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