- Research Article
- Open Access

# Characterization of ambient seismic noise near a deep geothermal reservoir and implications for interferometric methods: a case study in northern Alsace, France

- Maximilien Lehujeur
^{1}Email author, - Jérôme Vergne
^{1}, - Jean Schmittbuhl
^{1}and - Alessia Maggi
^{1}

**3**:3

https://doi.org/10.1186/s40517-014-0020-2

© Lehujeur et al.; licensee Springer. 2015

**Received:**30 May 2014**Accepted:**2 December 2014**Published:**1 February 2015

## Abstract

### Background

Ambient noise correlation techniques are of growing interest for imaging and monitoring deep geothermal reservoirs. They are simple to implement and can be performed continuously to follow the evolution of the reservoir at low cost. However, these methods rely on assumptions of spatial and temporal uniformity of seismic noise sources. Violating them can result in misinterpretation of seismic velocities owing to preferential noise propagation directions.

### Methods

Using several years of seismic data recorded around the two geothermal sites of Soultz-sous-forêts and Rittershoffen in northern Alsace, France, we propose a detailed characterization of the spatial and temporal properties of the high frequency seismic noise (0.2 to 5Hz). We consider two fundamental properties of the cross correlation functions (CCFs) of ambient noise. Firstly, the reliability of the Green's function reconstruction, an important indicator for tomographic studies. Secondly, the temporal repeatability of the CCFs between 0.2 and 0.5 seconds.

### Results and conclusions

At periods below 1s, we observe a sharp decrease in signal to noise ratio resulting from the non uniform distribution of anthropogenic sources. At periods above 1s, we show that the high directivity of the northern Atlantic microseismic peak biases the CCFs' phase significantly. We show that nocturnal noise is the most suited for temporal analysis of the CCFs. Using nocturnal noise, we should be able to monitor temporal variations induced by the geothermal activities inside the reservoir.

## Keywords

- Ambient noise
- Cross-correlation
- Surface waves
- Anthropogenic noise

## Background

Projects dedicated to the exploitation of deep geothermal resources need to probe the upper crustal structure of the targeted area in order to characterize the reservoir and its relation to pre-existing geological formations. Active seismic sounding is a commonly used approach; its dense spatial and temporal sampling provides high-resolution images of the reflectivity of the subsurface layers and of fault geometry. However, such seismic data are not readily available everywhere, and acquisition of new data, especially in 3D, is often very expensive compared to the profitability of geothermal resources. Its high cost also excludes using repeated active seismic sounding to follow the evolution of the medium during production.

Images of the upper crustal structure can also be obtained from tomographic inversion of arrival times of natural or induced local earthquakes. These inversions can be repeated over time to map velocity changes (e.g., Calò et al. 2011; Calò and Dorbath 2013) much more cheaply than active seismic sounding. Producing good-quality tomographic images of geothermal reservoirs using arrival times requires having induced seismicity around the wells, but geothermal operators need to minimize induced seismicity to reduce the seismic risk associated with their exploitation. The need to minimize seismic risk excludes using time-lapse arrival-time tomography for continuous reservoir imaging.

Over the past 10 years, another promising passive seismic imaging technique has emerged. Known as ‘ambient noise tomography’ , it uses seismic noise as a permanent source of energy that propagates through the target region. The cross-correlation function (CCF) of long records of seismic noise at a pair of stations provides an estimation of Green's function between them (Lobkis and Weaver 2001; Shapiro and Campillo 2004; Sabra et al. 2005a). The resulting correlogram is similar to the signal that would be obtained if an impulsive source occurred at one station and was recorded by the other one. This method allows us to perform tomographic studies using all possible pairs of stations over a network (Shapiro et al. 2005; Sabra et al. 2005b). The resolution of the recovered seismic velocity models only depends on the geometry of the stations. This technique has been widely applied at various scales, from the structure of the mantle using worldwide broadband stations (Poli et al. 2012; Lin and Tsai 2013; Lin et al. 2013) to laboratory samples using piezoelectric sensors (e.g., Lobkis and Weaver 2001; Derode et al. 2003a, b; Larose et al. 2007). At the local scale, the method has been applied in various environments from offshore oil reservoirs (Bussat and Kugler 2011; Mordret et al. 2013) to active volcanic systems (Brenguier et al. 2008, 2011). Although the applicability of ambient noise tomography in the context of geothermal reservoirs is still under debate, at least one application has already been attempted using a local network of short-period seismometers around the geothermal site of Soultz-sous-Forêts (Calò et al. 2013). Beyond its use in seismic tomography, the continuous nature of seismic noise can also be exploited to observe subtle variations in the seismic velocity or the diffracting character of the crust. For example, Brenguier et al. (2008, 2011) and Obermann et al. (2013) were able to produce 4D pictures of the Piton de la Fournaise volcano by applying interferometric analysis to the coda part of the correlograms.

