Using Back Projection to Image Earthquake Source Complexity Claudio Satriano, Viviana Dionicio, Jean-Pierre Vilotte, Pascal Bernard Institut de Physique du Globe de Paris - Sorbonne Paris Cité, Université Paris Diderot, UMR CNRS 7154 satriano@ipgp.fr S43C-2253 Introduction In recent years a new approach to earthquake rupture imaging has emerged, based on the exploitation of the coherency of the seismic signal recorded at dense seismic networks (e.g. Ishii et al., 2005). The back-projection method (BPM) has been initially proposed as a tool for rapidly assessing extended earthquake source. It has however subsequently proven to be an efective approach in constraining some key source parameters (fault extension, rupture velocity…) and in retrieving “hidden”, features of the rupture process, like secondary events embedded in the main shock (Allmann and Shearer, 2007). The full potential of the BPM has however still to be exploited. The strength of this methodology is in its capacity of directly imaging the rupture process from the radiation emitted from the source - and coherently received at recording array - providing a natural framework for studying the radiation in time, space and frequency. In this poster we outline the basics steps of the back projection approach, and we discuss the important aspects of resolution and calibration of the back projection images. We apply the method to the Mw 9.0 Tohoku earthquake and show how back projection can be used to constrain some key kinematic parameters for fnite fault slip inversion. The combined interpretation of the back-projection and slip images opens up interesting questions about the complexity of the rupture of mega-thrust earthquakes. 200 km 3. Resolution and Calibration Array Response Function (ARF) We evaluate the resolution of the back projection analysis by simulating a virtual point source that has the same frequency characteristics of the main shock: § We take the main shock signal recorded at a central station of the array and assign it to all the stations, with a delay corresponding to the propagation time from the hypocenter. § We back project the resulting virtual data set. The size of the resulting spot is an empirical estimate of the Array Response Function of the given station confguration. Improving resolution by station weighting The resolution can be improved by weighting each station’s contribution by the local station density. For this purpose we use a Voronoi tessellation with weights proportional to the size of each cell. −20˚ −20˚ −10˚ −10˚ 0˚ 0˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 40˚ 40˚ 50˚ 50˚ 40˚ 40˚ 50˚ 50˚ 60˚ 60˚ 70˚ 70˚ Voronoi tessellation of VEBSN VEBSN central station Filtered between 0.50 and 4.00 Hz 200 km 200 km 200 km 200 km 200 km 200 km ARF @ 0.07-0.20 Hz no-weight ARF @ 0.07-0.20 Hz weighted ARF @ 0.20-0.50 Hz weighted ARF @ 0.50-4.00 Hz no-weight ARF @ 0.50-4.00 Hz weighted ARF @ 0.20-0.50 Hz no-weight 200 km Back Projection @ 0.50-4.00 Hz 200 km Local Peaks @ 0.50-4.00 Hz 200 km Convolved Local Peaks @ 0.50-4.00 Hz Extract local peaks Convolve by ARF Local Back Projection Peaks The back projection (BP) images can be interpreted in terms of convolution of the local BP peaks (extracted using a local maximum flter) and the resolution spot provided by the Array Response Function. Analysis of the Calibration We check the time-lag calibration of the VEBSN, calculated for the main shock, by performing the back projection of foreshocks and aftershocks of Mw 5.6 - 6.5 with similar fault mechanism respect to the main shock. The results show a good agreement between the centroid locations of the analyzed earthquakes and the back projection maxima. 1. Rupture imaging from the back projection of body waves 1. The Back Projection Method (BPM): § is a signal processing technique (not an inversion) based on coherent interferometry at the scale of the recording array; § does not require assumptions about rupture kinematic parameters (but can help in assessing them). 