Seismic Coda Waves. L. Margerin. CNRS, Toulouse, France

Transcription

1 Mesoscopic Physics in Complex Media, 11 (21) DOI:1.151/iesc/21mpcm11 Owned by the authors, published by EDP Sciences, 21 Seismic Coda Waves L. Margerin CNRS, Toulouse, France In collaboration with B. Van Tiggelen, M. Campillo, E. Larose, C. Sens-Schoenfelder, V. Rossetto, N. Shapiro Students: D. Anache-Ménier, T. Planès, A. Obermann This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3., which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly cited. Article published online by EDP Sciences and available at or

2 Seismic Coda Waves L. Margerin CNRS, Toulouse, France Mesoscopic physics in complex media In collaboration with B. Van Tiggelen, M. Campillo, E. Larose, C. Sens-Schoenfelder, V. Rossetto, N. Shapiro Students: D. Anache-Ménier, T. Planès, A. Obermann L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 1 / 35

3 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 2 / 35

4 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 3 / 35

5 Crustal Coda Waves Space and Time Scales Frequency > 1 Hz Wavelength tens of meters to kilometers Mean free path?? Crustal Earthquakes in Japan L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 4 / 35

6 Inner Core Coda Waves Vidale and Earle, Nature (2) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 5 / 35

7 Mesoscopic physics with seismic waves Equipartition (Hennino et al., PRL, 21) Weak localization (Larose et al., PRL, 24) Green function retrieval from coda waves (Campillo and Paul, Science, 23) Green function retrieval from noise (Aki, Bull. Earthquake Res. Institute, 1956 ; Shapiro and Campillo, GRL, 24) Tomography Monitoring Coda wave interferometry (Diffusing Acoustic Wave Spectroscopy) (Poupinet et al., JGR, 1984; Sens-Schoenfelder and Wegler, GJI, 26; Brenguier et al., Nature Geoscience 27)... L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 6 / 35

8 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 7 / 35

9 Pynion Flats Observatory Array 1 km 12 PFO Nevada Test 37 Site RECORDED LOCAL EVENTS Grid Geometry meters L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 8 / 35

10 Data from California y (m) time (s) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 9 / 35

11 Array Analysis Wagner, JGR, 13, 1998 L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 1 / 35

12 Stablization of Vertical to Horizontal Kinetic Energy Ratio Ballistic Waves Energy 1 1 Coda V 2 /H Noise.4 Stabilization Time (s) V 2 = H 2 = t+t t T t+t t T ρω 2 u 2 z (ω, τ)dτ ρω 2 (u 2 x(ω, τ) + u 2 y (ω, τ))dτ Time (s) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

13 Frequency-dependent V 2 /H 2 partition ratio V 2 H Frequency Hz L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

14 Equipartition In a small frequency band, all the modes are excited to equal energy (Weaver, 1982) "Reference" Earth = Layered Half Space "True" Earth = Disordered Half Space vs1,d1,vp1,h1 vs1,d1,vp1,h1 vsi,di,vpi,hi vsi,di,vpi,hi vsn,dn,vpn,hn vsn,dn,vpn,hn Half Space u (t, r) = n a nφ n (r)e iω nt Half Space u (t, r) = n a n(t)φ n (r)e iω nt Assumption: a n (t)a n (t) = σ 2 (t)δ nn Consequence: u i (x A, ω)u j (x B, ω) C Im G ij (x A, x B, ω) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

15 Theory vs Observations Velocity Model h 1 = 4m α 1 = 3m/s β 1 = 15m/s ρ 1 = 22kg/m 3 h 2 = 11m α 2 = 9m/s β 2 = 5m/s ρ 2 = 22kg/m 3 h 3 = 5m α 3 = 31m/s β 3 = 16 m/s ρ 3 = 27kg/m 3 α = 54m/s β = 3m/s ρ = 27kg/m 3 V 2 H Frequency Hz L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

16 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

17 Experimental Set-Up L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

18 Cross-correlation of coda waves C ij (x a, x b, τ) = ui (x a, t τ/2)u j (x b, t +τ/2)dt Source average Reconstruction of Rayleigh and Love waves fundamental mode Temporal asymmetry L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

