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Unformatted text preview: Seismic Moment and Stress – Aki (1966) introduced Mo A D μ For crustal rocks = 3.3 × dyne/cm2 μ Seismic moment ( M) is measured in Nm or dyn cm (1 Nm = 107 dyncm). 11 10 ✦ Kanamori (1977) used momemt to define the moment magnitude scale M o given here in Nm M W = 2 / 3 * log(M o )  10.73 Stress Fault rupture is caused by stress in the earth. The relative slip on both sides of the dislocation surface occurs when shear stress exceeds the available friction stress. str ess dr op, = Δσ initial  final state of shear stress 1 σ σ =  Stresses are measured in bar , dyn/cm2, and N/m2 (Pa). The r elated conver sions ar e: 1 bar = 106 dyn/cm2, 1 Pa = 10 dyn/cm2, and 1 Mpa = Stress The aver age str ess is defined as the mean value of the shear stresses acting before and after the earthquake: σ ( 29 1 1 / 2 ( / 2) o σ σ σ σ σ = + = + ∆ The total Strain energy, W, released by the fracture will be simply : . W DA av Stress slip area σ = = Some of the strain energy is lost to Friction , H. So the Radiated energy E E= WH = f DA DA σ σ f σ = frictional stress. E = 1 1 ( / 2) ( ) ( ) f o f DA DA E DA σ σ σ σ σ ∆ +  = +  o= lower bound of the radiated energy = ( / 2) ( / 2 ) DA M σ σ μ ∆ = ∆ 11 2 5 10 / , 50 dyne cm bar μ σ = ∆ = I f ( 29 4 ; 2 10 o M E = log log 4.3 E M =  Where E is in ergs. Substituting M o we will get log 1.5 11.8 o w E M = + Moment and Energy Stress and Fault L W D Let the average slip = for a fault of length L and width W The strain According to Hook’s law , the stress drop and strain could be related as Where =Characteristic rupture dimension(either L or W) C = constant depends on the fault geometry Circular fault (radius a) strike slip fault Dip slip fault D D D or L W D ( ) D C L σ μ ∆ = L 3 7 16 o M a σ ∆ = 2 2 o M W L σ π ∆ = 2 8 3 o M W L σ π ∆ = Rupture Model V is either Pwave or Swave velocity The time taken by the wave to reach station from the far end of the rupture R V L V r T = V r T T o R = Rupture Model Due to the finite rupture length the radiated pulse varies in the time duration as a function azimuth. Area of the pulse is same at all azimuths, The magnitude of the source time function varies inversely with the duration. This is called Directivity effect Directivity Doppler effect. Shifts the Frequency of moving oscillator to higher frequency when oscillator moves towards the observer and lower frequency when its move away. Rupture Model Aki (1987) relate stress drop and slip velocity of a rupture as r D K T μ σ β ∆ = If is the time taken by the rupture to sweep a fault of length L, then r r L T V D We assume here that = shearwave velocity. K = Scaling factor varies Between 0.5 to 1....
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This note was uploaded on 10/26/2008 for the course CIVIL 602 taught by Professor Duta during the Spring '08 term at Air Force Institute of Technology, Ohio.
 Spring '08
 Duta

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