Slip-inversion artifacts common to two independent methods J. Zahradník, F. Gallovič Charles University in Prague Czech 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.

HYPO and DD relocation: A. Serpetsidaki, Patras PSLNET BB and SM (SER, MAM, LTK, PYL co-operated by Charles Univ.) ITSAK SMNOA BB Synthetic data mimic the Mw 6.3 Movri Mountain 2008 (Andravida) earthquake, Greece

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 center in the input model 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 center in the input model 3 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 stations directive station anti-directive station Slip Rupture propagation along fault (x) time displacement ZAK SER

Forward simulation of two asperities (2 x 5 point sources) and two stations directive station anti-directive station Slip Rupture propagation along fault (x) time x t ‘locating’ the 2x5 sources back to source ZAK SER

Forward simulation of two asperities (2 x 5 point sources) and two stations directive station anti-directive station Slip Rupture propagation along fault (x) time x t ZAK SER Kinematic Projection Lines (trade-off between source position and time)

x t

True asperity x t

False asperity The unilateral case: False asperity biases the rupture velocity. x t

The bilateral case: False asperity appears as a separate ‘event’ on the intersection of two directive strips. true false x t SER 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 2 The 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 rupture toward x > 0 Dynamic Projection Strips derived from synthetic waveforms

Part 2 The DPS (at right), derived form waveforms, are analogical to kinematic projection lines (dashed). Unilateral rupture toward x > 0

Part 2 Intersecting DPS’ of the individual stations (so-called ‘dark spots’) delimit the source region. Unilateral rupture toward x > 0

Part 2 Final inversion result, already understandable in terms of the station contributions. Unilateral rupture toward x > 0

Part 2 Final inversion result, already understandable in terms of the station contributions. Unilateral rupture toward x > 0

Part 2 x t Unilateral rupture toward x > 0 Dynamic Projection Strips derived from synthetic waveforms

Part 2 This scenario gives similar result, but not exactly ‘mirror-like’. It is because the station network is not symmetric with respect to fault. Unilateral rupture toward x < 0

Part 2 SER is a directive station for one asperity. ZAK is directive for the other asperity. Bilateral rupture from x=0

Part 2 Intersection of the two directive strips attracts the solution to the fault center (false). Bilateral rupture from x=0

Part 2 FALSE ! Thus the false asperity is explained by separately analyzing waveforms of individual stations in terms of DPS. Bilateral rupture from x=0

Part 2 Thus the false asperity is explained by separately analyzing waveforms of individual stations in terms of DPS. FALSE ! Bilateral rupture from 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 …)

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 victims hundreds 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 SMNOA BB Near-regional slip inversion

Dynamic projection strips: real data Near-regional stations (< 200 km) f < 0.2 Hz

Aggregated strips of all 8 stations and 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) patch used to initialize the 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 rupture toward x > 0 Dynamic Projection Strips derived from synthetic waveforms

Part 2 This scenario gives similar result, but not exactly ‘mirror-like’. It is because the station network is not symmetric with respect to fault. Unilateral rupture toward x < 0

Part 2 Thus the false asperity is explained by separately analyzing waveforms of individual stations in terms of DPS. FALSE ! Bilateral rupture from 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 …)

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.