We introduce double‐corner‐frequency (DCF) source spectral models JA19 and JA19_2S, which, in conjunction with a stochastic ground‐motion model, can reproduce the mean peak ground acceleration (PGA) and mean peak ground velocity (PGV) of the Next Generation Attenuation‐West 2 database for magnitudes 3.3–7.3. Their displacement amplitude spectrum remains constant for frequencies less than , decays as between and , and decays as for frequencies greater than . The model JA19 is self‐similar. Its two corner frequencies and scale with moment magnitude () as (1) and (2) . We find that relation (1) is consistent with the known self‐similar scaling relations of the rupture duration (), in which Relation (2) may reflect the scaling relation of the average rise time (), where . Stochastic simulations of ground motion using JA19 cannot reproduce the sharp change in magnitude dependence of PGA and PGV at 5.3, suggesting a breakdown of self‐similarity. The magnitude dependence of PGA and PGV and this change in slope is well explained by JA19_2S, which results from perturbing the scaling relationship in JA19. For JA19_2S: for ; for . The scaling relation for is unchanged. When , the scaled energy (ratio of radiated energy and seismic moment) scales with . The scaled energy of JA19 is , independent of magnitude. Because JA19_2S is not self‐similar, its scaled energy is , increasing 2.2 times, when magnitude increases from 3.3 to 5.3, and, subsequently decreasing 2.2 times, as magnitude further increases from 5.3 to 7.3. Both agree with the global average () reported previously. Using our proposed empirical models, the standard deviation of average static stress drop from seismological studies can be significantly greater than the standard deviation of the stress parameter used to estimate PGA and PGV.