Scripted finite element tools for global electromagnetic induction studies

• Published in: Geophysical journal international Vol. 188; no. 2; pp. 435 - 446
• Main Authors: Ribaudo, Joseph T., Constable, Catherine G., Parker, Robert L.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.02.2012
• Subjects: Electrical properties; Electromagnetic induction; Finite element method; Frequency domains; Geomagnetic induction; Geomagnetism; Magnetic field; Magnetic fields; Mathematical analysis; Mathematical models; Numerical solutions; Resistivity; Satellite magnetics
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1111/j.1365-246X.2011.05255.x

SUMMARY Numerical solution of global geomagnetic induction problems in two and three spatial dimensions can be conducted with commercially available, general‐purpose, scripted, finite‐element software. We show that FlexPDE is capable of solving a variety of global geomagnetic induction problems. The models treated can include arbitrary electrical conductivity of the core and mantle, arbitrary spatial structure and time behaviour of the primary magnetic field. A thin surface layer of laterally heterogeneous conductivity, representing the oceans and crust, may be represented by a boundary condition at the Earth–space interface. We describe a numerical test, or validation, of the program by comparing its output to analytic and semi‐analytic solutions for several electromagnetic induction problems: (1) concentric spherical shells representing a layered Earth in a time‐varying, uniform, external magnetic field, (2) eccentrically nested conductive spheres in the same field and (3) homogeneous spheres or cylinders, initially at rest, then rotating at a steady rate in a constant, uniform, external field. Calculations are performed in both the time and frequency domains, and in both 2‐D and 3‐D computational meshes, with adaptive mesh refinement. Root‐mean‐square accuracies of better than 1 per cent are achieved in all cases. A unique advantage of our technique is the ability to model Earth rotation in both the time and the frequency domain, which is especially useful for simulating satellite data.