One of the more intriguing and indeed difficult problems in mathematical physics and the applied sciences is the determination of an impurity in an otherwise homogeneous region from the measurements available of an energy field scattered by the inhomogeneity. Such problems frequently arise when analysing various ultrasonic diagnostic techniques and other non-destructive testing processes; typical areas include radar, sonar, geophysics and medical diagnosis. Physical systems such as these can often be modelled in terms of perturbations of the wave equation. In this paper we shall confine attention to a perturbed wave equation of the form