Dependence of the energy released during earthquake on ambient shear stress
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Abstract
Starting with dislocation model, using the result of the fracture mechanics: the slip displacement at the crack tip is proportional to the length of the crack and the applied ambient shear stressτ 0 2 , we consider the dislocation in the earthquake to be the slip displacement at the crack tip and have obtained the analysis expresses of displacement and velocity pulse for the circular crack and have calculated the seismic wave energy radiated by earthquake. The seismic wave energyE ∞M 0 τ 0 2 f(v) r , i. e.E is proportional to the seismic momentM 0 and the square of the ambient shear stressτ 0 2 and increases with the rupture velocityv r .
In frequency domain, integrating the square of source velocity spectrum derived from our the scaling law model, we have also obtained the seismic wave energyE released by earthquake and earthquake radiated effficiencyη.E ∞M 0 τ 0 2 also. If takingτ 0 = 10.0 MPa, E=4.79M 0. This result is consistent with the estimate by Vassiliou and Kanamori (1982). Theη=5.26%. The distribution of the seismic wave energy is that most of the energy contains in the frequency range between the first corner frequencyf c1 and thirdf c3, amount to 92.3% the energy in the rangef<f c1 is about 3.85% and 3.85% whenf>f c3. Thef c3 is about 8Hz forM ⩾ 6, thus most of radiated energy is below 2Hz. This phenomenon had been verified by Vassiliou Kanamori.
Previous results show the energy radiated by earthquake to be strongly dependent on ambient shear stress.
Key words
energy radiated by earthquake environment shear stress field scaling law source spectrumPreview
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References
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