Supplementary Information

Transcription

1 Supplementary Informaton Procedure for nose cross-correlaton computaton and stackng Fgure S syntheszes the cross-correlaton procedure. To normalze the sesmc nose n tme and spectral domans, we appled a spectral whtenng followed by a onebt normalzaton. For spectral whtenng, we take the sesmc sgnal Fourer transform and normalze ts modulus to one n the selected frequency band and force ts modulus to 0 elsewhere (smoothed boxcar wndow). We do not change the phase of the Fourer transform. We fnally perform an nverse Fourer transform to retreve the whtened sgnal. By dong so, we do not change the spectral phase of the sgnal. We also computed the RTP usng a dfferent normalsaton when the runnng-absolute-mean normalzaton n tme doman was followed by the spectral whtenng. Results of ths test shown n Fg. S2 demonstrate that the RTP anomales computed wth dfferent data processng methods are very smlar to each other. Fnally, we prefer to use the one-bt normalzaton because t s faster than the runnng-absolute-mean normalzaton and better removes strong gltches from the sgnal. In ths study, we compute the reference Green functons by stackng the one-day cross-correlaton functons (CCF) accordng to a sgnal to nose rato crteron (CCF sgnal energy larger than.5 tmes the CCF nose energy, 4 over 550 one-day CCF stacked on average). Procedure for measurng Relatve Tme Perturbatons (RTP) We remnd that the cross-correlaton of sesmc nose between recevers A and B yelds the Green functons between A and B (postve tmes, causal) and between B and A (negatve tmes, ant-causal). In case of perfect reconstructon, these two Green functons are dentcal. In Fg. S3a, we schematcally llustrate possble paths for the reconstructed dffracted surface waves. We now consder a unform relatve shear wave velocty decrease wthn the sampled medum ( β/β = const.). In ths case, scattered waves that travelled along longer paths accumulated larger tme delays ( τ). The Green functon estmated after the velocty change (red sgnal) wll, therefore, correspond to a

2 2 stretched verson of the reference functon (Fg. S3b). We then consder a small wndow of wdth T and centred on tme τ. We compute a cross-spectrum between the reference and current Green functons taken wthn ths small wndow and measure the spectral phase shft Φ at dfferent frequences f (Fg. S3c). For each frequency, the phase error E Φ s estmated by: E = " (/ 2! ), 2 " B " T # c $ where c s the coherency and B! s the spectral wdth. The local tme shft between the current and the reference Green functons s then estmated as the slope b = τ = Φ/(2 π f) by a lnear regresson that takes nto account the phase error E Φ as a weghtng factor. The error on the slope estmate ( τ ) s calculated as: % # E$ & = wth M _ 2 ( f f ) " =! M # _ 2 (! "!) _ = $! =, # = 2%! " $! f, M where M s the number of frequency samples and f _, the average frequency. By repeatng ths operaton for a seres of small wndows centred at dfferent tmes we estmate the local tme shft as a functon of tme: τ (τ ). In a case of a unform velocty perturbaton wthn the meda t s expected to be a lnear functon (Fg. S3d). Therefore, we measure the slope of the travel tme shfts along the estmated Green functons (for postve and negatve tmes, Fg. S3d) to estmate the Relatve Tme Perturbaton (RTP) that the opposte of the medum s unform relatve shear wave velocty varaton. The error on the RTP estmate ( τ/τ) s calculated as: $ " " / = # # M E # wth 2!(# ) = M _ 2 %(#! $ #! ) _ = " #! =, #! = #! /! "! N,

3 3 where N s the number of tme samples. We emphasze that only a physcal velocty varaton of the sampled medum can explan the symmetry n the tme shfts along the coda of the postve and negatve tme cross-correlaton functons 2. Moreover, measurng the tme shft lnear trend by lnear regresson (LSQR) passng through 0 allows us to bypass the artefacts of nstrumental errors. Ths makes our approach robust and allows us to measure relatve velocty varatons smaller than 0.%. Length of the movng wndow We use 0-days-long movng wndows to compute "current" nose cross correlatons. Ths value was selected as a trade-off between tme resoluton and stablty of the Green functon reconstructon. Our tests showed that usng shorter movng wndows deterorates n stablty of reconstructon ncreasng the nose level of the RTP measurements. Ths s llustrated wth Fg. S4a that shows the RTP measured usng "current" cross-correlatons computed from fve-days-long movng wndows. In ths case, ampltudes of pre-eruptve anomales are slghtly ncreased whle the level of the measurement nose s ncreased sgnfcantly. At the same tme, t can be seen that the length of the movng wndow does not affect sgnfcantly the precursors duraton. We also tested measurements usng one-day movng wndows. In ths case, the RTP nose level becomes too strong and only the strongest precursor (before erupton 4) can be dstngushed. Regonalzaton method We localze the relatve velocty changes n space by applyng a regonalzaton procedure. We measure the Relatve Tme Perturbatons (RTP) for each recever par separately. The LTV (Long Term Varaton) s obtaned by estmaton of the order polynomal ft to the relatve velocty changes. The perodcty of the LTV s about 6 months. The STV (Short Term Varaton) s obtaned by subtractng the LTV from the relatve velocty changes (Fg. S5a). We dstrbute, for each recever par, for each day,

