The physical basis ofmb:Msand variable frequency magnitude methods for earthquake/explosion discrimination

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 themb:Msdiscriminant: 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 withmb< 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 isPwave speed) to the ratio of surface wave amplitude to body wave amplitude. Interference of ρpimproves discrimination for large, deeply buried explosions but may degrade or preventmb:Msdiscrimination of small, shallow explosions. If biases due to regional variations in propagation path are absent, or corrected for, we predict that themb:Msmethod 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 betweenPwaves produced by earthquakes and explosions. Theoretical separation of earthquake and explosion populations occurs for events withmb> 4.0, using a frequency band of 0.5–3.0 Hz. For small events the VFM discriminant is complementary tomb:Msin several ways: VFM is improved by ρpinterference, whilemb:Msis degraded; VFM is more effective for hard rock explosions, whilemb:Mswill preferentially discriminate explosions in low‐velocity materials; and VFM is insensitive to fault orientation. VFM is more sensitive to noise and regional attenuation differences thanmb:Ms. Simultaneous use of both methods should allow improved discrimination of small events.