Geoacoustic inversion using a matched-field inversion algorithm is a well-established technique for estimating the geoacoustic parameters of the seabed. This paper demonstrates how parameter estimation can be affected by unknown or wishfully ignored random range dependence of the true environment when the inversion model is--for practicality--assumed to be range independent. Simulations with controlled statistics were carried out using a simple shallow water model: an isospeed water column over a homogeneous elastic halfspace. The inversion parameters included water depth, compressional speed in the seabed, seabed density, and compressional wave attenuation. On average the environment is range independent: some parameters are constant while other parameters are random with range-independent means and variances. A Parabolic Equation underwater acoustic propagation model is used to calculate the simulated data fields for the range-dependent environment as well as to calculate the model fields for the range-independent inversion model. The Adaptive Simplex Simulated Annealing inversion algorithm is used to estimate the best-fit solution. It is found that ignoring the variability of even a single geoacoustic parameter leads to significant and correlated uncertainty (bias and variance) in the estimation of all inverted parameters. Results are presented for range variation of compressional sound speed and water depth.