Information carried by different magnetic observations: A review

The Macau satellites differ from their predecessors in their orbits: MSS-1 (Macau Science Satellite-1) is in low inclination and the planned MSS-2 will be in highly elliptical orbits. This paper reviews the fundamental advantages and disadvantages of the different possible magnetic measurements: the component (declination, intensity, etc.) and location (satellite, ground, etc.). When planning a survey the choice of component is the "What?" question; the choice of location the "Where?" question. Results from potential theory inform the choice of measurement and data analysis. For example, knowing the vertical component of magnetic field provides a solution for the full magnetic field everywhere in the potential region. This is the familiar Neumann problem. In reality this ideal dataset is never available. In the past we were restricted to declination data only, then direction only, then total intensity only. There have also been large swathes of Earth’s surface with no measurements at all (MSS-1 is restricted to latitudes below 41^\circ ). These incomplete datasets throw up new questions for potential theory, questions that have some intriguing answers. When only declination is known uniqueness is provided by horizontal intensity measurements on a single line joining the dip-poles. When only directions are involved uniqueness is provided by a single intensity measurement, at least in principle. Paleomagnetic intensities can help. When only total intensity is known, as was largely the case in the early satellite era, uniqueness is provided by a precise location of the magnetic equator. Holes in the data distribution is a familiar problem in geophysical studies. All magnetic measurements sample, to a greater or lesser extent, the potential field everywhere. There is a trade-off between measurements close to the source, good for small targets and high resolution, and the broader sample of a distant measurement. The sampling of a measurement is given by the appropriate Green’s function of the Laplacian, which determines both the resolution and scope of the measurement. For example, radial and horizontal measurements near the Earth’s surface give a weighted average of the radial component over a patch of the core surface beneath the measurement site about 30^\circ in radius. The patch is smaller for shallower surfaces, for example from satellite to ground. Holes in the data distribution do not correspond to similar holes at the source surface; the price paid is in resolution of the source. I argue that, in the past, we have been too reluctant to take advantage of incomplete and apparently hopeless datasets.