## Coordinate Transformation Software

This page provides software and coefficients for transforming a spherical harmonic (SH) expansion from Geocentric Solar Magnetospheric (GSM) or Solar Magnetic (SM) coordinates to Geographic (GEO) coordinates. These transforms are required whenever induction by large-scale external magnetic fields in the rotating Earth is to be taken into account.

gsm2geo.zip:

Contains the routines (gsm2geo.c) for transforming a constant SH expansion in GSM into a time-varying SH expansion in GEO and the GSM to GEO transform coefficient array (gsm2geo_coeff_3_6.txt) for maximum spatial degree 3 and temporal degree 6. The routines also supply the phase information required for computing the fields induced in the Earth.

sm2geo.zip: Contains the corresponding routines from SM to GEO (sm2geo.c) and the SM to GEO transform coefficient array (sm2geo_coeff_3_6.txt) for maximum spatial degree 3 and temporal degree 6

For further information see Maus and Luehr, Geophys. J. Int., doi:10.1111/j.1365-246X.2005.02691.x

### GSM Coordinate System

The x-axis of the GSM coordinate system is defined along the line connecting the center of the Sun to the center of the Earth. The origin is defined at the center of the Earth, and is positive towards the Sun. The y-axis is defined as the cross product of the GSM x-axis and the magnetic dipole axis; directed positive towards dusk. The z-axis is defined as the cross product of the x- and y-axes. The magnetic dipole axis lies within the xz plane.

### Solar Magnetic Coordinates

In Solar Magnetic Coordinates (SM) the Z-axis is chosen parallel to the north magnetic pole and the Y-axis perpendicular to the Earth-Sun line towards dusk. The difference between this system and the GSM system is a rotation about the Y-axis. The amount of rotation is simply the dipole tilt angle as defined in the previous section. We note that in this system the X-axis does not point directly at the Sun. As with the GSM system, the SM system rotates with both a yearly and daily period with respect to inertial coordinates.

### Geographic Coordinates

The Geographic Coordinate system (GEO) is defined so that its X-axis is in the Earth's equatorial plane but is fixed with the rotation of the Earth so that it passes through the Greenwich meridian (0° longitude). Its Z-axis is parallel to the rotation axis of the Earth, and its Y-axis completes a right-handed orthogonal set (Y = Z x X).