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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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Author information

Authors and Affiliations

  1. Seismic Modeling and Inversion Group, King Abdullah University of Science and Technology, Thuwal, 23955, Saudi Arabia

    Muhammad Izzatullah & Daniel Peter

  2. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

    Sergey Kabanikhin & Maxim Shishlenin

  3. Novosibirsk State University, 630090, Novosibirsk, Russia

    Sergey Kabanikhin & Maxim Shishlenin

  4. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia

    Sergey Kabanikhin & Maxim Shishlenin

  5. Mathematical Center in Akademgorodok, 630090, Novosibirsk, Russia

    Sergey Kabanikhin & Maxim Shishlenin

Authors
  1. Muhammad Izzatullah
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  2. Daniel Peter
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  3. Sergey Kabanikhin
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  4. Maxim Shishlenin
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Corresponding author

Correspondence to Muhammad Izzatullah .

Editor information

Editors and Affiliations

  1. Fundamental and Applied Sciences Department, Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Seri Iskandar, Selangor, Malaysia

    Samsul Ariffin Abdul Karim

  2. Electrical and Electronic Engineering Department, Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Seri Iskandar, Selangor, Malaysia

    Nordin Saad

  3. Electrical and Electronic Engineering Department, Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Seri Iskandar, Selangor, Malaysia

    Ramani Kannan

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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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