Geomagnetic induction in a heterogeneous sphere: fully three-dimensional test computations and the response of a realistic distribution of oceans and continents

Abstract

Long‐period geomagnetic data can resolve large‐scale 3‐D mantle electrical conductivity heterogeneities which are indicators of physiochemical variations found in the Earth’s dynamic mantle. A prerequisite for mapping such heterogeneity is the ability to model accurately electromagnetic induction in a heterogeneous sphere. A previously developed finite element method solution to the geomagnetic induction problem is validated against an analytic solution for a fully 3‐D geometry: an off‐axis spherical inclusion embedded in a uniform sphere. Geomagnetic induction is then modelled in a uniform spherical mantle overlain by a realistic distribution of oceanic and continental conductances. Our results indicate that the contrast in electrical conductivity between oceans and continents is not primarily responsible for the observed geographic variability of long‐period geomagnetic data. In the absence of persistent high‐wavenumber magnetospheric disturbances, this argues strongly for the existence of large‐scale, high‐contrast electrical conductivity heterogeneities in the mid‐mantle. Lastly, for several periods the geomagnetic anomaly associated with a mid‐mantle spherical inclusion is calculated. A high‐contrast inclusion can be readily detected beneath the outer shell of oceans and continents. A comparison between observed and computed c responses suggests that the mid‐mantle contains more than one order of magnitude of lateral variability in electrical conductivity, while the upper mantle contains at least two orders of magnitude of lateral variability in electrical conductivity.

On the role of oceans in the geomagnetic induction by Sq along the 210° magnetic meridian region

“…In fact, in such regions, where there is a strong lateral heterogeneity at upper mantle depths, the estimation of the geomagnetic tensor induction response, defined as the ζ (ω)-response, introduced by Zhang and Schultz (1992) might be more appropriate, since this new response function better resolves the upper mantle electrical conductivity. Incidentally, since the fully validated 3-D FEM forward solver of Weiss and Everett (1998) can readily calculate the ζ (ω)-response, such a response calculated for Sq periods over a realistic distribution of oceans and continents, as in the present case, can be aptly modelled following their approach and thus the electrical state of the upper mantle can be reasonably mapped.…”

“…Later, a few more studies concerning the ocean influence on induction due to a variety of geomagnetic variaCopy right c The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. tions have been made both in terms of theory (Beamish et al, 1983;Fainberg et al, 1990a) and numerical computations (Fainberg et al, 1990b;Takeda, 1991). Recently, considering a realistic model distribution of oceans and continents, Weiss and Everett (1998), through finite element modelling of the long-period induction response, reported that the influence of oceans at periods greater than 2 days is not significant in the observed geographic variability of the induction responses. This implies that oceans show considerable influence on the induction response at periods of less than 2 days; these periods are of prime concern in the present study.…”

3-D Global Induction in the Oceans and Solid Earth: Recent Progress in Modeling Magnetic and Electric Fields from Sources of Magnetospheric, Ionospheric and Oceanic Origin

“…For frequency-domain forward calculations we have now a number of 3-D solvers based on finite-difference (Uyeshima and Schultz 2000), finite-element (Everett and Schultz 1996;Weiss and Everett 1998;Yoshimura and Oshiman 2002), volume integral equation (Kuvshinov et al 2002a;Koyama et al 2002) and spectral (Tarits 1994;Martinec 1999;Plotkin 2004) methods. Each type of solution has its own advantages and drawbacks.…”

“…Numerical modeling studies of the ocean effect using realistic conductivity models have been performed during the past 20 years Takeda 1993;Tarits 1994;Weiss and Everett 1998) to estimate this effect in local C-responses-transfer functions which are used in geomagnetic deep sounding of the Earth. The common understanding was that the ocean effect in the responses becomes negligible for periods greater than a few days.…”

Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

“…At the same time, a number of implementations are also available to simulate the EM fields excited in 3-D spherical earth models, including those based on the spectral decomposition (Tarits, 1994;Grammatica and Tarits, 2002), finite-element (Everett and Schultz, 1996;Weiss and Everett, 1998;Yoshimura and Oshiman, 2002), spectral finite-element (Martinec, 1999), finite-difference (Uyeshima and Schultz, 2000) and integral equation (Koyama et al, 2002;Kuvshinov et al, 2002Kuvshinov et al, , 2005 approaches. Also, in order to deal with the complicated spatial and temporal variability of the satellite induction data, several time-domain techniques for computing 3-D EM fields of a transient external source have recently been developed (Hamano, 2002;Velimsky et al, 2003;Kuvshinov and Olsen, 2004).…”