The seismic noise-based methods described above all rely on strong assumptions concerning the noise sources. For tomography applications, noise sources should be homogeneously distributed (Lobkis and Weaver 2001; Roux et al. 2005). Under this assumption, only the sources located in a narrow area along the continuation of the path joining the two stations contribute to the recovered Green's function (Roux et al. 2004; Sabra et al. 2005c; Larose 2005; Gouédard et al. 2008). For applications that monitor time-dependent perturbations of the medium, noise sources may be inhomogeneously distributed, but in this case, they must be repeatable. If the seismic noise sources move too much over time, the resulting changes in the signal could be mistaken for perturbations of the medium (Hadziioannou et al. 2009; Weaver et al. 2011).

The consequences of violating these assumptions have been studied theoretically and numerically using synthetic data (Weaver et al. 2009; Froment et al. 2010). Although the seismic noise distribution on Earth is rarely homogeneous in time and space, the CCFs approximate Green's functions correctly if the inter-station distances are long and the azimuthal distribution of the noise is smooth. However, when the noise source distribution is highly heterogeneous, some studies using real data report significant bias and incorrect estimation of seismic velocities between the station pairs (Pedersen and Krüger 2007).

Here, we focus on the application of the ambient noise correlation technique in the context of a geothermal reservoir (i.e., a kilometer scale) using seismic data around geothermal sites in northern Alsace. We analyze the characteristics of the seismic noise in the period range between 0.2 and 5 s (0.2 to 5 Hz). We then study the correlograms of ambient noise records between pairs of stations and show how the seismic noise distribution influences the quality and reliability of the reconstructed Green's functions in this particular period range. Finally, we examine the stability of the high-frequency CCF coda for future analysis of temporal changes within the reservoir.

## Data

In order to extend our understanding of the origins of seismic noise to higher frequencies, we deployed two small aperture arrays, ARIT and AKUL, close to the location of the permanent stations RITT and KULH (Figure 1). The arrays operated for 2 months during fall 2012. Each array contained six vertical short-period sensors (1-Hz corner frequency) with one three-component L4C sensor at the center. All the sensors were connected by cables to a central acquisition system that provided a common time reference for the nine recorded channels. They were deployed in a helical configuration with a 300-m maximum aperture.

## Methods

### Frequency content and temporal variability of seismic noise

Empirical Green's functions constructed from the correlation of vertical component ambient seismic noise records are dominated by surface waves, because most noise sources occur close to the Earth's surface. Therefore, the dispersive character of the Rayleigh waves is the primary information that can be extracted from correlograms (Campillo et al. 2011). Dispersion measurements for each pair of stations (group or phase dispersion curves) can be regionalized to provide spatial variations of surface-wave velocities at each period. Inversion can then be used to convert surface-wave velocities as a function of period to S-wave velocities as a function of depth (the longer the surface-wave period, the greater the investigation depth). At Soultz-sous-Forêts and Rittershoffen, the reservoir lies between 2- and 5-km depths. In order to map S-wave velocities from the surface to that depth using the dispersive character of the Rayleigh waves, we must work in the period range of 0.2 to 5 s. This range is compatible with the bandwidth of our seismometers (cutoff period of 1 s) and benefits from low instrumental noise.

Between 0.2 and 5 s, seismic noise has differing origins and properties. For periods above 2 s, seismic noise spectra everywhere on Earth contain a broad, highly energetic peak called the ‘secondary micro-seismic peak.’ This peak results from pressure variations on the sea bottom induced by interferences of oceanic waves traveling in opposite directions (Longuet-Higgins 1950). A few dominant zones in the north Atlantic (south of Greenland, along the Canadian coasts and around the mid-Atlantic ridge) generate most of the secondary micro-seismic peak energy recorded in Europe (Gutenberg 1936; Kedar et al. 2008; Sergeant et al. 2013).

At periods below 2 s, numerous phenomena are responsible for the observed seismic noise. They can be split into two categories: natural sources, among which the wind acting on trees or structures sealed into the ground in the vicinity of the recording stations (Withers et al. 1996; Bonnefoy-Claudet et al. 2006), and anthropogenic sources like road traffic, industries, or other types of human activities (McNamara and Buland 2004; Groos and Ritter 2009). As seismic noise from these high-frequency sources propagates only to local distances, its characteristics change from one region to another. A region-specific analysis of the high-frequency noise spectrum is therefore recommended before applying ambient noise correlation techniques (Campillo et al. 2011).

