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A robust probabilistic approach for variational inversion in shallow water acoustic tomography
Berrada, M.; Badran, F.; Crépon, M.; Hermand, J.-P.; Thiria, S. (2009). A robust probabilistic approach for variational inversion in shallow water acoustic tomography. Inverse problems (Print) 25(11): 115016. dx.doi.org/10.1088/0266-5611/25/11/115016
In: Inverse Problems. Institute of Physics: Bristol. ISSN 0266-5611; e-ISSN 1361-6420
Peer reviewed article  

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Auteurs  Top 
  • Berrada, M.
  • Badran, F.
  • Crépon, M.
  • Hermand, J.-P.
  • Thiria, S.

Abstract
    This paper presents a variational methodology for inverting shallow water acoustic tomography (SWAT) measurements. The aim is to determine the vertical profile of the speed of sound c(z), knowing the acoustic pressures generated by a frequency source and collected by a sparse vertical hydrophone array (VRA). A variational approach that minimizes a cost function measuring the distance between observations and their modeled equivalents is used. A regularization term in the form of a quadratic restoring term to a background is also added. To avoid inverting the variance–covariance matrix associated with the above-weighted quadratic background, this work proposes to model the sound speed vector using probabilistic principal component analysis (PPCA). The PPCA introduces an optimum reduced number of non-correlated latent variables ?, which determine a new control vector and a new regularization term, expressed as ?T?. The PPCA represents a rigorous formalism for the use of a priori information and allows an efficient implementation of the variational inverse method.

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