2. Stacking Technique § The construction of the stack (the “beam”) can be done either by simple summation, or using some more refned procedure. § Here we employ the “Nth-Root” stacking (with N=4, Xu et al. 2009), designed to mitigate the efect of a spike or a glitch on a single trace. § It is defned as: where B(t) is the fnal beam and b j (t) is the j-th trace. B  (t)= 1 M M  j =1 |b j (t)| 1/N · sign{b j (t)} B (t)= |B  (t)| N sign{B  (t)} 3. Efect of the 3D structure: Calibration § Generally a radial Earth model is used to predict the travel times (e.g. AK135). § These models are however not accurate enough to correctly align the phases, with the efect of defocusing the beams. § An extra step is therefore to compute time corrections at each station by cross- correlating and re-aligning a reference arrival (generally the P arrival from the hypocenter). 1. Grid of possible source locations 2. Predicted P-wave travel time at the receiver network 3. Stacking along the predicted travel-time curves 4. The value of the stack is assigned to the corresponding grid point 5. Repeat through time T0 T1 T3 T2 Unmodelled velocity perturbations ◀ First 15 seconds of P–wave from the Tohoku earthquake recorded at the vertical components of the Virtual European Broadband Seismic Network (see section 2). Left: traces fltered between 0.50 and 4.00 Hz Right: traces fltered between 0.20 and 0.50 Hz Top: traces aligned using the travel-times from the hypocenter predicted by the AK135 model (Kennet et al., 1995). Bottom: traces re-aligned using cross- correlation. The stations lags are always constrained using the highest frequency band. (redrawn from Shearer, 2009) 2. The Mw 9.0 Tohoku earthquake: high-frequency images of the rupture from back projection 30 60 90 0.07 - 0.20 Hz 0.20 - 0.50 Hz 0.50 - 4.00 Hz 10 -3 10 -2 10 -1 10 0 10 1 10 2 frequency (Hz) 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 amplitude Velocity Spectra - Europe ◀ We use 210 stations of the Virtual European Broadband Seismic Network (VEBSN – Data downloaded from http://www.orfeus-eu.org/Data-info/ vebsn.html) Based on the velocity spectra, we selected three frequency bands for the back projection analysis. For each band we calculate the normalized back projection image, which can be interpreted as the relative coherent radiated energy emissivity in space and time. Back projection results► The back projection (BP) images can be represented in diferent ways: § As a function of time and space (Time Evolution); § In a single time-combined snapshot, where for each point we keep the maximum BP value (Time-Combined Image); § By plotting the maximum BP value for each time (Energy Time Function); § Showing the peaks in space and time (Peak Values and Along-dip and Along-strike propagation). ▼ 200 km 200 km 0 20 40 60 80 100 120 140 160 180 200 Time (s) −250 −200 −150 −100 −50 0 50 100 150 200 250 Along−strike distance (km) 0 20 40 60 80 100 120 140 160 180 200 Time (s) 1.0 km/s 1.5 km/s 2.0 km/s 2.5 km/s 3.0 km/s −250 −200 −150 −100 −50 0 50 100 150 200 250 Along−dip distance (km) 1.0 km/s 1.5 km/s 2.0 km/s 2.5 km/s 3.0 km/s Along-dip propagation Along-strike propagation 0.0 0.2 0.4 0.6 0.8 1.0 Relative Power −10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (s) Energy Time Function Time-Combined Image Peak Values 0.07 - 0.20 Hz 200 km 200 km 0 20 40 60 80 100 120 140 160 180 200 Time (s) −250 −200 −150 −100 −50 0 50 100 150 200 250 Along−strike distance (km) 0 20 40 60 80 100 120 140 160 180 200 Time (s) 1.0 km/s 1.5 km/s 2.0 km/s 2.5 km/s 3.0 km/s −250 −200 −150 −100 −50 0 50 100 150 200 250 Along−dip distance (km) 1.0 km/s 1.5 km/s 2.0 km/s 2.5 km/s 3.0 km/s Along-dip propagation Along-strike propagation Energy Time