We use recent results from deterministic numerical modeling of earthquakes and explosions to develop an improved physical basis for earthquake/explosion discrimination. We use six three-dimensional finite difference simulations of earthquakes for the earthquake source models and four empirical and four numerical models for explosions in different materials. Four factors contribute to the success of the mb: Ms discriminant: source spectra, focal mechanism, near-source elastic properties, and interference of ρp. Spectral differences contribute about 0.5 magnitude unit to the separation between earthquake and explosion populations for large events, but this difference vanishes for events with mb < 4.5. The difference in focal mechanism (quadrupole versus monopole) contributes about 0.35 magnitude unit on the average but also introduces a scatter of ±0.5 magnitude unit into the earthquake population. Differences in near-source elastic properties tend to increase the separation, contributing a factor of approximately (ρα3)½ (ρ is density and α is P wave speed) to the ratio of surface wave amplitude to body wave amplitude. Interference of ρp improves discrimination for large, deeply buried explosions but may degrade or prevent mb: Ms discrimination of small, shallow explosions. If biases due to regional variations in propagation path are absent, or corrected for, we predict that the mb: Ms method will successfully discriminate most earthquakes from explosions, but there will be some overlap between populations at small magnitudes. The variable frequency magnitude (VFM) discriminant is based on spectral differences between P waves produced by earthquakes and explosions. Theoretical separation of earthquake and explosion populations occurs for events with mb > 4.0, using a frequency band of 0.5–3.0 Hz. For small events the VFM discriminant is complementary to mb: Ms in several ways: VFM is improved by ρp interference, while mb: Ms is degraded; VFM is more effective for hard rock explosions, while mb: Ms will preferentially discriminate explosions in low-velocity materials; and VFM is insensitive to fault orientation. VFM is more sensitive to noise and regional attenuation differences than mb: Ms. Simultaneous use of both methods should allow improved discrimination of small events.