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]