Function 0.0 0.2 0.4 0.6 0.8 1.0 Relative Power −10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (s) Time-Combined Image Peak Values 19.5 s 200 km 36.5 s 200 km 62.5 s 200 km 110.5 s 200 km 135.5 s 200 km 165.5 s 200 km Time Evolution 0.20 - 0.50 Hz 200 km 200 km 0 20 40 60 80 100 120 140 160 180 200 Time (s) Along-dip propagation Along-strike propagation −250 −200 −150 −100 −50 0 50 100 150 200 250 Along−strike distance (km) 0 20 40 60 80 100 120 140 160 180 200 Time (s) 1.0 km/s 1.5 km/s 2.0 km/s 2.5 km/s 3.0 km/s −250 −200 −150 −100 −50 0 50 100 150 200 250 Along−dip distance (km) 1.0 km/s 1.5 km/s 2.0 km/s 2.5 km/s 3.0 km/s Energy Time Function 0.0 0.2 0.4 0.6 0.8 1.0 Relative Power −10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (s) Time-Combined Image Peak Values 0.5 s 200 km 36.5 s 200 km 62.5 s 200 km 90.5 s 200 km 126.5 s 200 km 159.5 s 200 km Time Evolution 0.50 - 4.00 Hz 4. The broad-band nature of the Tohoku earthquake 30 s 100 km 150 s 100 km 180 s 100 km 60 s 100 km 90 s 100 km 120 s 100 km 200 100 0 Depth(km) −300 −200 −100 0 Distance(km) Trench 140˚ 142˚ 144˚ 34˚ 36˚ 38˚ 40˚ 42˚ 300 s A B 100 km 0 5 10 15 20 25 30 35 40 45 50 Slip (m) ˚ 4 4 1 ˚ 2 4 1 ˚ 0 4 1 34˚ 36˚ 38˚ 40˚ 42˚ 100 km 0 20 40 60 80 100 120 140 160 180 200 Time (s) d~124 km t~80 s v~1.6 km/s d~150 km t~56 s v~2.6 km/s ◀ From the short-period back projection analysis, the main features of the Tohoku coherent radiation emission associated with the rupture process are a frst (0-80s) radiation episode, eastward of the epicenter, evidencing a slow (~ 1.6 km/s) mainly down-dip rupture propagation, preceded by a slow 10 initiation phase; and ultimately (80-160s) a deep radiation phase evidencing a faster (~2.5 km/s) southward rupture propagation. Back projection analysis was used to constrain the rupture dimension and the rupture velocity history for the kinematic fnite fault inversion. ► A broadband kinematic slip inversion has been performed using the Kikuchi and Kanamori (1991) method on a data-set of 53 broadband stations at teleseismic distance. From the point of view of broadband fnite fault inversion, the main features of the coherent slip and slip-velocity distribution associated with the rupture process are a frst (0-80s) slip episode, in a relatively limited zone around the epicenter, evidencing a initial up-dip slip propagation associated with a strong shallow slip asperity (> 40 m) toward the trench, followed by a weaker down-dip slip propagation; fnally a later episode (80-160s) characterized mainly by a week-slip southward propagation. ▼ For more information, please check-out the poster: U51B-0035. Preliminary analysis of the rupture process of 11 March 2011 Tohoku-Oki earthquake Tomorrow from 8:00 AM to 12:20 AM 0 20 40 60 80 100 120 140 160 180 200 Time (s) Moment Rate Function Conclusions and Perspectives § Thanks to the availability of dense seismic arrays, new coherent interferometry methods - such as the back projection method – provide today an efective approach to imaging short-period radiation emissivity during the rupture process. § This approach, in combination with the kinematic fnite fault solution provides a multi-frequency observation window that opens up new questions about the complexity of the rupture of mega-thrust earthquakes. § The results on the Tohoku earthquake shows that low frequencies, tsunamigenic slip histories are preferentially generated up-dip, whereas high frequencies are generated preferentially down-dip (mantle wedge?). § A multi-scale distribution of asperities on the fault surface seems requested for explaining the complexity of this rupture dynamics. § The frequency-dependent observations of the rupture coherent radiation should provide new constraints for the frictional properties of the plate interface and of the asperities. 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