Two independent arguments indicate an upper bound of about 10 for the ratio ro/ri in the expressions for peak velocity v and peak acceleration a at close hypocentral distances R: v = (βΔτro/μR)[0.10(ro/ri) + 0.15] and a = (Δτ/ρR)[0.30(ro/ri)2 + 0.45], where ri is the radius of the most heavily loaded asperity that fails within an earthquake source region of radius ro, Δτ is the stress drop, β is the shear-wave velocity, μ is the modulus of rigidity, and ρ is the density; these relationships are for ground motion recorded in a whole-space. First, a recently reported data set was augmented by observations for six earthquakes in the magnitude range 4 ≦ ML ≦ 6.6, for which ground motion was recorded at a minimum of five sites at hypocentral distances of the order of 10 km; the new events include the 1979 Coyote Lake and 1979 Imperial Valley shocks. The entire data set of 22 events, spanning a range in seismic moment from 5 × 1016 to over 1026 dyne-cm, is consistent both with the bound ro/ri < 10 and with the previous conclusion that this ratio does not depend systematically on earthquake size. Second, a theoretical argument, using the result of Savage and Wood that the apparent stress acting on the earthquake fault plane is less than half of the stress drop, is made to the effect that ro/ri < 10. In addition, absolute limits, independent of earthquake size, for peak acceleration are related to the state of stress in the crust; for an extensional state of stress a ≦ 0.40 g and for a compressional stress state a ≦ 2.0 g, where a now represents the maximum horizontal acceleration as recorded at the surface directly above the seismic source.