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]