves are often used as a very simple model for the ocean tides. A Kelvin wave is a coastally trapped, nondispersive solution to the linearized shallow water equations. LARSEN (1968) examined electromagnetic induction for a Kelvin wave in a conducting ocean underlain by an insulating lithosphere. CRAVE (1983) extended this to include a conducting seafloor. The tide in a 4km deep ocean), in which the source electric currents must turn to remain in the ocean. This gives rise to a very large TM mode magnetic field if the electric current is allowed to flow into the earth. Figures 1 and 2 show the offshore and longshore components of the horizontal magnetic and electric fields as a function of distance normal to the coastline the situation treated by LARSEN (1968). The electrical conductivity below 100 km in the earth is taken as 0.05S/m, in accord with rnagnetotelluric results, while three values for the upper lithospheric conductivity are used, ranging from a near insulator to highly conducting material. The low conductivity case is identical to Larsen's result. As the near surface conductivity rises, TM mode currents flow into the earth, causing the observed differences in Fig. 1. The electric field is dominated by electrostatic effects associated with the source electric currents in the ocean, and is less strongly influenced by seafloor conductivity. The vertical magnetic field (not shown) is entirely PM mode, and is not especially sensitive to low values for the near surface conductivity. Note that the TM mode is largely confined to the coast due to Kelvin wave dynamics. For the actual tides, water depth changes, the Coriolis force, and the astronomical forces driving the tides all change with location on the earth, and the hydrodynamic wavenumber forms a quasi-continuum, so that TM modes will exist in the open ocean in association with large fluid vorticity. This means that the induced electromagnetic fields will be sensitive to the earth's electrical conductivity over a wide interval in the upper mantle, and suggests the use of tidal induced electromagnetic fields to probe the earth. The tidal velocity field

5 Electromagnetic Induction by Ocean Currents 495 in the open ocean is reasonably well determined (SCHWIDERSKI, 1980) and global models can only improve as satellite altimetry becomes available. Possible difficulties with departure of the electrical conductivity from one dimensionality, especially near continental margins, seafloor topography, and contamination by internal tides of short spatial scale remain to be evaluated. While the barotropic tides are the most obvious oceanic source of electromagnetic fields, other contribution are certainly present. Transport measurements using seafloor cables are discussed most recently by SANFORD (1982), and Cox et. al. (1980) detected the signature of intense mesoscale eddy activity in the northwest Atlantic Ocean. Aside from surface wind waves and swell, shorter period sources appear not to have been studied extensively. Figure 3 shows some preliminary results from a correlation analysis between seafloor elctromagnetic data collected 700km off California (FILLOUX, 1980) and land data from the standard observatory at Tucson 1,600km to the east, If the ionospheric source fields are sufficiently broad, as is widely believed, then the correlated part of these data represents the effect of induction by the ionosphere and magnetosphere and the uncorrelated part is the result of oceanic induction. The uncorrelated part is a factor of 2-4 smaller in power than the correlated

6 496 A. D. CRAVE and C. S. Cox Fig. 2. The offshore (top) and longshore (bottom) components of the electric field at the seafloor for the Kelvin wave of Fig. 1. See Fig. 1 caption for details. part for the horizontal magnetic field at frequencies lower than 2cph, but the correlated horizontal electric field is larger only from 0.3 to 2cph. Model studies indicate that both a background, long barotropic gravity wave and an internal wave contribution is required to explain the uncorrelated spectra. The effect of sub-oceanic conductive structure on these two components is very different: long period barotropic waves have wavelengths of hundreds to thousands of km, while internal waves are limited to a few km at most. In either case, TM modes are important at periods longer than a few hours, the source field sructure departs from the plane-wave approximation, and the signal-to-noise ratio seen in Fig. 3 is quite low. This has implications for seafloor magnetotellurics that have not yet been assessed. 4. Magnetotelluric Polarization at the Continent-Ocean Boundary The abrupt transition between the highly conducting ocean and poorly conducting continental crust probably polarizes the flow of electric current induced by ionospheric sources near the continental edge of the ocean, rendering the magnetotelluric response function anisotropic. The electric current normal to the coast must either be deflected down into the resistant lithosphere or enter the continental slope. The current flow is likely to be impeded by the low conductivi-

7 Electromagnetic Induction by Ocean Currents 497 Fig. 3. Power spectra of the east electric (top) and north magnetic (bottom) fields on the seafloor 700km off California separated into parts that are correlated (solid line) and uncorrelated (dashed line) with Tucson observatory 1,600km away at the same geomagnetic latitude. The spectra have 90 degrees of freedom (0-0.2cph), 180 degrees of freedom ( cph), and 360 degrees of freedom ( cph) per estimate. anisotropy of the magnetotelluric response function can be used to constrain the unknown lithospheric conductivity. This problem has been treated qualitatively by Cox (1980) and quantitatively by RANOANAYAKI and MADDEN (1980). Let L be the width of the boundary layer where electric polarization is appreciable. Both Cox (1980) and RANGANAYAKI and MADDEN (1980) give (15) (16) Pb is the integrated resistivity of the undersea basement to a depth H where

