Quality assessment of sub-Nyquist recovery from future gravity satellite missions

Abstract

Drawing on experience from Gravity Recovery and Climate Experiment (GRACE) data analysis, the scientific challenges were already identified in several studies. Any future mission should focus on improvement in both precision and resolution in space and time. For future gravity missions which use high quality sensors, aliasing of high frequency time-variable geophysical signals to the lower frequency signals is one of the most serious problems. The aliasing problem and the spatio-temporal resolution are mainly restricted by two sampling theorems describing the space-time sampling of satellite missions: (i) a Heisenberg-like uncertainty theorem which states that the product of spatial resolution and time resolution is constant, and (ii) the Colombo–Nyquist rule (CNR), which requires the number of satellite revolutions in a repeat period to be at least twice a given maximum spherical harmonic degree. The CNR holds under the assumption of equal ground-track spacing, and limits the spatial resolution of the gravity solution.This study investigates the quality of sub-Nyquist time interval recoveries (when the time intervals are shorter than what is required by the Colombo–Nyquist rule) of different orbit configurations and formation flights, in particular, the dependence of the gravity field accuracy on the measurement duration and ground-track patterns of the satellite formations. It is shown that the fulfillment of the modified CNR, the mission altitude and avoidance of large unobserved gaps by satellite ground-track patterns have the strongest effect on the quality of the recoveries, while the sub-cycle concept does not appear to play an imortant role. It is also found that the modified CNR holds for architectures including two satellite pairs when accounting for the orbital revolutions of both pairs. Moreover, the quality of the solution in the double pair scenario, consisting of a near-polar and an inclined inline pairs, exceeds that of a single near-polar inline pair solution with twice the observations. One important reason is the East–West information of the inclined pair adds to the North–South measurements of the near-polar mission.The simulations of the gravity recoveries of this study are based on a quick-look tool. The tool assumes nominal repeat orbits for satellite missions. Based on the quality assessment of the recoveries and the technical concerns of advanced formation flights as e.g. Pendulum or Cartwheel, a search space for optimal satellite mission scenarios is suggested.