Sequential integral inversion in regional gravity field modelling

Two sequential strategies for the integral inversion of multi-platform gravimetric observations are presented for regional gravity field modelling. In contrast to conventional batch solutions, the proposed approaches enable the progressive combination of large, heterogeneous and ill-conditioned systems while preserving full stochastic information. In the first, a priori background information and its variance–covariance matrix (VCM) are incorporated in a formulation conceptually analogous to data assimilation, allowing the sequential update of the solution and its precision measures. In the second, multiple ill-conditioned systems derived from discretised integral equations are combined sequentially without external background information. For both approaches, rigorous models are derived for the sequential propagation and combination of observations, VCMs, a posteriori variances and regularisation-induced biases within a Tikhonov regularisation framework. The methods are applied to the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient data over Central Europe during August–September 2013. A total of 94,540 observations are divided into ten subsets and processed sequentially to recover gravity anomalies at sea level. The results are compared with a conventional batch inversion. When reliable background information is available, the first algorithm yields stable and consistent solutions. The second algorithm produces results largely equivalent to the batch solution, with differences generally below 1 mGal in standard deviation. The proposed formulation provides a computationally feasible and fully stochastic alternative to batch integral inversion for large gravimetric data sets and enables the consistent integration of multi-platform observations in regional gravity field modelling.