Some linearized inverse problems for acoustic media

We describe a method for solving several different inverse problems for a weakly inhomogeneous acoustic medium. We will obtain an uncoupled system of one dimensional, second kind Volterra integral equations which is equivalent to the original problem; this equivalence suggests certain numberical solution methods as well as a somewhat syatematic way of analyzing uniqueness and continuous dependence properties for the inverse problem. The common feature of the problems for which this reduction is possible is an invariance with respect to translation in directions parallel to the measurement surface.