b values and. omega. /sup -gamma/ seismic source models: Implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion

Journal Article · Thu May 10 04:00:00 EDT 1979 · J. Geophys. Res.; (United States)

DOI:https://doi.org/10.1029/JB084iB05p02235· OSTI ID:6028924

Hanks, T C

In this study the tectonic stress along active crustal fault zones is taken to be of the form sigma-bar (y)+ ..delta..sigma/sub p/(x,y), where sigma-bar (y) is the average tectonic stress at depth y and ..delta..sigma/sub 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 ..delta..sigma/sub 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 > or =r is of the form N approx. 1/r/sup 2/ and that the spectral composition of ..delta..sigma/sub p/(x,y) is of the form vertical-barDelta-tildesigma/sub p/(k) vertical-bar approx. 1/k/sup 2/, where Delta-tildesigma/sub p/(k) is the two-dimensional Fourier transform of ..delta..sigma/sub p/(x,y) expressed in radial wave number k. The ..gamma.. = 2 model of the far-field shear wave displacement spectrum is consistent with the spectral composition vertical-barDelta-tildesigma/sub p/(k) vertical-bar approx. 1/k/sup 2/, provided that the number of contributions to the spectral representaiton of the radiated field at frequency f goes as (k/k/sub o/)/sup 2/, consistent with the quasi-static frequency of occurrence relation N approx. 1/r/sup 2/; k/sub o/ is a reference wave number associated with the reciprocal source dimension. Separately, a variety of seismologic observations suggests that the ..gamma..=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 ..gamma.. = 2 model, and the constancy of earthquake stress drops independent of size are all related to the average spectral composition of ..delta..sigma/sub p/(x,y), vertical-barDelta-tildesigma/sub p/(k) vertical-bar approx. 1/k/sup 2/.

• Research Organization: U. S. Geological Survey, Menlo Park, California 94025
• OSTI ID: 6028924
• Journal Information: J. Geophys. Res.; (United States), Journal Name: J. Geophys. Res.; (United States) Vol. 84:B5; ISSN JGREA
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
580201* -- Geophysics-- Seismology & Tectonics-- (1980-1989)
FOURIER TRANSFORMATION
FUNCTIONS
GEOLOGIC FAULTS
GEOLOGIC STRUCTURES
GROUND MOTION
INTEGRAL TRANSFORMATIONS
MATHEMATICAL MODELS
MOTION
SEISMIC SOURCES
SPECTRAL FUNCTIONS
STRESSES
TRANSFORMATIONS