Geomagnetic induction in multiple eccentrically nested spheres

Summary We present a semi-analytic solution to the 3-D forward modelling of electromagnetic induction in a heterogeneous model consisting of multiple eccentrically nested spheres. A number of numerical methods for 2-D and 3-D global electromagnetic modelling have been applied recently, including thin-sheet, perturbation-expansion, finite-element and spectral–finite-element schemes. The present semi-analytical approach may be used as an aid for testing more general algorithms of electromagnetic induction modelling. The multiple eccentrically nested spheres solution has been tested by comparing against the analytical solution for electromagnetic induction in a uniform sphere and in two eccentrically nested spheres with an azimuthal structure of electrical conductivity, and good agreements have been obtained. We further solve the electromagnetic induction problem in three and four eccentrically nested spheres configurations and compute the global response function and the spherical components of magnetic intensity within the model.

[1]  A. T. Price,et al.  Electromagnetic induction in non-uniform conductors, and the determination of the conductivity of the Earth from terrestrial magnetic variations , 1939 .

[2]  Adam Schultz,et al.  Geomagnetic induction in eccentrically nested spheres , 1995 .

[3]  Wei-jia Su,et al.  Degree 12 model of shear velocity heterogeneity in the mantle , 1994 .

[4]  A. Schultz,et al.  A 3‐D perturbation solution for the EM induction problem in a spherical earth—the forward problem , 1992 .

[5]  Appreciation of Spherically Symmetric Models of Electrical Conductivity , 1987 .

[6]  A. Schultz.  On the vertical gradient and associated heterogeneity in mantle electrical conductivity , 1990 .

[7]  Z. Martinec,et al.  Matrix approach to the solution of electromagnetic induction in a spherically layered earth , 1985 .

[8]  M. Everett,et al.  Geomagnetic induction in a heterogenous sphere: Azimuthally symmetric test computations and the response of an undulating 660‐km discontinuity , 1996 .

[9]  A. Schultz,et al.  On the electrical conductivity of the mid‐mantle‐I. Calculation of equivalent scalar magnetotelluric response functions , 1987 .

[10]  A. T. Price.  Electromagnetic Induction in a Conducting Sphere , 2022 .

[11]  E. B. Fainberg,et al.  Thin Sheet Modelling of Subsurface and Deep Inhomogeneities , 1993 .

[12]  P. Tarits,et al.  Electromagnetic studies of global geodynamic processes , 1994 .

[13]  S. P. Srivastava,et al.  Theory of the Magnetotelluric Method for a Spherical Conductor , 1966 .