A robust probabilistic approach for variational inversion in shallow water acoustic tomography

• Published in: Inverse problems 2009-11, Vol.25 (11), p.115016-115016 (16)
• Main Authors: Berrada, M, Badran, F, Crépon, M, Hermand, J-P, Thiria, S
• Format: Article
• Language: English
• Subjects: Earth Sciences; Environmental Sciences; Exact sciences and technology; Geophysics; Global Changes; Physics; Sciences of the Universe
• ISSN: 0266-5611; 1361-6420
• DOI: 10.1088/0266-5611/25/11/115016

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 eta, which determine a new control vector and a new regularization term, expressed as etaTeta. The PPCA represents a rigorous formalism for the use of a priori information and allows an efficient implementation of the variational inverse method.