Slip-inversion artifacts common Slip-inversion artifacts common to two independent methodsto two independent methods

J. Zahradník, J. Zahradník, F. GalloviF. Gallovičč

Charles University in PragueCharles University in Prague

Czech RepublicCzech Republic

Guess the correct answer:

If two methods yield a stable slip feature, that feature is likely true.

If two methods yield a stable slip feature, that feature might still be wrong.

Guess the correct answer:

If two methods yield a stable slip feature, that feature is likely true.

If two methods yield a stable slip feature, that feature might still be wrong.

Two methods:

• iterative deconvolution of the point-source contributions (Kikuchi and Kanamori, 1991) and ISOLA code (Sokos & Zahradnik, 2008); modified to allow a less concentrated distribution of the slip (Zahradnik et al., JGR, in press)

• a new technique (Gallovic et al., GRL 36, L21310, 2009), iterative back-propagation of the waveform residuals by the conjugate gradients technique; gradient of the waveform misfit with respect to the model parameters being expressed analytically; the positivity and fixed scalar moment constraint applied

The two methods do not need

prior knowledge of the nucleation point and rupture velocity.

Part 1

An incorrect rupture velocity and spurious (false) patches from

error-free synthetic data.

Synthetic data mimic

Mw 6.3 earthquake, Greece 2008

discussed at the end.

Low-frequency inversion (f<0.2 Hz) of synthetic near-regional data: a line source

The station distribution fixed (as in real data case).Three scenarios of the rupture propagation direction.Two asperities symmetric with respect to the fault center.

Low-frequency inversion (f<0.2 Hz) of synthetic near-regional data: a line source

The station distribution fixed (as in real data case).Three scenarios of the rupture propagation direction.Two asperities symmetric with respect to the fault center.

Iterative method(color;

slip velocity)

ISOLA

free and modified(green circles;

proportional to moment)

x

t

‘free’

‘modified’

‘Free’ = very concentrated‘Modified’ = better distributed

Vr = 3.28 km/s(instead of 3 km/s)

Unilateral propagation(from the left)

3 km/s

Vr = 3.68 km/s(instead of 3 km/s)

Unilateral propagation(from the right)

3 km/s

Vr = 5.68 and 5.26 km/s (instead of 3 km/s),

i.e. a larger temporal delay closer to the fault center

and a FALSE ASPERITY at the center !

Common to both methods.

Bilateral propagation(from the center),

no slip at the fault centerin the input model

3 km/s3 km/s

Vr = 5.68 and 5.26 km/s (instead of 3 km/s),

i.e. a larger temporal delay closer to the fault center

and a FALSE ASPERITY at the center !

Common to both methods.

Bilateral propagation(from the center),

no slip at the fault centerin the input model

3 km/s3 km/s

the worst case

Where the problems may arise from?

Explanation in terms of concepts of the ‘source tomography’ (80’s), e.g.,Ruff (1984), Menke (1985), Frankel & Wennerberg (1989)

kinematic approach

Forward simulation of two asperities

(2 x 5 point sources)and

two stations0 10 20 30a lo n g p ro file (km )

4

6

8

10

12

0 10 20 30 40tim e (se c)

120

160

200

240

280

SE5

ZAK

directive station

anti-directive station

Slip

Rupture propagation along fault (x)

time

dis

pla

cem

ent

ZAK

SER

Forward simulation of two asperities

(2 x 5 point sources)and

two stations0 10 20 30a lo n g p ro file (km )

4

6

8

10

12

0 10 20 30 40tim e (se c)

120

160

200

240

280

SE5

ZAK

directive station

anti-directive station

Slip

Rupture propagation along fault (x)

timex

t

‘locating’the 2x5 sources back to source

ZAK

SER

Forward simulation of two asperities

(2 x 5 point sources)and

two stations0 10 20 30a lo n g p ro file (km )

4

6

8

10

12

0 10 20 30 40tim e (se c)

120

160

200

240

280

SE5

ZAK

directive station

anti-directive station

Slip

Rupture propagation along fault (x)

timex

t

0 10 20 30 40a lo n g p ro file (km )

0

4

8

12

16

20

time

(se

c)

SER

ZAK

ZAK

SER

Kinematic Projection Lines(trade-off between source position and time)

0 10 20 30 40a lo n g p ro file (km )

0

4

8

12

16

20tim

e (

sec)

SER

ZAK

Vr = 3 km/sec

x

t

0 10 20 30 40a lo n g p ro file (km )

0

4

8

12

16

20tim

e (

sec)

SER

ZAK

Vr = 3 km/sec

True asperity

True asperity

x

t

0 10 20 30 40a lo n g p ro file (km )

0

4

8

12

16

20tim

e (

sec)

SER

ZAK

Vr = 3 km/sec

False asperity

False asperity

The unilateral case:False asperity biases the rupture velocity.

x

t

-20 -10 0 10 20a lo n g p ro file (km )

0

4

8

12

16

time

(se

c)

SER

ZAK

Vr = 3 km/sec

The bilateral case:False asperity appears as aseparate ‘event’ on theintersectionof two directive strips.

true true

false x

tSER station is directive for one asperity

ZAK station is directive for the other asperity

Partial results

The projection lines of the individual stations explain the spurious patches.

We need a generalization of the Kinematic Projection Lines, or Strips (KPS) for complete

wavefields in heterogeneous media.

New: thus we introduce

the Dynamic Projection Strips (DPS).

Dynamic Projection Strips(still on synthetic data)

Key concept: Mapping the correlation between a complete observed waveform at a station and a synthetic waveform due

to a single x-t point source.

It works like a ‘multiple-signal detector’.

