In this study the tectonic stress along active crustal fault zones is taken to be of the form ??(y) + ????p(x, y), where ??(y) is the average tectonic stress at depth y and ???? 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 ????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 ????p(x, y) is of the form |????p(k)| ?? l/k2, where ????p(k) is the two-dimensional Fourier transform of ????p(x, y) expressed in radial wave number k. The y = 2 model of the far-field shear wave displacement spectrum is consistent with the spectral composition |????p(K)| ?? l/k2, provided that the number of contributions to the spectral representation of the radiated field at frequency f goes as (k/ko), consistent with the quasi-static frequency of occurrence relation N ?? 1/r2; K o is a reference wave number associated with the reciprocal source dimension. Separately, a variety of seismologic observations suggests that the ?? = 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 y = 2 model, and the constancy of earthquake stress drops independent of size are all related to the average spectral composition of ???? p(x, y), |????p(k)| ?? l/k2. Should one of these change as a result of premonitory effects 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 y = 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 arme = 0.85[21/2(2??)2/106] (????/pR)(f max/f0)1/2, where ???? is the earthquake stress drop, p 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, a rms holds considerable promise as a measure of high-frequency strong ground motion for engineering purposes. Copyright ?? 1979 by the American Geophysical Union.
Additional Publication Details
B values and ??-?? seismic source models: Implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion