# Modeling the Earth's Magnetic Field

Models:

- International Geomagnetic Reference Field (IGRF)
- World Magnetic Model (WMM)
- Enhanced Magnetic Model (EMM)

Earth's magnetic field consists of:

- Main field generated by the Earth's core. Strongest in wavelengths down to about 3000 km
- Crustal field caused by magnetized rocks in the crust and upper mantle. Dominates wavelengths less than 2500 km.

And to a lesser extent:

- Ionosphere
- The Sun

The IGRF and WMM model the Main field where as the EMM also includes the Crustal field.

WMM applicable between 1 km below sea level to 850 km above.

The models are implemented through (Schmidt semi-normalized) spherical harmonic expansions of empirically determined spherical harmonic coefficients. These coefficients, along with secular variation coefficients for the spherical harmonic coefficients, are released and updated in five year periods known as epochs.

Spherical harmonics description goes here.

The IGRF gives up to degree and order 13 coefficients and the WMM gives up to 12, totaling 208 and 180 in number. The EMM provides up to degree and order 720 coefficients, thats over 500,000 total. This allows the EMM to model wavelengths down to 52 km for a resolution of 26 km but at a cost of much longer calculation time.

## Our Implementation

Currently we are using the WMM but ideally we would like to use the EMM. To do so would require improvements to the code currently committed to PSAS as it begins to underflow at around degree 404 or 405.

Switching between IGRF and WMM should be easy, it is just a matter of interchanging the coefficient files.

Another thing to look at is implementing a (inverse) Fast Spherical Harmonic Transform, the spherical harmonics equivalent to the (inverse) Fast Fourier Transform.

## Links:

- NOAA geomagnetic page has links to the three model's home pages.
- 2010 WMM Technical report (22MB) Defines and describes the World Magnetic Model (Update link in 2015)
- USGS (US Geological Survey) Geomagnetism Program
- http://geomag.usgs.gov/
- USGS Magentic field models: http://geomag.usgs.gov/models.html
- Java applet "model" calculator: http://intermagnetusa.org/geomag/geomagAWT.html

- http://public.tgf.tc.faa.gov/documentation/magneticDecl/Verification.pdf - FAA verification of the WMM. They claim less than "0.5 degrees"... must mean if you use it as a 2D compass.