### Spatial distribution of seismic noise

To estimate the spatial origin of the seismic noise over the whole period range of interest, we apply a classical beamforming technique (e.g., Rost and Thomas 2002) to the local monitoring network and the small aperture arrays. This technique allows us to determine the dominant back azimuth and phase velocity of an incoming seismic wave, so long as the network's station spacing is less than half the wavelength. By applying the method on a sliding window, we can estimate the directivity and phase velocity of the noise as a function of time. The longer the period of the noise to be processed, the wider the array must be.

## Results and discussion

### Cross-correlation functions and dispersion measurements

These observations are confirmed by the dispersion analysis performed on individual CCFs. We measure the Rayleigh wave dispersion on the CCFs by frequency time analysis (FTAN), which provides an estimation of the group velocity at each period (e.g., Dziewonski et al. 1969; Bensen et al. 2007). Figure 5 (bottom right) illustrates a typical dispersion diagram obtained for the station pair KUHL-BETS. Despite its noisy aspect, we can clearly identify the dispersion of the fundamental mode Rayleigh wave at periods longer than 1 s (solid black curve on Figure 5, bottom right). This mode can be easily identified on most station pairs. The dispersion diagrams change markedly around 1 s, and we cannot estimate group velocities at shorter periods. This inability occurs regardless of the chosen station pair and the time range (from weeks to years) used to compute the CCF. This transition period of approximately 1 s is similar to the one observed on the seismic noise spectrograms (Figure 2) and corresponds to the transition between the noise originating from oceanic sources and that generated by local anthropogenic activities.

We propose two possible explanations for the poor quality of the reconstructed Green's function at periods below 1 s: (1) because of attenuation, the noise generated by low-energy local sources cannot travel far enough to be coherently recorded by two separate stations and/or (2) the non-uniform distribution of the local sources limits the reconstruction of Green's function, as theoretically predicted. The consequences of non-uniform noise sources are described in the following section.

### Impact of a directive noise

We display the measured time shifts as a function of the orientation of the station pair (Figure 6, top right). Because of the chosen orientation convention, phase shifts measured on the positive (resp. negative) part of the CCFs are attributed to azimuths ranging from 180° to 360° (resp. 0° to 180°) and are caused by eastward (resp. westward) propagating noise. We observe a sinusoidal shape with a minimum occurring for station pairs oriented approximately 300°, corresponding to the case in which the station pairs are aligned with the dominant direction of oceanic noise in this period range (Figure 3). Even though these phase shifts might be due to spatial variations of the phase speed at depth, the sinusoidal-shaped variation combined with a minimum phase shift at 300° suggests that the phase shifts might in reality be caused by noise directivity. In another context, Pedersen and Krüger (2007) observed apparent variations of the group speed that were actually caused by strong noise directivity.

To corroborate the claim that our phase shifts are essentially caused by noise directivity, we propose a synthetic test with a homogeneous medium (constant phase speed of 2.45 km/s at 2-s period). Using the work of Weaver et al. (2009) and Froment et al. (2010), we estimate the theoretical phase shifts predicted by a given azimuthal distribution of the noise energy (ADNE). We find that a simple synthetic ADNE made of two Gaussian functions centered at 150° and 300° (the principal back azimuths of the noise directivity observed in Figure 3) reproduces the main features (sinusoidal shape and amplitudes) of the phase shifts measured on real data. Because the synthetic medium is homogeneous, these phase variations can be attributed unambiguously to the noise directivity. Interestingly, as soon as the ADNE contains an isotropic component, however small (even 0.01% of the dominant arrival), the phase shifts become negligible. This confirms the main conclusion of Weaver et al. (2009) and implies that a complete lack of coherent isotropic noise strengthens our observed phase variations.

*a priori*velocity of 2.45 km/s, and set the smoothing distance to 5 km. As the computed phase shifts are all positive, most grid cells exhibit overestimated phase speeds that can reach 30% more than the true value (green/blue zones). These artefacts are heightened by the large number of station pairs oriented perpendicularly to the dominant noise arrival (300°). The inverse problem also produces zones of underestimated phase speeds (yellow zones) to balance the overestimations and satisfy most of the observations. Future work will focus on how to take this bias into account for a reliable estimation of velocity variations at depth.

