Modelling Earth’s lithospheric magnetic field using satellites in low-perigee elliptical orbits

Summary The sensitivity of magnetic measurements taken by satellites in elliptical orbits to the lithospheric magnetic field is studied by comparing the formal error variances of the lithospheric Gauss coefficients for various satellite orbital constellations. Analytical expressions are presented for the variances of the Gauss coefficients when either all three magnetic vector components or only the radial component are used. We compare the results obtained using a satellite in a near-polar circular orbit at 350 km altitude with those from a satellite in an elliptical orbit with perigee at 140 km (and apogee at 1500 km) and find that the latter leads to Gauss coefficient variances at spherical harmonic degree n = 180 (corresponding to a horizontal wavelength of λ = 220 km) that are 104 times smaller compared to those derived from a similar number of data measured at 350 km altitude. The improvements in variance ratio at degree n = 145 (λ = 275 km) and n = 110 (λ = 360 km) are 103 and 102, respectively. These findings are supported by an analysis of synthetic magnetic data along simulated satellite orbits from which the lithospheric Gauss coefficients are estimated and compared with the original ones used to generate the synthetic data. Coefficients at degree n are successfully determined if the power of the difference between retrieved and original coefficients at that degree is smaller than the power of the lithospheric field (i.e. of the input coefficients). Using 3 years of simulated data we conclude that magnetic measurements from a satellite in an elliptical orbit with perigee at 140 km allow for a reliable determination of the lithospheric field up to spherical harmonic n ≈ 170 while a satellite in a circular orbit at 350 km height only enables lithospheric field modelling up to n ≈ 100. The analysis demonstrates that low-altitude magnetic data collected by satellites in low-perigee elliptical orbits – although only available for a fraction of each orbit – enable improved global lithospheric field modelling at spatial wavelengths well beyond what is currently possible with data from satellites in circular orbits that do not reach such low altitudes. We applied the approach to the orbital configuration proposed for the Daedalus satellite mission (140 km perigee); the method will however also help in the preparation for other satellite missions in near-polar low-perigee elliptical orbits like the Macau Science Satellite pair MSS-2A and MSS-2B (perigee of 200 km or lower).