4 - Seismic Moment and Stress Aki (1966) introduced Mo A D...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Seismic Moment and Stress Aki (1966) introduced Mo A D For crustal rocks = 3.3 dyne/cm2 Seismic moment ( M) is measured in N-m or dyn- cm (1 N-m = 107 dyn-cm). 11 10 Kanamori (1977) used momemt to define the moment magnitude scale M o given here in N-m 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, = initial - final state of shear stress 1 = - 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: ( 29 1 1 / 2 ( / 2) o = + = + The total Strain energy, W, released by the fracture will be simply : . W DA av Stress slip area = = Some of the strain energy is lost to Friction , H. So the Radiated energy E E= W-H = f DA DA - f = frictional stress. E = 1 1 ( / 2) ( ) ( ) f o f DA DA E DA + - = + - o= lower bound of the radiated energy = ( / 2) ( / 2 ) DA M = 11 2 5 10 / , 50 dyne cm bar = = 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 Hooks 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 = L 3 7 16 o M a = 2 2 o M W L = 2 8 3 o M W L = Rupture Model V is either P-wave or S-wave 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 = 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 = shear-wave velocity. K = Scaling factor varies Between 0.5 to 1....
View Full Document

Page1 / 67

4 - Seismic Moment and Stress Aki (1966) introduced Mo A D...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online