Regional models of the earth's magnetic field have developed considerably since the days of hand contouring. They have incorporated varying levels of mathematical sophistication, from partial “mutual consistency” on a surface to full electromagnetic consistency in three-dimensional space. Each method has its advantages and its limitations. Some of the methods allow for radial variation so that data acquired at different altitudes can be analyzed directly, and so that fields from the resulting models can be calculated at any altitude. For other methods, altitude continuation is theoretically possible but numerically difficult and statistically unreliable. Some methods are limited, for numerical reasons, to small areas or are able to represent only fairly long wavelengths. The different methods also differ greatly with respect to their mathematical and computational complexity, the less complex methods also usually being more subjective.
Society of Geomagnetism and Earth, Planetary and Space Sciences