earthquake source parameters inferred from teleseismic source time functions orfeus workshop...
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Earthquake source parameters inferred from teleseismic source
time functions
Orfeus Workshop
“Waveform Inversion”
June, 19th, 2008
Martin Vallée and Jean Charléty
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, (Mw<7.5) but surface waves are
likely to control the inversion for larger magnitudes
Identification of large earthquake source parameters
Illustration of body waves mixing for the 2004 Sumatra event
Earthquake duration is longer than time difference between arrival of body waves
Vel
oci
ty (
m/s
)
Time (x100s)
P
P
S
S?
Mainshock
(2004/12/26)
Nearby
Mw 7.2 earthquake
(2002/11/02)
Vertical seismic recordings at CAN station (Geoscope, Australia)
Principle of Surface wave analysis
Kanamori and Given, 1982
The vertical displacement Ur(r,t) is related with the
independent components of the moment tensor using
known excitation functions
Equation governing the low frequency Rayleigh waves radiation (similar for Love waves)
Using stations in different azimuths, the inverse problem should simultaneously retrieve Mxx, Myy, Mzz, Mxy,
Myz, Mxz
Limitation of surface waves
- Late arrivals ( problem for very rapid information / tsunami alert )
- Trade-off between Dip and Moment
Surface wave radiation
X
Ur(r,t) ~ sin(2xdip) M0
Consider a superficial inverse earthquake (example: subduction interplate event) :
- Qr ~ 0
- λ = 90°
Moment tensor components
Catalog of large subduction interplate earthquakes (1990-2007; inverse mechanism; depth<50km; 7.7<Mw Global CMT<8.9)
1) Comparison with aftershocks
Clues of dip determination problems with surface waves
Small blue star: mean dip of aftershocks
(Global CMT)
Number of used aftershocks is
written for each earthquake
Large red star:
Global CMT dip of the
mainshock
Dip is significantly different and almost always (15 of 17) smaller for the mainshock
2) Comparison with more detailed studies
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
1994 Java earthquake : 7° -> 12° (Abercrombie et al., 2001) BW+SW
1995 Jalisco earthquake : 9° -> 14° (Mendoza & Hartzell,1999) BW
2001 Peru earthquake :18 ->23° (Bilek and Ruff, 2002) BW
2003 Hokkaido earthquake : 11° -> 20° (Yagi, 2004) BW +SM
11° -> 20°; Mw=8.3->8.1 (Miyazaki et al. 2004) GPS
- Most studies take Global CMT for further analyses
- Some examples of studies searching a refinement of Global CMT mechanism:
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
Example of low frequency effects seen by body waves
For a deep event
Modele de glissement
Modele de glissement
Clear effect of doubling the seismic moment
DEEP EARTHQUAKE
Depth ~ 155km
Mo = 3.1x1021 N.m ; Mw = 8.25 Mo = 6x1021 N.m ; Mw = 8.45
Dist=82.5°Az=10°
Slip model (strike,dip,rake = 318, 20,65°)Same slip model contaminated by large
constant slip area
Teleseismic P-wave displacement
For a superficial event
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
For a deep event
Modele de glissement
Modele de glissement
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
Dist=82.5°Az=10°
Mo = 2.8 1021 N.m Mo = 5.3 1021 N.m
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).
= H (φ,δ,λ,zh,Z1,Z2,Vrz)
We can numerically determine G0 and hence H as a function of the 7 parameters (φ,δ,λ,zh,Z1,Z2,Vrz). The deconvolution of H from U gives the
horizontal apparent source time function, equal to :
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
F has a simple physical property, independent of the station:
We use the stabilized deconvolution method of Vallée (2004), which imposes the causality and positivity of F
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)
Inversion program: optimization of function H (in terms of (φ,δ,λ,zh,Z1,Z2,Vrz)), so that the moments defined by function F at all stations remain as stable as possible.
- Example for the 2005 Northern Sumatra earthquake :119s
*-1 =
Filtered P wave signal Function H Apparent source time function F
- Second step (P and SH waves optimized deconvolution)
Use of Neighborhood algorithm (Sambridge, 1999)
Example for one P-
signal
Obtained Focal mechanisms and moment
Focal mechanism results compared with Global CMT
Very good general agreement between this study and global
CMT
Dip results compared with Global CMT and aftershocks
The mainshock dip is generally closer from the aftershocks dip
The tendency of underestimating
the aftershocks dip has disappeared
This study
Moment results compared with Global CMT and aftershocks
Moment is found
sometimes close but generally
smaller than global CMT
moment
Do our results agree with the M sin(2xdip) “rule” ?
This study
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
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
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
1) It is important to check if the focal mechanisms we propose here would be “accepted” by surface wave analysis
2) The apparent source time functions should allow, quickly after an earthquake, to define its length (useful for quick information/ tsunami alert).
3) Further analysis of apparent source time functions should give information on the degree of complexity of large earthquakes
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