We calculate the median of individual (observed) seismic spectra over 3-hour time slots.

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1 Methods Seismic data preparation We calculate the median of individual (observed) seismic spectra over 3-hour time slots. Earthquake and instrument glitches are easily identified as short pulses and are removed by applying a threshold on the second derivative and local variance of the times series. As stated above, the DFM that we target in this study are intrinsically linked to oceans waves, in terms of frequency content. Therefore, to avoid problems raised by the highly dispersive nature of ocean waves, we restrict our analysis to a narrow frequency band. We use the range Hz. We prefer to focus on these relatively low frequencies, because the associated ocean waves (f<0.057 Hz) are observed only during large storms, which are less common and thus easier to isolate and track. We do not use longer periods, because the level of noise energy decreases toward the lower bound of the DFM domain (0.1 Hz), and contamination from primary noise ( Hz) may occur. Synthetic sources computation To assess the distribution of DFM, we use a numerical approach based on the WAVEWATCH III framework [Tolman, 2008; Ardhuin et al., 2010], in which the second-order pressure spectrum [Miche, 1944; Longuet-Higgins, 1950; Hasselmann, 1963] is computed from the wave frequency spectrum E(f) and the directional integral I(f) that depends only on the ocean wave energy distribution M over the direction θ [Ardhuin et al., 2011], 1

2 % $ I( f ) = M( f,") # M( f,$ + ")d" 0 Our approach simulates the generation of Rayleigh surface-waves that dominate the microseismic spectrum [Haubrich et al., 1963]. Following [Hasselmann, 1963], the pressure spectra at seismic frequency f s =2f, where f is the ocean wave frequency, and k s =k-k, the difference between the wave number of ocean waves propagating in almost opposite directions, is given in deep water by: F p 3 D (k s, f s ) = " w2 g 2 f s E 2 ( f )I( f ) where ρ w is the water density. The seismic response for a uniform crust, as shown on Figure 2E, depends on the water depth, crust density and period: S DF ( f s ) " 4# 2 f s c 2 F $ 2 s % 5 p 3D (k s, f s ) where ρ s is the crustal density, β the shear wave speed, and c 2 a non-dimensional coupling factor between ocean and seismic waves [Longuet-Higgins, 1950]. For β=2600 m/s, the value of c 2 ranges from 0.05 to 0.84 and depends on the period and water depth. At seismic frequency of 0.12 Hz, c 2 has a narrow peak for a water depth between 1.5 and 2.2 km. The spectrum of the vertical ground displacement observed at longitude λ and latitude ϕ is thus obtained by summing the effective sources (contours on Figures 2F and 3) over the area of ocean, ie including geometrical attenuation and dissipation or scattering represented by a quality factor Q, F " ) = +' / 2 2' S DF ( f s ) s%r R E sin% e&2'f E /(VQ ) 2 ( ( R &' / 2 0 E sin $ ) d #) d $ ) where V is the seismic group speed, R E the earth radius and α the angular distance from the source located at longitude λ and latitude ϕ. An important aspect of our 2

3 computations is that the effect of ocean waves reflection on the coast is taken into account. Following [Ardhuin et al., 2011] we compute the sources with and without reflection and then combine them using a fixed reflection coefficient: F " ) = ( 1% 10R 2 )& F ",no ref ) + 10R 2 & F ",ref ) Based on synthetic tests (Fig. A3), we use a rather conservative value R 2 =5%. A second key aspect of the seismic noise model parameterization is the estimation of quality factor Q. The larger the value of Q, the further a station can see sources. This factor is expected to vary spatially, for example with the age of the Pacific Plate and also at the ocean-continent interface. evertheless, to our knowledge, attenuation models are not available for the Pacific Plate at microseismic frequencies ( 0.05 to 0.2 Hz). We thus estimate one single value of Q for each event-station pair. This value is adjusted by maximizing the correlation coefficient: r = # ( ) ( Z obs,i " Z obs ) Z syn,i " Z syn #( Z obs,i " Z obs ) 2 # Z syn,i " Z syn ( ) 2 and minimizing the normalized root mean square error: nrmse = # ( Z obs,i " Z syn,i ) 2 # 2 Z obs,i where Z obs and Z syn are the observed and synthetic root mean square vertical ground displacements (RMSVRG), respectively. This way, the fitted value integrates the possible variations of Q along the seismic paths. evertheless, the noise generated close to the orth American coast propagates through young, low Q oceanic crust. In contrast, the 3