8 498 A. D. CHAVE and C. S. Cox (17) At present there are very few magnetotelluric observations on the seafloor which pertain to the width of this boundary layer. Measurements near the Juan de Fuca Ridge (LAW and GREENHOUSE, 1981) and on the East Pacific Rise 500 km off of Central America (FILLOUX, 1982) may be misleading due to current channeling under the spreading ridge and because the depth to conducting matter H is atypical of most of the ocean basins. For what it is worth, LAW and GREENHOUSE (1981) report little anisotropy, while FILLOUX (1982) reports a factor of 3 between the maximum and minimum values with an unspecified principal direction. Anisotropy of a factor of 1.5 is found at a site 700km off of California (FILLOUX, 1980), and at another location 2,200 km off of California (FILLOUX, 1977; CRAVE et al. 1981). The principal direction is roughly normal to the coast in both cases. Whether or not the effect is caused by a resistive ocean basement is uncertain since complications from three dimensionality or anisotropy of the conductive structure and possible contamination by oceanic sources have not been considered. We do note that the deep conductivity structures for both the 700km and the 2,200km sites are consistent with global estimates from geomagnetic depth sounding studies. This suggests only a limited effect of basement resistivity, and the boundary layer width L is probably less induced by mesoscale eddies. Thinner regions of much higher resistivity are not ruled out by this analysis. There are a number of processes which can greatly reduce the resistance locally, so that current flow between the ocean and the deep mantle may be dominated by a few conductive pathways. Spreading ridges are a possible example. RANGANAYAKI and MADDEN (1980) suggest that the continental margins may have a high conductivity. There are strong indications that sea water penetrates deep enough to reach molten rock (GREGORY and TAYLOR, 1981; YOUNG and Cox, 1981), and transform faults may provide conduits for even deeper penetration of sea water. Post-accretionary volcanism may revive the opportunities for electric current flow on older lithosphere that would otherwise be lost as the reflect the resistivity of the bulk of cool, old upper mantle rocks, but only the local contribution from highly conductive regions.

9 Electromagnetic Induction by Ocean Currents 499 It is worth noting that the process of creation of the oceanic lithosphere may be capable of leaving the bulk of the upper mantle in a highly resistive state after cooling. The major controlling factors for conduction in unweathered peridotite are partial melting and water content. In the accretionary process, the rise of basaltic liquids at the spreading axis tends to sweep out low melting point constituents and may drastically reduce the water content of the residue. Unless sea water penetrates deeply into the cooling lithosphere by hydrothermal means, there may well be a region of resistive, depleted peridotite many km thick under the oceans. Such rocks will have resistivities several orders of magnitude larger than the stated limit. Our work is sponsored by the U. S. Office of Naval Research. REFERENCES CRAVE, A. D., On the theory of electromagnetic induction in the earth by ocean currents, J. Geophys. Res., 88, , CHAVE, A. D., R. P. von HERZEN, K. A. POEHLS, and C. S. Cox, Electromagnetic induction fields in the deep ocean northeast of Hawaii: implications for mantle conductivity and source fields, Geophys. J. R. Astr. Soc., 66, , CRAVE, A. D. and C. S. Cox, Controlled electromagnetic sources for measuring electrical conductivity beneath the oceans, 1, forward problem and model study, J. Geophys. Res., 87, , Cox, C. S., Electromagnetic induction in the oceans and inferences on the constitution of the earth, Geophys. Surv., 4, , Cox, C. S., J. H. FILLOUx, D. I. COUGH, J. C. LARSEN, K. A. POEHLS. R. P. von HERZEN, and R. WINTER, Atlantic lithosphere sounding, J. Geomag. Geoelectr., 32, Supp. I, 5113-S132, FILLOUX, J. H., Ocean floor magnetotelluric sounding over north central Pacific, Nature,, 269, , FILLOUX, J. H., Magnetotelluric sounding over NE pacific may reveal spatial dependence of depth and conductance of the asthenosphere, Earth Planet Sci. Lett., 46, , FILLOUX, J. H., Magnetotelluric experiment over the ROSE area, J. Geophys. Res., 87, , GREGORY, R. T, and M. P. TAYLOR, An oxygen isotope profile in a section of Cretaceous ocean seawater-hydrothermal circulation at mid-ocean ridges, J. Geophys. Res., 86, , LARSEN, J. C., Electric and magnetic fields induced by deep sea tides, Geophys. J. R. Astr. Soc., 16, 47-70, LAW, L. K, and J. Greenhouse, Geomagnetic variation sounding of the asthenosphere beneath the Juan de Fuca Ridge, J. Geophys. J. R. Res., 86, , RANGANAYAKI, R. and T. R. MADDEN, Generalized thin sheet analysis in magnetotellurics: an extension of Price's analysis, Geophys. J. R. Astr. Soc., 60, , SANFORD, T. B., Motionally induced electric and magnetic fields in the sea, J. Geophys. Res., 76, , SANFORD, T. B., Temperature transport and motional induction in the Florida current, J. Mar. Res., 40, , SCHWIDERSKI, E., an charting global ocean tides, Rev. Geophys. Space Phys., 18, , YOUNG, P. D. and C. S. Cox, Electromagnetic active source sounding near the East Pacific Rise, Geophys. Res. Lett., 8, , 1981.