Acoustic interface treatment with an adjoint operator for linear range-dependent ocean index of refraction inversions

Hursky et al. [J. Acoust. Soc. Am. 115(2), 607-619 (2004)] introduced the adjoint method and incorporated local sound-speed measurements into range-dependent ocean sound-speed inversion. They left two practical issues for the implementation of this method unresolved in this paper: the collection of appropriate environmental measurements and the implementation of bottom boundary conditions. The first of these issues was considered in a simulation study that used an oceanographic glider to collect range-dependent sound-speed measurements [Richards, CMRE memorandum (2012)]. A covariance matrix was constructed from the changes observed in the range-dependent sound-speed field. The adjoint inversion was performed in a reduced element subset of the empirical orthogonal functions (EOF) base of the covariance matrix. The second issue is the focus of this paper, which describes a bottom boundary condition with a defined adjoint operator. A horizontal fluid-bottom interface is implemented using the implicit finite difference form of the parabolic equation introduced by McDaniel and Lee [J. Acoust. Soc. Am. 71(4), 855-858 (1982)]. Combined with local range-dependent sound-speed statistics gathered with gliders, this development may provide a method of near real-time acoustic measurement of ocean sound-speed variations between an acoustic source and vertical hydrophone array. © 2013 Acoustical Society of America