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Stress Drop Estimation from Small Earthquakes

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Need for a robust estimator for the corner frequency f0. (1) Sato and Hirasawa, 1973 ... Corner frequency (fc) Radiated energy (Es) Stress Drop from Surface ... – PowerPoint PPT presentation

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Title: Stress Drop Estimation from Small Earthquakes


1
Stress Drop Estimation from Small Earthquakes
  • S. Barbot Plate Boundaries Seminar
  • Discussion around Imanishi et al., Earthquake
    source parameters determined by the SAFOD Pilot
    Hole seismic Array, GRL, 2004

2
Stress Drop Estimation from Small Earthquakes
  • Content
  • Stress Drop from wave spectrum
  • Application in SAFOD Pilot Hole (Imanishi et al)
  • Stress Drop Determination from surface data
    (Prieto et al)

3
Stress Drop ?
  • Stress Drop is important for
  • Investigate source scaling relationships
  • Monitor stress level in the crust
  • Is stress drop independent of earthquake size
    (self-similarity assumption)?

4
Stress Drop and Wave Spectrum
  • Integrated displacement pulse u(x,t) is related
    to seismic moment M0
  • Integrated velocity squared v2(x,t) is related
    to radiated energy ES

5
Stress Drop and Wave Spectrum
  • Displacement wave spectrum is modeled with
    spectral level W0 and corner frequency f02/t.

W0
f0
t
Boatwright, 1978
6
Source Properties
  • Source properties can be inferred from wave
    spectrum

Uncertainty in f0 yields large discrepancies in
Ds.
(2)
(1)
Need for a robust estimator for the corner
frequency f0.
  • Sato and Hirasawa, 1973
  • Eshelby, 1957

7
Wave Convolution Model
  • Accounting for real effects
  • Source s(t)
  • Path effect p(t)
  • Attenuation a(t)

8
SAFOD Pilot Hole
  • Clean Borehole data consisting in
  • 32 seismometers 856m to 2096m depth
  • M1.3 earthquake 3.32km deep

9
Inversion Process
  • Robust Inversion method
  • Constrained Least-Squares (smoothness)
  • Optimal Lagrange multipliers

10
Inversion Result
No Constraints
With Constraints
11
First Conclusion
  • Conclusion on Imanishi et al.
  • Good result
  • Only one single result!
  • No real contribution to the problem

12
Stress Drop from Surface Data (Prieto et al)
  • Path-Station term
  • Earthquake term

13
Stress Drop from Surface Data (Prieto et al)
  • From model fit obtained
  • Corner frequency (fc)
  • Radiated energy (Es)

14
Stress Drop from Surface Data (Prieto et al)
  • Evidence for self-similarity
  • Shifted spectrum
  • Similar shape
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