vallee by pengxiang


									                              June, 19th, 2008

  Orfeus Workshop
“Waveform Inversion”

              Earthquake source parameters
             inferred from teleseismic source
                       time functions

                    Martin Vallée and Jean Charléty
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

      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
                 Illustration of body waves mixing for the 2004 Sumatra event

Vertical seismic recordings at CAN station (Geoscope, Australia)

Velocity (m/s)

                       P                  S?

                                                                              Mw 7.2
                       P                 S                                  earthquake
                                  Time (x100s)

                              Earthquake duration is longer than time
                              difference between arrival of body waves
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
   Kanamori and Given, 1982
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

                                             Consider a superficial inverse earthquake
                                             (example: subduction interplate event) :
                                                        - λ = 90°
                                                        - Qr ~ 0

                                                        Ur(r,t) ~ sin(2xdip) M0
Catalog of large subduction interplate earthquakes (1990-2007; inverse
         mechanism; depth<50km; 7.7<Mw Global CMT<8.9)
 Clues of dip determination problems with surface waves

      1) Comparison with aftershocks

                                                                Small blue star:
                                                                  mean dip of
                                                                 (Global CMT)

                                                                 Large red star:
                                                                 Global CMT dip
                                                                     of the

                                                                Number of used
                                                                 aftershocks is
                                                                written for each

Dip is significantly different and almost always (15 of 17) smaller for the mainshock
     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° -> 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

              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
What about Body waves ?


       - 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”


       - 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

                                                   Same slip model contaminated by large
    Slip model (strike,dip,rake = 318, 20,65°)               constant slip area

  For a deep event

             Modele de
                                                        Modele de
         Mo = 3.1x1021 N.m ; Mw = 8.25                Mo = 6x1021 N.m ; Mw = 8.45

EARTHQUAKE                                                           Teleseismic P-wave
Depth ~ 155km


                           Clear effect of doubling the seismic moment
 For a deep event

  For a superficial event

           Modele de
                                                      Modele de

         Mo = 2.8 1021 N.m                                  Mo = 5.3 1021 N.m

SUPERFICIAL                                                                Why such small
EARTHQUAKE                                                                  differences?

Depth ~ 25km                                                              pP and sP reflected
                                                                           phases arrive just
                                                                           after P phase and
                                                                           have generally an
                                                                           opposite polarity
                                               Az=10°                      Destruction of the
                                                                          low frequency part

   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
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 :

     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
 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)

for one P-                            -1                        =
  signal                              *
             Filtered P wave signal           Function H                   Apparent source
                                                                            time function F
 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.

                                 Use of Neighborhood algorithm (Sambridge, 1999)
       Focal mechanism results compared with Global CMT
Obtained Focal mechanisms and moment

                                       Very good general agreement
                                       between this study and global
Dip results compared with Global CMT and aftershocks

                                                        This study

                                                       The mainshock
                                                       dip is generally
                                                       closer from the
                                                       aftershocks dip

                                                         The tendency of
                                                       the aftershocks dip
                                                         has disappeared
Moment results compared with Global CMT and aftershocks

                                                           Moment is
                                                            close but
                                                          smaller than
                                                          global CMT
Do our results agree with the M sin(2xdip) “rule” ?

                                                      The results of this
                                                           study are
                                                       validated by the
                                                         fact that the
                                                        M sin(2xdip)
                                                      is very similar the
                                                         one deduced
                                                      from global CMT

                                This study
Further analyses are possible, using the apparent source time
             functions retrieved by this analysis

                                                                Peru earthquake,

                                                                 As shown by
                                                                 more detailed
                                                                  studies, this
                                                                 earthquake is
                                                                  made of two
                                                                subevents, the
                                                                  second one
                                                                  being much
                                                                larger than the

     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.


     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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