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

download EQ Moments Stresses -  Moment D A=Areaof*rupture* D M o=AD A= Area of the fault that ruptures during the earthquake D = Average displacement on fault =shear modulus for an ...

If you can't read please download the document

  • date post

    09-Feb-2018
  • Category

    Documents

  • view

    221
  • download

    0

Embed Size (px)

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]