An investigation is made of the Lg waves from 15 nuclear tests at the Nevada Test Site (NTS) and 25 shallow western United States earthquakes to obtain a scheme for discriminating between possible source mechanisms. The data were recorded at four broadband stations, operated by Lawrence Livermore National Laboratory (LLNL), which encircle the NTS. The Lg wave spectra are modeled through a genetic algorithm search to find optimal values for (1) the seismic moment (Mo), (2) the corner frequency of the amplitude spectrum (fc), (3) the 1-Hz attenuation quality factors (Qo) for all of the paths, and (4) the frequency dependence (η) of attenuation along the paths. Because the inversion solves for the path attenuation characteristics, little a priori information is needed for the analysis. The resulting Mo and fc values are used in conjunction with the mb values as seismic discriminants. The populations of earthquakes and explosions have nearly identical relationships between their moments and corner frequencies. For earthquakes, the relationship is log Mo = 16.07 – 2.93 log fc. For the set of NTS explosions (using an earthquake source model), the relationship is log Mo = 15.87 – 2.76 log fc. A source discriminant is found, however, through a comparison of the moments and mb values. This gives a line, log Mo = 10.20 + 1.16mb, which cleanly separates the earthquake and explosion populations, with earthquakes falling above and explosions below the line. Reliability tests examine the inverse trade-off between moments and Qo values. Noise in the Lg spectra has a limited effect on the scaling relations.