# Bayesian Inversion of Log-normal Eikonal Equations

@article{Yeo2021BayesianIO, title={Bayesian Inversion of Log-normal Eikonal Equations}, author={Zhan Fei Yeo and Viet Ha Hoang}, journal={ArXiv}, year={2021}, volume={abs/2111.11087} }

We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation, given noisy observation data on its solution at a set of spatial points. We contribute rigorous proof on the existence and well-posedness of the problem. We then study approximation of the posterior probability measure by solving the truncated eikonal equation, which contains only a ﬁnite number of terms in the Karhunen-Loeve expansion of the slowness function, by the Fast Marching…

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