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

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Mechanics of Earthquakes and Faulting Mechanics of Earthquakes and Faulting 4 Apr. 2007 Energy Balance of Dynamic Faulting Earthquake quantification, Energy, Moment, Magnitude, Scaling laws Corner frequency, Brune Stress 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 where we assume that the initial stress, σ 1 , is equal to the critical stress for failure. That is, the net change in strain energy due to cracking is just equal to the work of faulting W f . σ 1 σ 2 σ Slip, u
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Energy Balance of Dynamic Faulting If we assume that shear stress during slip is equal to a frictional stress, a dynamic friction term, σ f , we can define a dynamic stress drop ∆σ d = ( σ 1 σ f ). where σ 1 is the initial stress –which is not necessarily equal to the yield strength σ y In this case the seismic energy is , if we assume that σ 2 equals σ f –e.g, the final stress is exactly the same as the dynamic frictional strength. (But what about dynamic overshoot, or healing pulse rupture models?) σ 1 σ 2 σ Slip, u The above equation for E
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This note was uploaded on 07/23/2008 for the course GEOSC 508 taught by Professor Marone during the Spring '07 term at Pennsylvania State University, University Park.

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

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