A Fully Bayesian Inversion for Spatial Distribution of Fault Slip with Objective Smoothing

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Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters (2010, methodology): “…Criterion (ABIC) (e.g. Yabuki & Matsu’ura 1992; Nishimura et al. 2000; Yoshioka 2001), Cross Validation (e.g. Matthews & Segall 1993; Johnson et al. 2001; Hreinsdóttir et al. 2003), and a fully Bayesian, probabilistic, approach that is adopted in this paper and also by Fukuda & Johnson (2008).”
Inversion of Surface Deformation Data for Rapid Estimates of Source Parameters and Uncertainties: A Bayesian Approach (2018, methodology): “…function for multiple data sets, assuming independence, can therefore be expressed as the product of the likelihoods of the data sets (e.g., Fukuda & Johnson, 2008): p djmð Þ ¼ ∏Kk¼1 2πð Þ Nk=2 Σkj j 1 2 exp 1 2 rTk Σ 1 k rk (4) where Nk is the number of data points and rk are the residual…”