Bayes Meets Tikhonov: Understanding Uncertainty Within Gaussian Framework for Seismic Inversion

Abstract

In this chapter, we demonstrate the sound connection between the Bayesian approach and the Tikhonov regularisation within Gaussian framework. We provide an uncertainty analysis framework to answer the following two fundamental questions: (1) How well is the estimate determined by the a posteriori PDF, i.e. by the combination of observed data and a priori information? (2) What are the respective contributions of observed data and a priori information? To support the proposed methodology, we demonstrate it through numerical application in linear inverse problem for the seismic travel-time tomography.