Full-Bayesian GNSS-A seafloor positioning solution derived by the Markov-Chain Monte Carlo method

For the seafloor geodesy, the GNSS-A is an only tool to directly solve the global positions with the precision of centimeters. Different from the terrestrial GNSS observations, the GNSS-A has a lot of difficulties both in the observation operation and the error corrections. For the latter issue, the researchers should take care that the GNSS-A solutions strongly affected by the underwater sound speed perturbation because it uses acoustic waves for ranging between the sea-surface and seafloor instruments. To solve this issue, the authors had developed the GNSS-A analysis software named “GARPOS” (Watanabe et al., 2020, Front. Earth Sci.), which simultaneously solves the seafloor positions and the perturbation effects based on the empirical Bayes (EB) approach. It can search the appropriate strength of smoothness constraint to the temporal change of perturbation field using the statistical criterion, to avoid the overfitting of the travel-time residuals. This software provided the sufficiently stable solutions to discuss the time-dependent crustal deformation (e.g., Watanabe et al., 2021, Earth Planets Space). Meanwhile, to provide the information on the variance of estimated positions as the joint posterior probability, the probability distributions of hyperparameters should be accounted. Therefore, we developed the program for sampling from the full-Bayesian (FB) posterior probability, based on the Markov-Chain Monte Carlo (MCMC). In this presentation, we introduce the methodology of GARPOS and its expansion to the MCMC mode. We will also show the MCMC results for the GNSS-A data obtained at sites of the Seafloor Geodetic Observation Array (SGO-A) operated by the Japan Coast Guard, to discuss the difference between the EB-based and FB-based solutions.