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b values and ω−γ seismic source models: Implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion

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DOI: 10.1029/JB084iB05p02235

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Abstract

In this study the tectonic stress along active crustal fault zones is taken to be of the form inline image, where inline image is the average tectonic stress at depth y and Δσp(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 Δσp(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 Δσp(x, y) is of the form inline image, where inline image is the two-dimensional Fourier transform of Δσp(x, y) expressed in radial wave number k. The γ = 2 model of the far-field shear wave displacement spectrum is consistent with the spectral composition inline image, provided that the number of contributions to the spectral representation of the radiated field at frequency ƒ goes as (k/k0)2, consistent with the quasi-static frequency of occurrence relation N ∼ 1/r2;k0 is a reference wave number associated with the reciprocal source dimension. Separately, a variety of seismologic observations suggests that the γ = 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 γ = 2 model, and the constancy of earthquake stress drops independent of size are all related to the average spectral composition ofinline image. 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 γ = 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(2π)2/106] (Δσ/ρR)(ƒmax0)1/2, where Δσ is the earthquake stress drop, ρ is density, R is hypocentral distance, ƒ0 is the spectral corner frequency, and ƒmax 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.

Additional Publication Details

Publication type:
Conference Paper
Publication Subtype:
Conference Paper
Title:
b values and ω−γ seismic source models: Implications for tectonic stress variations along active crustal fault zones and the estimation of high-frequency strong ground motion
DOI:
10.1029/JB084iB05p02235
Volume
84
Issue:
B5
Year Published:
1979
Language:
English
Publisher:
AGU Publications
Description:
8 p.
First page:
2235
Last page:
2242
Online Only (Y/N):
N
Additional Online Files(Y/N):
N