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Abstract:
As one of the seafloor geodetic techniques, precise seafloor positioning by the GNSS—Acoustic ranging combination technique (GNSS-A) is applied for the observations of the crustal deformation in the plate subduction zones (e.g., Spiess et al., 1998; Fujita et al., 2006). For the precise positioning with the GNSS-A, it is required to appropriately cancel or correct the effects of sound speed variation on acoustic travel time. We have developed static GNSS-A analysis methods where the sound speed effects were simultaneously corrected with well-distributed acoustic data, by introducing the perturbation field model (Watanabe et al., 2020). Based on the empirical Bayes approach, it was implemented in an open-source software GARPOS (the latest version is v1.0.1, https://doi.org/10.5281/zenodo.6414642), in which hyperparameters are selected to minimize the Akaike Bayesian Information Criterion (ABIC; Akaike, 1980). Watanabe et al. (under review, preprint https://doi.org/10.21203/rs.3.rs-1881756/v1) developed the upgraded version of GARPOS, i.e., GARPOS-MCMC (the latest version is v1.0.0, https://doi.org/10.5281/zenodo.6825238), with a full-Bayes GNSS-A analysis scheme, where the hyperparameters are also expressed as probability density functions. The parameters are estimated with the Markov chain Monte Carlo method, which enabled us to directly sample from the joint posterior of parameters including any hyperparameters and evaluate the correlations between those parameters. However, it requires computational resources as the number of acoustic data becomes large. To overcome the disadvantage, we introduced the widely applicable Bayesian information criterion (WBIC; Watanabe, 2013) for model selection for some hyperparameters, to partly take an empirical Bayes approach, and implemented it on GARPOS-MCMC.
