Earthquake source parameters inferred from teleseismic source time functions

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June, 19th, 2008
Orfeus Workshop Waveform Inversion
Earthquake source parameters inferred from
teleseismic source time functions
Martin Vallée and Jean Charléty
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Identification of large earthquake source
parameters
Low frequency surface waves are generally
considered as the most reliable data for
retrieving focal mechanism and moment - Their
low frequency content gives an easier access to
the global parameters of the source - When
earthquakes are complex (i.e. multiple subevents
with different mechanisms), surface waves
are able to give an average focal mechanism
(example 2002 Denali earthquake) - For
exceptional events (i.e. Sumatra), surface waves
are the only adapted waves because of the
mixing of the different body waves
Surface waves are routinely used by Global
CMT - Body waves are also included for
moderate to large earthquakes, (Mwlt7.5)
but surface waves are likely to control the
inversion for larger magnitudes
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Illustration of body waves mixing for the 2004
Sumatra event
Vertical seismic recordings at CAN station
(Geoscope, Australia)
Mainshock (2004/12/26)
Nearby Mw 7.2 earthquake (2002/11/02)
Earthquake duration is longer than time
difference between arrival of body waves
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Principle of Surface wave analysis
The vertical displacement Ur(r,t) is related
with the independent components of the moment
tensor using known excitation functions
Using stations in different azimuths, the inverse
problem should simultaneously retrieve Mxx, Myy,
Mzz, Mxy, Myz, Mxz
Equation governing the low frequency Rayleigh
waves radiation (similar for Love waves)
Kanamori and Given, 1982
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• Limitation of surface waves
• Late arrivals ( problem for very rapid
  information / tsunami alert )
• Trade-off between Dip and Moment

Surface wave radiation
Moment tensor components
X
Consider a superficial inverse earthquake
(example subduction interplate event)
- ? 90
- Qr 0
Ur(r,t) sin(2xdip) M0
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Catalog of large subduction interplate
earthquakes (1990-2007 inverse mechanism
depthlt50km 7.7ltMw Global CMTlt8.9)
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Clues of dip determination problems with surface
waves
1) Comparison with aftershocks
Small blue star mean dip of aftershocks (Global
CMT)
Number of used aftershocks is written for each
earthquake
Dip is significantly different and almost always
(15 of 17) smaller for the mainshock
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2) Comparison with more detailed studies
- Most studies take Global CMT for further
analyses
- Some examples of studies searching a refinement
of Global CMT mechanism
1994 Java earthquake 7 -gt 12 (Abercrombie et
al., 2001) BWSW 1995 Jalisco earthquake 9 -gt
14 (Mendoza Hartzell,1999) BW 2001 Peru
earthquake 18 -gt23 (Bilek and Ruff, 2002)
BW 2003 Hokkaido earthquake 11 -gt 20 (Yagi,
2004) BW SM 11 -gt 20 Mw8.3-gt8.1
(Miyazaki et al. 2004) GPS
Need to constrain with other data - Geodesy
(but what about rigidity?) - Other wave types
which do not suffer from the same trade-off
between dip and moment
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What about Body waves ?
Advantages

• Arrive before
• No trade-off between focal mechanism and moment
• - High frequency body waves much easier to model
  than high frequency surface waves
• better to explain rupture details

Drawbacks
- Low frequency content more difficult to
retrieve for superficial events
- Limitations for giant or very complex
earthquakes
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Example of low frequency effects seen by body
waves
Same slip model contaminated by large constant
slip area
Slip model (strike,dip,rake 318, 20,65)
For a deep event
Modele de glissement
Modele de glissement
Mo 6x1021 N.m Mw 8.45
Mo 3.1x1021 N.m Mw 8.25
DEEP EARTHQUAKE Depth 155km
Teleseismic P-wave displacement
Dist82.5 Az10
Clear effect of doubling the seismic moment
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For a deep event
For a superficial event
Modele de glissement
Modele de glissement
Mo 2.8 1021 N.m
Mo 5.3 1021 N.m
SUPERFICIAL EARTHQUAKE Depth 25km
Why such small differences? pP and sP reflected
phases arrive just after P phase and have
generally an opposite polarity Destruction of
the low frequency part
Dist82.5 Az10
Are we able to detect these small differences in
the global network seismograms?
If yes, moment can be retrieved, and body waves
are useful from low to high frequencies
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Goal of the method Quasi-automatic technique for
retrieving simultaneously the first order
parameters (focal mechanism and depth) and finer
details (duration and shape of the source time
function).
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H (f,d,?,zh,Z1,Z2,Vrz)
We can numerically determine G0 and hence H as a
function of the 7 parameters (f,d,?,zh,Z1,Z2,Vrz).
The deconvolution of H from U gives the
horizontal apparent source time function, equal
to
We use the stabilized deconvolution method of
Vallée (2004), which imposes the causality and
positivity of F
F has a simple physical property, independent of
the station
Principle of the inverse problem what is the set
of the 7 parameters which simultaneously -
minimizes the variance of M0 computed at each
station - best explains the waveforms of U, when
reconvolving H with F
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Practical implementation

• First step (signal duration)
• Define the duration of the P wave signal
• We use the 1Hz duration of the velocity
  seismograms (eg. Ni et al., 2005 Lomax et al.,
  2006)

- Example for the 2005 Northern Sumatra
earthquake 119s
- Second step (P and SH waves optimized
deconvolution)
Example for one P-signal
-1


Filtered P wave signal
Function H
Apparent source time function F
Inversion program optimization of function H (in
terms of (f,d,?,zh,Z1,Z2,Vrz)), so that the
moments defined by function F at all stations
remain as stable as possible.
Use of Neighborhood algorithm (Sambridge, 1999)
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Focal mechanism results compared with Global CMT
Obtained Focal mechanisms and moment
Very good general agreement between this study
and global CMT
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Dip results compared with Global CMT and
aftershocks
This study
The mainshock dip is generally closer from the
aftershocks dip
The tendency of underestimating the aftershocks
dip has disappeared
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Moment results compared with Global CMT and
aftershocks
Moment is found sometimes close but generally
smaller than global CMT moment
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Do our results agree with the M sin(2xdip) rule
?
The results of this study are validated by the
fact that the product M sin(2xdip) is very
similar the one deduced from global CMT
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Further analyses are possible, using the apparent
source time functions retrieved by this analysis
Peru earthquake, 23/06/2001
As shown by more detailed studies, this
earthquake is made of two subevents, the second
one being much larger than the first
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Conclusions

• 1) We have shown that the low frequency content
  of large earthquakes can be
  retrieved by body waves analysis
• - Potential for reliable rapid information
• The difficulty is related to the reduction of
  low frequency energy due to reflected phase
  interactions.
• 2) As theoretically known, we show that global
  CMT is likely to lack resolution for dip
  and moment separation. This trade-off generally
  leads to a dip underestimate and a moment
  overestimate.

Perspectives

• It is important to check if the focal mechanisms
  we propose here would be accepted by surface
  wave analysis
• The apparent source time functions should allow,
  quickly after an earthquake, to define its length
  (useful for quick information/ tsunami alert).
• Further analysis of apparent source time
  functions should give information on the degree
  of complexity of large earthquakes