Analysis of 59 time series from ten small magnitude earthquakes recorded in 1981 by portable digital seismic systems at the southern Nevada Test Site (NTS) yielded several significant results. We find that moment magnitude (M/sub L/) (local magnitude determined from seismic moment) correlates closely with coda duration magnitudes M/sub d/ determined by the Southern Great Basin Seismic Network (SGBSN). Further, local magnitude M/sub W A/ computed from displacement seismograms simulating Wood-Anderson response are, on average, 0.38 magnitude units larger than M/sub d/ and 0.44 magnitude units larger than (M/sub L/). Another result is that stress drops for the ten earthquakes are significantly smaller than typical stress drops for earthquakes of similar seismic moment in California. Similarly, determinations of the peak ground motion parameter Rv are up to 10 to 20 times smaller than a previously determined empirical formula relating Rv to seismic moment. We conclude that seismic waves from southern Nevada Test Site earthquakes suffer from significant anelastic attenuation, possibly in the near-surface crust under the recording sites, yielding reduced amplitude and frequency of the peak ground motion and shifting the apparent corner frequency of the source spectrum to lower values, thereby producing unexpectedly low stress drops.