The precision of Ms‐yield‐scaling results is exploited to place tighter constraints on the volumetric moment due to source‐medium damage than previously estimated for Pahute Mesa explosions on the Nevada Test Site (NTS). Results for two coupling scenarios, one based on P waves to set a lower bound and one based on Rayleigh waves to set an upper bound, bracket the predictions of a model based on moment tensor theory for an explosion monopole and the accompanying damage. This study confirms that the apparent explosion moment MI is a consequence of direct effects of the energy release with a volumetric moment Mt due to cavity formation and the effects due to source‐medium damage. The source model predicts that MI=Mt(K+2)/3, where K is a damage index and a value of 1 means no permanent deformation due to damage. Excess moment due to dilation of the source medium (K>1) is quantified and shown to be a factor increasing the apparent yield (W) scaling of Ms from 0.80log[W] for a pure explosion with cube‐root containment practice and uniform coupling to ∼1.0log[W], a scaling commonly accepted by the explosion community. Scaling observations are related to the source model by establishing the equivalence between network Ms and the theoretical Rayleigh‐wave radiation for an azimuthal‐independent source component. This equivalence motivates a physical basis for transporting observations to other test sites. Transported Ms scaling results for NTS indicate that damage is a more important source of Rayleigh waves for Balapan explosions, most likely due to better energy coupling of upgoing shock waves and stronger free‐surface interactions than for NTS explosions.