Magnetic Held Models

Michael Plett

Spherical Harmonic Model. This appendix presents some computational aspects of geomagnetic field models. A more qualitative description of the field characteristics is given in Section 5.1. As discussed there, the predominant portion of the Earth's magnetic field, B, can be represented as the gradient of a scalar potential function, V, i.e.,

V can be conveniently represented by a series of spherical harmonics,

V{r,9,4>) = a £ + I £ (&»cosi»* + h?smm<l>)P?(0) (H-2)

where a is the equatorial radius of the Earth (6371.2 km adopted for the International Geomagnetic Reference Field, IGRF); g? and A™ are Gaussian coefficients (named in honor of Karl Gauss); and r, 0, and 4> are the geocentric distance, coelevation, and East longitude from Greenwich which define any point in space.

The Gaussian coefficients are determined empirically by a least-squares fit to measurements of the field. A set of these coefficients constitutes a model of the field. The coefficients for the IGRF (Section 5.1; [Leaton, 1976]), are given in Table H-l. The first-order time derivatives of the coefficients, called the secular

Table H-l. IGRF Coefficients for Epoch 1975. Terms indicated by a dash (-) are undefined.

n

m

SlnTI

hlnTI

llnT/yrl

MnT/yrl

n

m

SlnTI

MnT)

slnT/yi)

hlnT/Tf)

0 0

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