A nonlinear method is developed for the simultaneous inversion of Lg source spectra and path Q. The method is applicable to both earthquakes and explosions. The unknowns are the source corner frequency and seismic moment, as well as Lg Q0 and η values (Lg Q at 1 Hz and its power-law frequency dependence) along paths to the recording stations. The inverse algorithm determines different Q0 and η values for each of the several paths, it is event-based, and it is suitable for real-time processing. The algorithm is further characterized by an exhaustive, nonlinear search for source parameters and linear searches for Q0 and η values. The search process is implemented in successive, increasingly refined steps, designed to accelerate the computation. With these characteristics, the inverse algorithm requires neither a starting model, nor a priori information on the source of Q; it thus avoids convergence to local minima, and is fast enough to be mini-computer based.
The method is applied to three underground nuclear explosions in eastern Kazakhstan. The resulting seismic moment (M0) and corner frequency (fc) for the largest (JVE) event are 1.3 (±0.1) × 1023 dyne-cm and 0.56 (±0.02) Hz, respectively. These values are consistent with previous estimates using other methods and phases, as well as the source scaling relationships developed for NTS explosions. Based on the same scaling relationships, the M0 values obtained for the smaller events in this study suggest seismic yields that are consistent, within reasonable uncertainties, with those predicted by using the ISC mb values and an mb-yield scaling relationship. The path-averaged apparent Q0 and η values agree with previous estimates in roughly the same area, but the values from individual paths can vary significantly. The apparent Q0 values are higher than 750 in two northeasterly directions, and are between 475 and 591 in three other directions. These values correlate with the regional tectonic features. These values also agree, within the uncertainties, with estimates based on a tomographic Lg coda Q0 map by Xie and Mitchell (1991).