The IGRF-13 model for epoch 2020.0 gives surface values of the geomagnetic power…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The geomagnetic field: potential, spectrum, induction and the palaeomagnetic record

Problem

The IGRF-13 model for epoch 2020.0 gives surface values of the geomagnetic power spectrum

R_2(a)=8.23\times10^{7}\,\mathrm{nT^2}

and

R_{13}(a)=140\,\mathrm{nT^2}

. Take

a = 6371.2\,\mathrm{km}

. ((a)) Continue both degrees downward to a radius

r

and find the radius at which they carry equal power. ((b)) Assuming the source has no preferred scale, say what this radius tells you about where the main field originates, comparing it with the core radius

r_{\rm c}=3480\,\mathrm{km}

. ((c)) A gravity anomaly coefficient of degree

n

, continued over the same interval, is multiplied in power by the same factor as a magnetic coefficient of that degree. Explain in one or two sentences why, even though the two fields have entirely different sources.

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