A systematic analysis of the frequency-dependent source scaling of regional phase data observed from underground nuclear explosions conducted at the former Soviet Semipalatinsk Test Site, the Chinese Lop Nor Test Site, the Russian Novaya Zemlya Test Site, and the U. S. Nevada Test Site has been conducted in an attempt to derive improved, quantitative constraints on proposed physical mechanisms for S-wave generation by explosion sources. The source scaling results for all these testing areas have been found to be remarkably consistent indicating that the observed Sn and Lg spectra scale with explosion yield in a manner that is very comparable to that of the corresponding direct Pn spectra, which differs significantly only over narrow frequency bands defined by differences in the P- and S-wave source corner frequencies. More specifically it has been found that the observed frequency-dependent source scaling of S/P spectral ratios at each of these test sites is very consistent with the simple phenomenological model proposed by Fisk et al. (2005), in which the S-wave source is obtained from the corresponding Mueller/Murphy P-wave source by scaling the corner frequency by the S/P velocity ratio of the source medium. While these results have not yet led to the identification of a specific physical mechanism for S-wave generation by explosions, they do provide very strong constraints that must be satisfied by any plausible proposed physical mechanism.