The waveform is mapped into equivalent x-t points, similar to kinematic location, hence analogy with the projection lines.

Part 2The directive station SER is strongly affected by both patches,

but ‘sees’ them as a single one.

The anti-directive (backward) station ZAK ‘sees’ both patches.

x

t Unilateral rupturetoward x > 0

Dynamic Projection Stripsderived from

synthetic waveforms

Part 2

The DPS (at right),derived form waveforms,

are analogical to kinematic projection lines

(dashed).

Unilateral rupturetoward x > 0

Part 2

Intersecting DPS’ of the individual stations

(so-called ‘dark spots’) delimit the source region.

Unilateral rupturetoward x > 0

Part 2

Final inversion result, already understandable

in terms of the station contributions.

Unilateral rupturetoward x > 0

Part 2SER is a directive station

for one asperity.

ZAK is directive for the other asperity.

Bilateral rupturefrom x=0

Part 2

Intersection of the two directive strips

attracts the solution to the fault center (false).

Bilateral rupturefrom x=0

Part 2

FALSE !

Thus the false asperity is explainedby separately

analyzing waveforms of individual stations

in terms of DPS.

Bilateral rupturefrom x=0

Partial results (still synth. data)

The dynamic projection strips (DPS) can be constructed from complete waveforms.

The strips illuminate the role played by each station in the slip inversion.

The strips enable quick identification of the major slip features: the predominant rupture

direction, multiple asperities, etc.

Possible constraints to reduce artifacts

Position of the nucleation point

Position of a partial patch

Caution:Constraining with wrong parameter values may bias the solution!

(if known …) (if known …)

Part 2

Real earthquake data (Mw 6.3 strike-slip)

Can the Dynamic Projection Strips

be extracted from real waveforms ?

Application

Movri Mountain (Andravida)

Mw 6.3 earthquake, June 8, 2008

NW Peloponnese, Greece

Gallovic et al., GRL 36, L21310, 2009

ITSAK, Greece

2 victimshundreds of injuries

More details of the practical application in the presentation by Sokos et al. (T/SD1/MO/06)

HYPO and DD relocation: A. Serpetsidaki, Patras

PSLNET BB and SM (SER, MAM, LTK, PYL co-operated by Charles Univ.)

ITSAK SM NOA BB

Near-regional slip inversion

Dynamic projection strips: real data

Near-regional stations(< 200 km)

f < 0.2 Hz

Aggregated strips of all 8 stationsand the slip inversion: real data

Data indicate a predominant unilateral rupture propagation,with an almost 5-sec delay of the rupture at the hypocenter.

Zahradnik and Gallovic, JGR 2010, in press

Non-unique results: examples of slip models (green) equally well matching

real waveforms (var. red. 0.7):

Black circles: an (assumed) patchused to initializethe inversion.

Zahradnik and Gallovic, JGR 2010, in press

• The intention was to improve insight in the slip-inversion ‘black box’.

Conclusions:

• The intention was to improve insight in the slip-inversion ‘black box’.

• We suggest complementing the inversions by analyses of the Dynamic Projection Strips (constructed from complete waveforms). • DPS illuminate the individual station roles and indicate the major slip features. They also explain the origin of possible artifacts, e.g. biased rupture velocities, or false asperities.

Conclusions:

• The intention was to improve insight in the slip-inversion ‘black box’.

• We suggest complementing the inversions by analyses of the Dynamic Projection Strips (constructed from complete waveforms). • DPS illuminate the individual station roles and indicate the major slip features. They also explain the origin of possible artifacts, e.g. biased rupture velocities, or false asperities. • Spurious asperities may be very stable and common to independent methods; thus easily misinterpreted as ‘real’ features in standard resolution checks.

• The same station distribution may create artifacts, or not, dependent on the true slip model.

Conclusions:

• The intention was to improve insight in the slip-inversion ‘black box’.

• We suggest complementing the inversions by analyses of the Dynamic Projection Strips (constructed from complete waveforms). • DPS illuminate the individual station roles and indicate the major slip features. They also explain the origin of possible artifacts, e.g. biased rupture velocities, or false asperities. • Spurious asperities may be very stable and common to independent methods; thus easily misinterpreted as ‘real’ features in standard resolution checks.

• The same station distribution may create artifacts, or not, dependent on the true slip model.

• For a mathematical counterpart of DPS in terms of Singular Value Decomposition, see Gallovic & Zahradnik (JGR submitted) and poster ES5/P9/ID112 in this session.

Conclusions:

Examples of slip models (A to E) equally well matching real

waveforms

Black circles: an (assumed) slip patch used to initialize the inversion

Part 2

x

t Unilateral rupturetoward x > 0

Dynamic Projection Stripsderived from

synthetic waveforms

Part 2

This scenario gives similarresult, but not exactly

‘mirror-like’.

It is because the station network is not symmetric

with respect to fault.

Unilateral rupturetoward x < 0

Part 2

Thus the false asperity is explainedby separately

analyzing waveforms of individual stations

in terms of DPS.

FALSE !

Bilateral rupturefrom x=0

Possible constraints to reduce artifacts

Position of the nucleation point

Position of a partial patch

Caution:Constraining with wrong parameter values may bias the solution!

(if known …) (if known …)

Part 2 … or increasing frequency

(if the structural model is known)

Trade-off between source position and time

Station Y

True position of a point asperity Xa

Trial position of a point asperity X

Tr (Xa) + T(Xa,Y) = const = Tr (X) + T(X,Y)

Knowing the asperity position and time, Xa and Tr(Xa), we can calculate all equivalent positions X and times Tr (X) characterized by

the same arrival time (=const): a hyperbola. For a station along the source line, the Tr = Tr(X) degenerates to a straight line.