Deviations from SelfSimilarity: the EGF approach

1
Deviations from Self-Similarity the EGF approach

• Germán Prieto
• IGPP, U.C. San Diego

February 23, 2005 US Geological Survey Menlo Park
2
Earthquake Scaling
3
The Question
Are the spectra of larger and smaller earthquakes
similar? How can we accurately describe the
source spectra for different sized events? How
can we describe the uncertainties of source
spectrum estimation when using state-of-the-art
techniques such as EGFs?
4
EQ Physics Outline

• Introduction
• Scaling of the earthquake process
• Radiated energy and uncertainties
• EGF and uncertainties
• Small earthquakes
• Larger earthquakes
• Some conclusions

5
Lots of data for big earthquakes (rupture
dimensions, slip history, etc.)
Small earthquakes are only observed from
seismograms no direct measurements of physical
properties
6
Seismology 101
In theory, far-field seismometer will record
displacement pulse from small earthquake (can be
either P or S wave), ignoring attenuation and
other path effects Area under displacement pulse
f(ht) is related to seismic moment M0 (one
measure of event size) Integrated velocity
squared f(h2/t) is related to radiated energy
ES, another measure of event size
7
Spectral Analysis 101
Time Series
Spectrum
8
(No Transcript)
9
EQ Physics Outline

• Introduction
• Scaling of the earthquake process
• Radiated energy and uncertainties
• EGF and uncertainties
• Small earthquakes
• Larger earthquakes
• Some conclusions

10
Self-Similarity

• Assuming dimensions are scaled proportionally,
  displacement D will increase by b

11
Self-Similarity

• Seismic moment and energy of the larger event
  contain a factor b3 more than the smaller event.
  Apparent stress is constant.

12
Self-Similarity

• Using the similarity theorem of Fourier
  transforms, we see spectra are same shape on
  log-log plot, shifted along w-3 line.
• Possible test of self-similarity, with no
  assumptions of source models (e.g. w-2, w-3).

13
EQ Physics Outline

• Introduction
• Scaling of the earthquake process
• Radiated energy and uncertainties
• EGF and uncertainties
• Small earthquakes
• Larger earthquakes
• Some conclusions

14
Energy Partitioning
Stress
ER Radiated Energy EG Fracture Energy EF Frictiona
l Heat Dc Critical Distance s0 s1 Initial final
stress Ds Stress Drop sf Frictional strength
Slip
Partition of energy for the earthquake process is
still unanswered. Do large and small earthquakes
follow this simple model?
15
Energy Uncertainties
(slide from Arthur McGarr, USGS)
16
Energy Integrals

• Instrumental and practical limitations determine
  upper limit fmax of integration.
• If fmax is too close to the corner frequency fc,
  the energy estimation is biased down.
• Smaller events will tend to have underestimated
  energy.
• - fmax an order of magnitude larger than fc for
  90 energy

17
Stress and Radiated Energy
Simple models follow self-similar
process. Differences in mechanics of EQ may be
explained by normal stress reduction (Brune,
1993), acoustic fluidization (Melosh, 1979),
shear melting (Kanamori and Heaton, 2000), etc.
Is the stress drop close to the absolute stress
level (weak faults) or just a small portion
(strong faults)?
(from Mori et. al, 2003)
18
EQ Physics Outline

• Introduction
• Scaling of the earthquake process
• Radiated energy and uncertainties
• EGF and uncertainties
• Small earthquakes
• Larger earthquakes
• Some conclusions

19
EGF of source spectra

• A flat spectrum is effectively a delta function
  in the time domain.
• If collocated events are available, we can use
  EGF.
• The spectrum of a smaller event represents the
  impulse response of the path between source and
  receiver.

20
EGF Corner frequency

• Result of EGF deconvolution may not be reliable
  at high frequencies.
• A shallower fall-off is obtained if EGF is
  carried out close to the fc of the smaller event.
• To obtain a reasonable result, EGF should go to
  about 1/5 fc of small event.
• A smaller EGF would be preferred, to obtain the
  correct source spectrum.

