The observation that P waves from an earthquake are generally more complex than those from an underground explosion was first noted in the 1960s. This difference in P-wave character may still be the only way of identifying small earthquakes close to the detection threshold of a given station network. However, there are certain earthquakes that produce simple seismograms. The frequency at which such earthquakes are mistaken for explosions, using the complexity criterion, is known as the false alarm rate. A simple seismogram can be defined as having only one large-amplitude phase that can be caused by several mechanisms. We examine the proportion of simple seismograms produced by a randomly oriented double-couple source buried in three different crustal structures, observed at a single station at a range of epicentral distances. The model predicts that if the hypocenter of a small earthquake (near the detection threshold) is in a region with thick sediments, then the false alarm rate at a single station can be as high as 50% in the teleseismic distance range (30° to 90°). The results suggest that the false alarm rate is minimized if (1) array stations are used, (2) the station is at a large epicentral distance, (3) the source region structure has few layers, or (4) the disturbance is recorded at more than one station.