In this study the tectonic stress along active crustal fault zones is taken to be of the form ? (y)+ Δ&sgr;p(x,y), where ? (y) is the average tectonic stress at depth y and Δ&sgr;p(x,y) is a seismologically observable, essentially random function of both fault plane coordinates; the stress differences arising in the course of crustal faulting are derived from Δ&sgr;p(x,y). Empirically known frequency of occurrence statistics, moment-magnitude relationships, and the constancy of earthquake stress drops may be used to infer that the number of earthquakes N of dimension ?r is of the form N ~ 1/r2 and that the spectral composition of Δ&sgr;p(x,y) is of the form ‖?&sgr;p(k) ‖ ~ 1/k2, where ?&sgr;p(k) is the two-dimensional Fourier transform of Δ&sgr;p(x,y) expressed in radial wave number k. The &ggr; = 2 model of the far-field shear wave displacement spectrum is consistent with the spectral composition ‖?&sgr;p(k) ‖ ~ 1/k2, provided that the number of contributions to the spectral representaiton of the radiated field at frequency f goes as (k/ko)2, consistent with the quasi-static frequency of occurrence relation N ~ 1/r2; ko is a reference wave number associated with the reciprocal source dimension. Separately, a variety of seismologic observations suggests that the &ggr;=2 model is the one generally, although certainly not always, applicable to the high-frequency spectral decay of the far-field radiation of earthquakes. In this framework, then, b values near 1, the general validity of the &ggr; = 2 model, and the constancy of earthquake stress drops independent of size are all related to the average spectral composition of Δ&sgr;p(x,y), ‖?&sgr;p(k) ‖ ~ 1/k2. Should one of these change as a result of premonitory effect leading to failure, as has been specifically proposed for b values, it seems likely that one or all of the other characteristics will change as well from their normative values. Irrespective of these associations, the far-field, high-frequency shear radiation for the &ggr; = 2 model in the presence of anelastic attenuation may be interpreted as band-limited, finite duration white noise in acceleration. Its rms value, arms, is given by the expression arms=0.85<21/2(2&pgr;)2/106>(Δ&sgr;/&rgr;R)(fmax/@qL fo) 1/2, where Δ&sgr; is the earthquake stress drop, &rgr; is density, R is hypocentral distance, fo is the spectral corner frequency, and fmax is determined by R and specific attenuation 1/Q. For several reasons, one of which is that it may be estimated in the absence of empirically defined ground motion correlations, arms holds considerable promise as a measure of high-frequency strong ground motion for engineering purposes.