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508L11.4.4.07 - Mechanics of Earthquakes and Faulting 4 Apr...

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Mechanics of Earthquakes and Faulting Mechanics of Earthquakes and Faulting 4 Apr. 2007 Energy Balance of Dynamic Faulting Earthquakequantification, Energy, Moment, Magnitude, Scaling laws Corner frequency, BruneStress drop. Mechanics of Faulting
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Energy Balance of Dynamic Faulting The rate of energy change is a balance between work terms, surface energy, kinetic energy, and frictional work. These terms operate over different regions. Recall that in the Linear Elastic Fracture Mechanics Approach to Dynamic Crack Propagation: LEFM assumes that cracks are cohesionless. In this case the crack tip energy term, U s , can be determined Σ Σ S 0 V V 0
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Energy Balance of Dynamic Faulting Energy Partitioning If we choose the bounding surface sufficiently large, work at external boundaries, W, is zero. Then the energy remaining to be radiated seismically is the dynamic change in kinetic energy ( implies a change in the state during dynamic rupture relative to the initial state). Σ Σ S 0 V V 0 Recall that in the Linear Elastic Fracture Mechanics Approach to Dynamic Crack Propagation: LEFM assumes that cracks are cohesionless. In this case the crack tip energy term, U s , can be determined
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Energy Balance of Dynamic Faulting Σ Σ S 0 V V 0 The change in internal strain energy can be written in terms of the drop in shear stress associated with rupture ∆σ = σ 1 σ 2 whereweassumethat theinitial stress, σ 1 , is equal to thecritical stress for failure. That is, thenet changein strain energy dueto cracking is just equal to thework of faulting W f . σ 1 σ 2 σ Slip, u
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Energy Balance of Dynamic Faulting If weassumethat shear stress during slip is equal to a frictional stress, a dynamic friction term, σ f , wecan definea dynamic stress drop ∆σ d = ( σ 1 σ f ). where σ 1 is theinitial stress –which is not necessarily equal to theyield strength σ y In this case the seismic energy is , if we assume that σ 2 equals σ f –e.g, thefinal stress is exactly the sameas thedynamic frictional strength. (But what about dynamic overshoot, or healing pulserupturemodels?) σ 1 σ 2 σ Slip, u
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