Sampling theorem of satellite gravimetry from the perspective of the Bender configuration

<p>Satellites in different orbital configurations acquire gravity signals differently. Thus, a difference in admissible spectral coefficients can be expected when the orbital geometry changes. A simple illustration of this phenomenon is seen in the Bender configuration of two GRACE-like satellite pairs - polar and inclined. In the Bender configuration, the polar pair covers the entire globe. In contrast, the inclined pair does not cover the higher latitudes leaving a local discontinuity around the poles in the acquired signal (better known as the <em>Polar Gap problem</em>). Similarly, due to its north-south orientation, the polar pair can capture the features that are predominantly oriented in the east-west direction. Trying to understand better the relationship between satellite geometry and signal acquisition led us to take our first steps in the direction of a unified sampling theory in satellite gravimetry. To this end, we employed the concepts behind the rotation of spherical harmonic coefficients built upon Inclination functions to express the geopotential functionals. Our work utilizes the Lomb-Scargle Periodogram based approach to ascertain limiting frequencies from the systemic quasi-regular sampling net formed on the satellite torus contrary to interpolation and FFT based techniques used in earlier such research endeavors. Through our work, we aim at improving our understanding of how the transformation of the geopotential occurs from the global to the spectral domain. We hope that this will help design future satellite missions with geometries best suited for their objective based on the precise determination of essential spectral coefficients.</p>

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

<p class="western" align="justify">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 <span lang="en-IN">in understanding the spectral resolution of the next generation gravity missions</span>.</p>