4 4 and for the STV and LTV separately, the values of v/v (= τ/τ) wthn grd cells whch dstances to the drect paths are smaller than 2 km (Fg. S5b). We then average, for every grd cell, ther assocated values of v/v. In case of denser recever networks, t would be worth optmzng ths procedure by takng nto account more realstc senstvty kernels of the coda tme shfts for localzed velocty perturbatons 3. Long Term Varatons (LTV) The analyss of the long-term velocty varatons (LTV) shows that they are related to processes varyng over several months wth a possble seasonalty (Fgs. S2b and S4a). A clear seasonal dependence of the sesmc velocty changes was observed from the analyss of short-perod nose cross-correlatons at the Merap volcano 4 and was related to varatons of the depth of the superfcal ground water layer because of precptaton. In the case of the Pton de la Fournase, the observed LTV can not be only related to the precptatons on La Réunon sland (Fgs S4a and S4c). Moreover, the LTV ampltude and locaton (east of Dolomeu crater) are very smlar to what was observed for the short-term precursors (Fgs. S5d and S5e) suggestng that the long-term velocty varatons reported n ths study are lkely to be partly related to the dynamcs of the volcano-magmatc system.

5 5 Supplementary Fgure : The Green functon reconstructon procedure. The presented Green functon s fltered ([0.-0.9] Hz). The postve and negatve tme Green functons are normalzed separately to hghlght the phase symmetry. Supplementary Fgure 2: Comparson of the RTP measurements obtaned wth dfferent data processng methods. The black curves are obtaned from cross-correlatons computed wth spectral whtenng followed by one-bt normalzaton. The red curves are obtaned from cross-correlatons computed wth runnng-absolute-mean normalzaton followed by spectral whtenng. (a) Fltered ([0.-0.9] Hz) reference cross-correlaton functons (recever par PBRZ-NCR). The postve and negatve tme Green functons are normalzed separately to hghlght the phase symmetry. (b) Raw Relatve Tme Perturbatons (c) Relatve Tme Perturbatons corrected from the Long Term Varatons.

6 6 Supplementary Fgure 3: Synthetc case llustratng the procedure of the RTP measurement. (a) Possble paths for the reconstructed dffracted Raylegh waves. The green crcle corresponds to the extensometer locaton. (b) The black sgnal s the reference Green functon for recever par PBRZ-NCR ([0.-0.9] Hz). The red sgnal s the synthetc current Green functon correspondng to a unform 4 % relatve velocty decrease wthn the volcano edfce. The postve and negatve tme Green functons are normalzed separately to hghlght the phase symmetry. (c) Tme shft estmaton from the lnear regresson of the cross-spectrum phase. (d) Measured tme shfts between the reference and the perturbed Green functons and a correspondng RTP measurement ( τ/τ).

7 7 Supplementary Fgure 4: (a) Relatve velocty changes calculated computed usng fvedays-long movng wndows. The STV and LTV are respectvely represented by black and red curves. (b) Extensometer (CHAF) data (see Fg. S3a). (c) Pluvometry provded by the NASA/Goddard Space Flght Center s Laboratory for Atmospheres 5. Realstc precptaton values for the Pton de la Fournase volcano are approxmatvely fve tmes greater. We use a hydrologcal model 4 to qualtatvely descrbe the temporal evoluton of the water table heght (red curve).

8 8 Supplementary Fgure 5: (a) Extracton of the short- and long-term varatons for recever par NTR-NCR. (b) A senstvty zone correspondng to measured relatve perturbatons. (c) Topographc map showng the recever pars used for the regonalzaton procedure. (d) Standard devaton of the regonalzed short-term negatve relatve velocty changes. The gray dashed lne represents the lmts of ray coverage. (e) Standard devaton of the regonalzed long-term relatve velocty changes.

9 9 References. Bensen, G.D., M.H. Rtzwoller, M.P. Barmn, A.L. Levshn, F. Ln, M.P. Moschett, N.M. Shapro, and Y. Yang, Processng sesmc ambent nose data to obtan relable broad-band surface wave dsperson measurements, Geophys. J. Int., 69, , do:0./j x x (2007). 2. L. Stehly, M. Campllo, N. M. Shapro, Travel tme measurements from nose correlaton: stablty and detecton of nstrumental errors, Geophys. J. Int. do:0./j x x (2007). 3. C. Pacheco, R. Sneder, Tme-lapse traveltme change of sngly scattered acoustc waves, Geophys. J. Int. 65, 485 (2006). 4. C. Sens-Schönfelder, U. Wegler, Passve mage nterferometry and seasonal varatons of sesmc veloctes at Merap Volcano, Indonesa, Geophys. Res. Lett. 33 (2006). 5. G. Huffman, et al., Global precptaton at one-degree daly resoluton from multsatellte observatons, J. Hydrometeorol. 2, 36 (200).