Statistically optimal estimation of surface mass anomalies by directly using GRACE level-2 spherical harmonic coefficients as measurements

Point-mass inversion is widely employed in GRACE level-2 data processing. Conventionally, the spherical harmonic (SH) coefficients are used indirectly: a set of pseudo measurements is generated first using the SH coefficients through SH synthesis; then the point-mass inversion is done with these pseudo measurements. To be statistically optimal, the covariance matrix of pseudo measurements should be calculated and used to appropriately weigh the parameter estimation. In this work, we propose a statistically optimal point-mass inversion scheme by directly using the SH coefficients as measurements. We prove the equivalence between this direct approach and the conventional indirect approaches. We also demonstrated their comparable performance through both simulation and real GRACE data processing. Choosing and calculating pseudo measurements, propagating covariance matrix, and potentially dealing with the singularity of the covariance matrix involved in the conventional indirect approaches are avoided in the proposed direct approach. This statistically optimal direct approach can readily be employed in mascon inversion of GRACE data and other radial basis functions-based approaches in regional gravity modeling.