A linear method is developed to reduce the effects of small sound-speed fluctuations in the water column on geoacoustic inversions. Sound-speed fluctuations are considered as a source of physical model error, and their influence on the acoustic data used for determining geoacoustic parameters is estimated by linear perturbation theory. The idea of this method is to project acoustic data onto a space that is insensitive to water sound-speed fluctuations. To determine this space, the singular value decomposition is applied to the kernel of the linear perturbation equation, which links the fluctuations to the acoustic data. This approach will reduce the number of data points available for inversion. Because of this, empirical orthonormal function analysis is employed to represent the sound-speed fluctuations by a small number of modes, which effectively increases the number of projected data points. This method is demonstrated by a numerical test case, using linear internal waves with the Garrett-Munk spectrum to vary the water column in time and space. The influence of the higher-order terms neglected in the linear perturbation equation on the performance of this method is also discussed.