19 Understanding the temporal asymmetry Results from 2-D F.D. simulation Early coda Late coda d u(r r/2, t τ/2)u(r + r/2, t + τ/2) dτ E(R, t) [G(r, τ) G(r, τ)] 3J(R, t) r [G(r, τ) G(r, τ)] (B.V.T., PRL, 23) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

20 GF reconstruction with the coda of noise based GF EMV GIMEL C C A A A C C A Noise GIMEL EMV Time [S] EMV GIMEL 45 Coda Noise Time [S] Figure 1. Upper panel: Green s function between EMV and GIMEL reconstructed by correlating one year of noise records (black) and by correlating coda waves reconstructed by noise correlations. We show with different L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

21 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 2 / 35

22 Earthquake doublets Same location Same mechanism Nearly identical waveforms Drawback: no continuous monitoring L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

23 Repeated shots recorded on Merapi Volcano 1998 E L E- - - L time, s (a) time, s (b) (c) time, s No changes on the first arrival Increasing delay time in the coda Stretching of the signal tiny velocity change in the medium Active source experiments are expensive L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

24 Monitoring with seismic noise Example on Piton de la Fournaise (a) Green function obtained from cross-correlation of seismic noise Time(s) (b).3.2 V /V (%).1.1 Eruption Measurement of stretching parameter in the coda Days of year 26 Passive image interferometry (Sens-Schoenfelder and Wegler, GJI, 26; Brenguier et al., Nature Geoscience, 28; Brenguier et al., Science, 28) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

25 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

26 Specific issues in seismology Detection operates at the surface Earthquakes sources are often at depth Problem 1: Weak localization has size of a wavelength around the source Problem 2: The source mechanism L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

27 Enhanced backscattering in a 2-D chaotic cavity Role of the source Monopole Dipole Normalized intensity y(mm) 5-5 x(mm) 5 Normalized intensity y(mm) x(mm) 2 De Rosny et al., PRE, 21 L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

28 Small-scale seismic experiment Velocity (norm.) Velocity (1 3 ) (a) (b) R(t) 1 5 1/2 (c) time (second) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

29 Observation of weak localization Frequency dependence 2 Rise time mean free time 1.7 s.7 s.3 s S( r) Hz 19 Hz, =27 m S( r) 1 S( r) meters S( r) Hz 23 Hz, =13 m Hz 3 Hz, =11 m meters L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

30 Content 1 Observation of seismic coda waves 2 Equipartition of seismic waves 3 Green function reconstruction 4 Monitoring the Earth with coda waves 5 Weak localization of seismic waves 6 Phase statistics of coda waves L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

31 Phase Statistics Phase of the analytic signal Easy with seismic waves: spatial and temporal resolution Free from effect of absorption Simplifying assumptions : Analyze the phase field of vertical components Wavefield obeys Circular Gaussian Statistics: L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese 21 3 / 35

32 Data from California y (m) time (s) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

33 Field and Intensity.6 Re ψ in A.U. 2 2 (a) I/ I (b) P (Re ψ) log(i/ I ) 6 L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

34 2-Point Statistics 1 1 P(φ )/δ P( φ) P ( φ) measured P ( φ u ) measured P (φ )/δ fit P ( φ) fit P ( φ u ) fit φ δ φ φ : Phase difference ( 2π, 2π] φ u : Unwrapped phase difference ( π, π] L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

35 Higher Phase Derivatives 1 P(φ (n) )/δ n P (φ ) measured P (φ ) measured P (φ ) fit P (φ ) fit φ (n) δ n Fitting Parameters: Coefficients of Taylor series of field correlation function Universal behavior for n th derivative: slope = (1 + 2/n) L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35

36 Phase Difference Correlation.2 2 C φ(r) = φu φu ln(r φu φu ) r (m) r (m) Correlation function 1 r e r/2l Van Tiggelen et al., EPL, 26; Anache et al., P.R.L., 29 L. Margerin (CNRS, Toulouse, France) Seismic Coda Waves Cargese / 35