Ground motions for large and moderately large earthquakes at short and moderate distances are particularly important for seismic hazard estimation in eastern North America (ENA). Very few direct observations of such ground motions have been obtained, however, because of the sparsity of recording sites and the relatively low rates of occurrence of large earthquakes inside the region. Estimation of strong ground motion must therefore rely heavily on theoretical models to extend empirical results obtained from small earthquakes and from the few larger ones for which reliable data are available. Because of the generally large distances between recording stations, the main source of useful data comes from Lg wave trains observed at relatively large distances. For the two largest earthquakes to have occurred near populated regions of southeastern Canada during the past decade, spectral ratios of the Lg wave trains of the mainshocks, with respect to those of their aftershocks, are found to depend almost entirely upon the source radiation characteristics of the sources alone. This result is utilized to derive elastodynamically-based kinematic rupture models that are consistent with the empirical spectral ratio data. Such models provide a firm physical basis from which to infer the most probable spectral characteristics for future large earthquakes in the region. In converse application, it is shown that spectral ratios obtained from such models, along with empirical seismograms from small earthquakes, can be used to accurately simulate strong ground motions at short and moderate (as well as large) distances. As such small-event seismograms are relatively plentiful, the problem of reliable strong ground motion estimation is therefore reduced to that of obtaining reliable representative source spectral models. The solution of this latter problem must continue to depend upon whatever empirical data are available and upon appropriately detailed theoretical modeling.