  We are concerned with inverse boundary problems for first order perturbations
of the Laplacian, which arise as model operators in the acoustic tomography of
a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on
the boundary of a bounded domain in $\mathbb{R}^n$, $n\ge 3$, determines the
first order perturbation of low regularity up to a natural gauge
transformation, which sometimes is trivial. As an application, we recover the
fluid parameters of low regularity from boundary measurements, sharpening the
regularity assumptions in the recent results of [1] and [3]. In particular, we
allow some fluid parameters to be discontinuous.
