Revisiting the sampling problem of satellite gravimetry – a perspective from the Bender configuration

The signal acquisition by the two different GRACE-like satellite pairs in a Bender configuration - polar and inclined, is dissimilar to each other. This difference is attributable to differing relative sampling geometry and global coverage. While the polar pair covers the entire globe, the inclined pair does not cover the higher latitudes leaving a local discontinuity around the poles in acquired signal (better known as the Polar Gap problem). Similarly, due to its north-south orientation, the polar pair can capture well the features that are predominantly oriented in the east-west direction. We simulated a Bender configuration using ESA's Earth System Model to see how the two satellite pairs contributed to the spherical harmonic coefficients. The general pattern was that the polar orbit contributed strongly to the zonal coefficients and the tesserals around it (near-zonal coefficients) while the inclined orbit contributed strongly to the other tesseral and the sectorial coefficients, which is well known. We also found out that the weak zonal and near-zonal inclined pair contributions lay inside a wedge in the spectral space, very similar to the polar gap error wedge. We want to discern how the satellites' relative geometry, particularly the polar gap issue in the inclined pair of a bender configuration, affects the solution's spectral resolution. In this study, we model the contribution coefficients of the polar and inclined pairs as a function of orbit geometries, employing the semi-analytical framework based on inclination functions. We hope that this will help in understanding the spectral resolution of the next generation gravity missions.