21
EGF and Noise

• Realistic seismic signals contain noise at both
  low and high frequencies.
• Seismic noise at low frequencies affects smaller
  events significantly.
• If not accounted for, one would effectively
  deconvolve noise, rather than path and site
  effects.

22
EGF and Noise

• Result of EGF deconvolution with low frequency
  earths noise.
• Using too small EGF leads to errors in the
  source spectrum.
• Still at high frequencies the larger EGF result
  is biased.

23
Weighted EGF?

• A weighted and combined EGF might be used to
  construct the source spectrum.
• At high frequencies, we use the EGF to about
  1/5fc.
• At low frequencies we only use SNRgt5, thus using
  only the larger EGFs.
• The shape of the spectrum is preserved at all
  frequencies.

24
EQ Physics Outline

• Introduction
• Scaling of the earthquake process
• Radiated energy and uncertainties
• EGF and uncertainties
• Small earthquakes
• Larger earthquakes
• Some conclusions

25
Anza Seismic Network
Network 9 stations Hard rock sites
250 samples/s UCSD operated
Source region 840 quakes 1982 1993
ML 0 3.4 5 km across
26
Stacking Spectra

• Path-Station term
• Earthquake term

Used in mantle Q study by Warren Shearer (2000,
2002)
27
Corner frequency

• Consistent with Mo ? fc-3.00.3 and fc(P) 1.6
  fc(S)

28
Self-Similarity

• Stacking spectra following ?-3, spectral shapes
  are similar within our uncertainties.
• Self-similarity implies that apparent stress is
  size independent

29
Comparison to previous studies
Our results for Anza give higher apparent stress
than Abercrombie (1995) results for similar size
events. This supports Ide and Beroza (2001)
argument for constant apparent stress.
30
EQ Physics Outline

• Introduction
• Scaling of the earthquake process
• Radiated energy and uncertainties
• EGF and uncertainties
• Small earthquakes
• Larger earthquakes
• Some conclusions

31
Comparison to Regional methods
32
Seven ML 4 - 6
Northridge
Joshua Tree/Landers
33
Corner frequency
fc-3 line
Anza results
New analysis of larger earthquakes
34
EGF spectra of larger events
Note shallow falloff here, real or EGF problem?
35
Study Area

• 10 stations (8 effec. used)
• Vel. and ground motion sensors.
• 100 samples/s
• Max S-R distance 50 km.
• 169 EGF ML 0 - 2.9
• 3 months after mainshock
• Mainshock ML 5.1 (Red) Oct. 31 2001
• Max. interevent distance 2km.
• Max. 5km. for M gt 2

36
Spectrum estimation
M5.1

• Spectral Window 12s.
• Includes P and S waves
• SNR from a similar pre-event waveform

M2.9
37
Weighted EGF

• A weighted and combined EGF leads to reliable
  estimates.
• Weighting based on SNR and expected 1/5fc.

EGF corrected spectra
Venkataraman et. al. (2002)
38
The source spectrum
w-0
w-1
w-2
Model 1 fc 0.88 Hz n 1.7
Model 2 fc 1.78 Hz n 2
39
Source scaling
Fall-off is better constraint. Better EGF used.
ML 5.1
Mw 4.7
Largest Anza bins
40
Source scaling
Largest Anza bins
Anza M5.1 EQ
41
Some conclusions

• The use of EGF may be biased to lead to shallow
  fall-off of the source spectrum.
• A weighted and combined or sectioned EGF may
  accomplish better results, taking into account
  both the low frequency SNR and the corner
  frequency of the EGF used.
• By the use of combined EGFs it should be possible
  to estimate uncertainties of the source spectrum.
  
• Similarity of the source spectra may not hold for
  the larger earthquakes, of course more analysis
  of different events is needed.
• Better analysis of spectra, and specifically
  uncertainties are needed to better constraint the
  scaling of earthquakes.