Observability and estimation of geocentre motion using multi-satellite laser ranging

Abstract

Artificial satellites orbit about the Earth’s system centre of mass, a point known as the geocentre that conventionally defines the long-term origin of the terrestrial reference frame (TRF). In a frame attached to the Earth’s crust, the geocentre exhibits motions on subdaily to secular time scales due to various geophysical processes. Annual variations induced by the redistribution of fluid mass in the Earth’s surface layer are most prominent and can bias ice mass balance and sea level change estimates if neglected. Theoretically, these annual variations are directly observable by any satellite geodetic technique, but orbit modelling complications affect the retrieval of geocentre motion from Global Navigation Satellite Systems (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) data. This study focuses on Satellite Laser Ranging (SLR), the only technique proven to yield reliable geocentre motion estimates via translational approaches. By means of collinearity diagnosis applied to the determination of geocentre motion using the network shift approach, it is shown that, subject to certain parameterisation constraints, the low Earth orbiters (LEOs) Starlette, Ajisai and the Laser Relativity Satellite (LARES) can beneficially supplement the traditionally employed pair Laser Geodynamics Satellite (LAGEOS) 1 and 2. In particular, the combination of LAGEOS-1 and 2 with LARES data can improve the observability of the geocentre coordinates by 25–30% on average compared to LAGEOS–only solutions due to both the larger number of observations and the proven higher sensitivity of LARES to geocentre motion. Tests involving different satellite combinations show that the contribution of Stella is minor owing to its quasi-polar orbit, whereas observations to the medium Earth orbiters (MEOs) Etalon-1 and 2 are too infrequently acquired to benefit the retrieval of geocentre motion and possibly other parameters of geophysical interest. An analysis of SLR data spanning two decades partitioned in weekly batches reveals that geocentre motion estimates derived from LAGEOS–Starlette–Stella–Ajisai combinations are contaminated by modelling errors to a larger extent than in LAGEOS–only solutions and, without considerable advances in orbit modelling, the exploitation of the high sensitivity of Starlette and Ajisai to geocentre motion appears remote. Compounded by the short tracking history of LARES, a conclusive assessment of the long-term quality of LAGEOS–LARES solutions is infeasible at present. iv Similar to other geodetic parameters, the geocentre coordinates exhibit temporal correlations that have been typically neglected in previous studies. The power spectral densities (PSDs) of weekly derived geocentre coordinates display a power-law behaviour at long periods and white noise flattening for frequencies above 4 cycles per year (cpy). When temporal dependencies are appropriately modelled using one of the readily available maximum likelihood estimation (MLE) software implementations, the uncertainties of the annual amplitude and phase estimates inflate by an average factor of 1.6 for weekly time series over 12 years in length. The formal errors of the linear and quadratic trend estimates amplify by a larger factor of 2.2–2.3. First-order autoregressive noise plus white noise and power-law noise are the preferred stochastic models in most cases based on model-selection criteria. As demonstrated through the analysis of independent time series, for sampling periods longer than one week the first-order autoregressive model becomes more competitive on its own due to the suppression of white noise at high frequencies, but the power-law noise model is also occasionally preferred. Kinematic estimates of geocentre coordinates are highly coherent with network shift results across the entire frequency range only when station positions are simultaneously solved for. Additionally, network shift estimates are more coherent with kinematic results when the scale parameter is omitted from the functional model of the similarity transformation linking the quasi-instantaneous frames and the secular frame. In addition to draconitic errors related to solar radiation pressure modelling, long-period tidal aliases due to mismodelled tidal constituents also contaminate geocentre motion estimates. Independent geodetic estimates and geophysical model predictions validating the results from this study agree that the annual geocentre motion signals have amplitudes of 2–3 mm in the equatorial components and 4–6 mm in the Z component. The maximum geocentre vector magnitude of about 7 mm is attained in July.