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