Journal ArticleDOI
Tectonic stress and the spectra of seismic shear waves from earthquakes
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In this paper, an earthquake model is derived by considering the effective stress available to accelerate the sides of the fault, and the model describes near and far-field displacement-time functions and spectra and includes the effect of fractional stress drop.Abstract:
An earthquake model is derived by considering the effective stress available to accelerate the sides of the fault. The model describes near- and far-field displacement-time functions and spectra and includes the effect of fractional stress drop. It successfully explains the near- and far-field spectra observed for earthquakes and indicates that effective stresses are of the order of 100 bars. For this stress, the estimated upper limit of near-fault particle velocity is 100 cm/sec, and the estimated upper limit for accelerations is approximately 2g at 10 Hz and proportionally lower for lower frequencies. The near field displacement u is approximately given by u(t) = (σ/μ) βr(1 - e−t/r) where. σ is the effective stress, μ is the rigidity, β is the shear wave velocity, and τ is of the order of the dimension of the fault divided by the shear-wave velocity. The corresponding spectrum is
Ω(ω)=σβμ1ω(ω2+τ−2)1/2(1)
The rms average far-field spectrum is given by
〈 Ω(ω) 〉=〈 Rθϕ 〉σβμrRF(e)1ω2+α2(2)
where 〈Rθϕ〉 is the rms average of the radiation pattern; r is the radius of an equivalent circular dislocation surface; R is the distance; F(e) = {[2 – 2e][1 – cos (1.21 eω/α)] +e2}1/2; e is the fraction of stress drop; and α = 2.21 β/r. The rms spectrum falls off as (ω/α)−2 at very high frequencies. For values of ω/α between 1 and 10 the rms spectrum falls off as (ω/α)−1 for e < ∼0.1. At low frequencies the spectrum reduces to the spectrum for a double-couple point source of appropriate moment. Effective stress, stress drop and source dimensions may be estimated by comparing observed seismic spectra with the theoretical spectra.read more
Citations
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References
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Journal ArticleDOI
Scaling law of seismic spectrum
TL;DR: In this paper, the authors investigated the dependence of the amplitude spectrum of seismic waves on source size by fitting an exponentially decaying function to the autocorrelation function of the dislocation velocity and found that the most convenient parameter for their purpose is the magnitude Ms, defined for surface waves with period of 20 sec.
Journal ArticleDOI
Stick-slip as a mechanism for earthquakes.
W. F. Brace,James D. Byerlee +1 more
TL;DR: Stick-slip often accompanies frictional sliding in laboratory experi ments with geologic materials and may represent stick slip during sliding along old or newly formed faults in the earth.
Journal ArticleDOI
Magnitude and energy of earthquakes
TL;DR: In this article, the relation of earthquake magnitude M to energy E (in ergs) was investigated and three different magnitude scales were proposed: M_L, the magnitude originally defined by Richter for local earthquakes in California as recorded on standard torsion seismometers, M_S, based on calculated ground amplitudes for surface waves of periods of about 20 sec. in shallow teleseisms, and M_B, that based on the amplitude/period ratio in body waves for both shallow and deep earthquakes.
Book ChapterDOI
Total energy and energy spectral density of elastic wave radiation from propagating faults
TL;DR: In this paper, it was shown that a shear fault is rigorously equivalent to a distribution of double-couple point sources over the fault plane, while a tensile fault is composed of force dipoles normal to the fault surface with a superimposed purely compressional component.
Journal ArticleDOI
Body force equivalents for seismic dislocations
R. Burridge,Leon Knopoff +1 more
TL;DR: In this paper, an explicit expression for the body force to be applied in the absence of a dislocation, which produces radiation identical to that of the dislocation was derived for dislocations in an anisotropic inhomogeneous medium.