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

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Advanced Methods for Processing and Visualizing the Renewable Energy

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 320))

Abstract

In this chapter, we demonstrate the sound connection between the Bayesian approach and the Tikhonov regularisation within Gaussian framework. We provide a thorough uncertainty analysis to answer the following two fundamental questions: (1) How well is the estimate determined by 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 applications in seismic inversions.

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Correspondence to Muhammad Izzatullah .

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Izzatullah, M., Peter, D., Kabanikhin, S., Shishlenin, M. (2021). Bayes Meets Tikhonov: Understanding Uncertainty Within Gaussian Framework for Seismic Inversion. In: Abdul Karim, S.A., Saad, N., Kannan, R. (eds) Advanced Methods for Processing and Visualizing the Renewable Energy. Studies in Systems, Decision and Control, vol 320. Springer, Singapore. https://doi.org/10.1007/978-981-15-8606-4_8

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