4 mid-pacific noise events are underlain by older crust where attenuation is weaker. Since we adjust Q over three months-long time slots, we tend to equally fit all these geographically distinct noise events. For this reason the fit of each individual peaks is sometimes over- or underestimated, for example the main event described in the present study (Figure 1). In spite of our use of a uniform Q, the fit to the data is satisfactory. For the stations used in this study, the estimated Q value ranges from 400 to 650 for the Hz band (Fig. A3). Polarization analysis We use polarization analysis [Schimmel and Gallart, 2003; Schimmel et al., 2011] to detect, count and characterize polarized signals embedded in noise records. The polarization describes the three-dimensional particle ground motion at the receiver considering seismic records along the three directions (orth-south, East-West, and vertical up). Directions to the incoming waves (back azimuth), and wave types can be inferred from the polarization. Microseisms are Rayleigh-wave dominated, which are elliptically polarized. All individual records are divided into 2 hours-long slots and transformed into the time-frequency domain, using the multi-resolution S-transform. Polarization attributes of the ellipse that best fits the observed ground motion are determined through an eigen analysis of spectral matrices built on the time-frequency representation of the three component seismograms. The polarization attributes are then analyzed as function of time and frequency and used to measure the instantaneous back azimuth of Rayleigh waves and their degree of polarization [Schimmel and Gallart, 2003; Schimmel et al., 2011], which is an instantaneous quality measure based on the stability 4

5 of an arbitrary polarization state with time. The 180-degrees ambiguity in the determination of the back azimuth is removed by assuming that the orientation of the ground motion ellipse is retrograde as is usually the case for fundamental mode Rayleigh waves recorded on rocky ground. Reference Ardhuin, F., E. Stutzmann, M. Schimmel, and A. Mangeney (2011), Ocean wave sources of seismic noise, J. Geophys. Res., 116, C09004, doi: /2011jc Ardhuin, F., E. Rogers, A.V. Babanin, J.F. Filipot, R. Magne, A. Roland, A.,Westhuysen, P. Queffeulou, J.M. Lefevre, L. Aouf, and F. Collard (2010), Semi-empirical dissipation source functions for ocean waves. Part I: Definition, calibration, and validation, J. Phys. Oceanography, 40, , doi: /2010jpo Hasselmann, K. (1963), A statistical analysis of the generation of microseisms, Rev. Geophys., 1, Haubrich, R. A., W. H. Munk, and F.E. Snodgrass (1963), Comparative spectra of microseisms and swell, Bull. Seismol. Soc. Am., 53, Longuet-Higgins, M. (1950), Theory of the origin of microseisms, Phil.Trans. R. Soc. A, 243, Miche, M. (1944), Mouvements ondulatoires de la mer en profondeur constante ou décroissante, Annal. Ponts Chaussées 114, Schimmel, M. and J. Gallart (2004), Degree of polarization filter for frequencydependent signal enhancement through noise suppression, Bull. Seismol. Soc. 5

6 Am., 94, Schimmel, M., E. Stutzmann, F. Ardhuin, and J. Gallart (2011), Polarized Earth s ambient microseismic noise, Geochem. Geophys. Geosyst., 12, Q07014, doi: /2011gc Tolman, H.L. (2008), A mosaic approach to wind wave modeling, Ocean Modelling, 25, 35-47, doi: /j.ocemod