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Estimating parameter uncertainties in matched field inversion by a neighborhood approximation algorithm.

Kunde Yang1, N Ross Chapman, Yuanliang Ma

  • 1College of Oceanic Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi, PR China. ykdzym@nwpu.edu.cn

The Journal of the Acoustical Society of America
|March 14, 2007
PubMed
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A new Neighborhood Approximation Bayes (NAB) algorithm offers a faster alternative to the Fast Gibbs Sampler (FGS) for Bayesian inversion. This method efficiently estimates posterior probability densities (PPDs) with reduced computational cost.

Area of Science:

  • Computational Geophysics
  • Bayesian Inference
  • Geophysical Inversion

Background:

  • Bayesian inversion relies on estimating the posterior probability density (PPD).
  • Traditional methods like the Fast Gibbs Sampler (FGS) are computationally intensive, especially for complex, multi-frequency, or range-dependent problems.
  • Accurate PPD estimation is crucial for characterizing inversion solutions.

Purpose of the Study:

  • To introduce and evaluate a novel Neighborhood Approximation Bayes (NAB) algorithm as an efficient alternative for Bayesian inversion.
  • To improve the accuracy and completeness of PPD estimation in higher-dimensional or sensitive parameter inversion problems.
  • To reduce the computational burden associated with traditional inversion techniques.

Main Methods:

Related Experiment Videos

  • Developed a Neighborhood Approximation Bayes (NAB) algorithm to approximate the posterior probability density (PPD).
  • Implemented a multi-step inversion scheme that flexibly adjusts parameter search intervals based on preliminary NAB estimations.
  • Incorporated all solved forward models into the appraisal stage for PPD approximation, a key feature of NAB.
  • Main Results:

    • The NAB algorithm demonstrated effective approximation of PPDs in lower-dimensional geoacoustic inversion.
    • A multi-step scheme enhanced NAB's accuracy for higher-dimensional problems and sensitive parameters, yielding more complete parameter uncertainties.
    • NAB provided reasonable estimates of PPD moments, comparable to FGS, but with significantly reduced computation time on synthetic and real data.

    Conclusions:

    • The Neighborhood Approximation Bayes (NAB) algorithm is a computationally efficient alternative to the Fast Gibbs Sampler (FGS) for Bayesian inversion.
    • The proposed multi-step inversion scheme improves NAB's performance in complex scenarios, offering a balance between accuracy and computational cost.
    • NAB presents a viable approach for geophysical inversion, delivering reliable results with substantial time savings.