The problem of detecting a source in shallow water is addressed. The complexity of such a propagation channel makes precise modeling practically impossible. This lack of accuracy causes a deterioration in the performance of the optimal detector and motivates the search for suboptimal detectors which are insensitive to uncertainties in the propagation model. A novel, robust detector which measures the degree of spatial stationarity of a received field is presented. It exploits the fact that a signal propagating in a bounded channel induces spatial nonstationarity to a higher degree than mere background noise. The performance of the proposed detector is evaluated using both simulated data and experimental data collected in the Mediterranean Sea. This performance is compared to those of three other detectors, employing different extents of prior information. It is shown that when the propagation channel is not completely known, as is the case of the experimental data, the novel detector outperforms the others in terms of threshold signal-to-noise ratio (SNR). In the presence of environmental mismatch, the threshold SNR of the novel detector for the experimental data appears 2-5 dB lower than the other detectors. That is, this detector couples good performance with robustness to propagation uncertainties.