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Transcript of EQ Moments Stresses - Moment D A=Areaof*rupture* D M o=AD A= Area of the fault that ruptures during...

• Earthquake Moments, energy released & stress drops

Ge11d

• Seismic Moment

D

A=Area of rupture

D

Mo = AD A = Area of the fault that ruptures during the earthquakeD = Average displacement on fault = shear modulus for an elastic solid(i.e. = 2, where and are the shear stress and strain, respectively)

• Seismic magnitudes and moment Since seismic magnitudes (like the Richter scale) Saturates for large earthquakes, seismologists measure the size of an earthquake with seismic moments, Mo

A New Magnitude scale based on moments has been developed, call Moment Magnitudes, Mw

For consistency with the old scales (where Mo is in N-m):

Mw =logMo1.5

6.06

• Stress drop during an earthquake

~ i.e. the elastic stress drop is from the strain, ,associated with the eqarthquake

~ ~ c D A1/ 2

A1/ 2 is a characteristic lengthc is a constant on the order of 1with the definition of the seismic momemt :Mo = AD we getMo = A

3 / 2

As shown in the next slide we can infer and it appears to be about 3 MPa for most earthquakesThis is a very small value.

• Fault area versus seismic moment implies small stress drop

Top: Large & great earthquakes

BoPom small and large earthquakes

100 MPa=1kBar

• Energy released during an earthquake

da = small patch of the faultdu = displacement of patch of faultEs = Force = distance a particle on fault moves = Stress dop = Force/unit area

Es ~ du daA ~ D A

When this is done more formally, for a rectangular fault :

Es 12D A

du

da

A

[Note: this is only the seismic Energy which is radiated seismically; Much energy Goes into melUng and fracturing the Rock]

• Recall for the defination of Seismic Moment :Mo = AD with

Es 12D A

we can write :

Es =2

Mo

Energy Release Versus Seismic Moment

• Heat flow, earthquakes, and the stress on faults

• This is Byerlees Law

Normal Stress, MPa

Shear Stress

100 MPa=1kBar

• Kanamori [1994]