Geomagnetic field mapping from a satellite: Spatial power spectra of the geomagnetic field at various satellite altitudes relative to natural noise sources and instrument noise

Abstract

For a low-level geomagnetic satellite survey, for which the motion of the satellite converts spatial variation into temporal variation, the limit on accuracy may well be background temporal fluctuations. The sources of the temporal fluctuations are current systems external to the Earth and include currents induced in the Earth due to these sources. The internal sources consist primarily of two components, the main geomagnetic field with sources in the Earth's core and a crustal geomagnetic field. Power spectra of the vertical geomagnetic field internal component that would be observed by a spacecraft in circular orbit at various altitudes, due to satellite motion through the spatially varying geomagnetic field, are compared to power spectra of the natural temporal fluctuations of the geomagnetic field vertical component (natural noise) and to the power spectrum for typical fluxgate magnetometer instrument noise. The natural noise is shown to be greater than this typical instrument noise over the entire frequency range for which useful measurements of the geomagnetic field may be made, for all geomagnetic latitudes and all times. Thus there would be little benefit in reducing the instrument noise below the typical value of 10 −4 gamma 2 Hz −1 plus a 1/ f component of 10 milligamma rms decade −1. For a given satellite altitude, there is a maximum frequency above which the natural noise is greater than the power spectrum of the crustal geomagnetic field vertical component. Below this maximum frequency, the situation is reversed. This maximum frequency depends on geomagnetic latitude (and to a lesser extent on time of day and season of year), being lower in the auroral zone than at lower latitudes. The maximum frequency is also lower at higher satellite altitudes. The maximum frequency determines the spatial resolution obtainable on a magnetic field map. The spatial resolution (for impulses) obtainable at low latitudes for a 100-km satellite altitude (possibly achievable by tethering a small satellite at this altitude to a space vehicle at a higher altitude) is 60 km, while at the auroral zone the obtainable spatial resolution is 100 km. At the higher satellite altitude of 300 km the obtainable spatial resolution is 230 km at low latitudes and 530 km at the auroral zone. At 500-km satellite altitude, the obtainable spatial resolution is 500 km at low latitudes, while maps cannot be made at all for the auroral zone unless the data are selected for “quiet” days. For the lower satellite altitudes, greater spatial resolution can be obtained than at higher altitudes. Furthermore since the crustal geomagnetic field power spectrum is larger at lower altitudes, the relative error due to the natural noise is less than for higher altitudes.