### Impact of localized and repetitive deterministic high-frequency sources

The late part of the correlation function (coda, e.g., after 16 s in the RITT-BETS case; Figure 9, left side) results from diffuse wave fields recorded coherently at both stations (seismic waves refracted on scatterers while traveling from one station to the other). Sens-Schönfelder and Wegler (2006) proposed to study the variability of the CCF coda over time to highlight velocity changes within the medium. This technique first establishes a reference coda by averaging the CCFs on a time span over which the medium is assumed to be invariant. Then, the CCFs computed on a sliding window are compared to this reference in order to identify infinitesimal variations (waveform stretching) of the coda. Obviously, the method requires the coda to be extremely repeatable so that any modification in its waveform can be attributed to changes into the medium.

We observe that the coda part of the CCF seems more stable during the night than during the day (Figure 9, left side). The early part of the coda (i.e., between 17 and 25 s, arrows labeled ‘A’) displays similar waveforms from 10 p.m. to 4 a.m., while no coherent phases can be seen in this part of the coda from about 8 a.m. to 9 p.m. (white dashed circle and arrow labeled ‘B’). We infer that the positions of diurnal sources change more than those of nocturnal sources within our time resolution of 5 min. The daytime coda of the CCFs results from illuminating the scatterers around the station pair in a randomly time-varying manner, making it less repeatable.

In order to determine which part of the day is most suited for temporal analysis of the medium, we quantify the repeatability of the coda over time using the techniques of Sens-Schönfelder and Wegler (2006) and Brenguier et al. (2008). We conduct this analysis separately for each hour of the day. We first calculate 24 reference CCFs by averaging the CCFs separately as a function of local hour over the whole acquisition period. Then, for each local hour, we estimate how the coda computed over a 30-day sliding window resembles its reference CCF. Finally, for each local hour, we obtain a set of stretching coefficients (SCs) and their corresponding correlation coefficients (CCs). Medians and standard deviations of the CCs are used as indicators of coda repeatability (for instance, a value of 100% ± 0% would correspond to a coda that always matches its reference whatever the position of the 30-day window). Results obtained in the RITT-BETS case, using the 17- to 30-s coda filtered between 0.2 and 0.5 s (2 to 5 Hz), are presented in Figure 9 (right side, black curves). The coda is confirmed to be more stable at nighttime (up to 40% ± 10% correlation between the coda and its reference). The standard deviation of the SCs obtained before the first drilling (190 days) is also displayed as a function of local hour (Figure 9, right side, red curve). This curve is used as an indicator of the smallest detectable relative speed variation (Δ*v*/*v*) that could be observed using our data set with a temporal resolution of 30 days. The detectable speed variation is about 0.1% during the day and 0.05% at night.

## Conclusions

In this work, we benefited from the high station density available close to the two geothermal sites of Soultz-sous-Forêts and Rittershoffen and the long duration of available data (up to 4 years). We propose a detailed analysis of the seismic noise recorded in the area. The period range of interest is constrained by the dimension of the targeted structures. Based on the estimated seismic velocity model of the area, investigating the first 5 km of the crust requires working at periods between 0.2 and 5 s, which include seismic noise that has various origins and properties. At periods above 1 s, the secondary micro-seismic peak dominates the signal. This peak is characterized by a strong directivity (approximately 300° back azimuth) in good agreement with its origin (northern part of the Atlantic Ocean). At periods below 1 s, the noise has clear daily and weekly periodicities, which indicate its anthropogenic origin. The spatial analysis of this noise reveals that the sources are numerous but clustered around a few zones that roughly correspond to the densely populated villages of the area.

We compute CCFs for all station pairs of the network and analyze two of their properties. Firstly, we examine how the CCFs resemble Green's functions in terms of signal-to-noise ratio (SNR), dispersive behavior, and phase. This property of the CCFs is required for modeling the geographical distributions of seismic velocities (tomography), which will lead to better knowledge of the geological structures and characterization of the geothermal reservoir. At periods above 1 s, the SNR is low and the spatial distribution of the (mainly anthropogenic) noise sources limits our ability to reconstruct Green's function, making dispersion measurements difficult. At periods below 1 s, the SNR is higher. However, the high directivity of the noise at these periods affects the phase of the CCFs in a way that cannot be neglected. We expect CCFs to provide reliable information about distributions of seismic velocities inside the reservoir only if accurate knowledge of the noise directivity and rigorous estimates of errors induced on the phase are taken into account. This issue will be addressed in a forthcoming study.

Secondly, we analyze the stability of the correlation functions in time. This property is commonly used to follow the temporal variations of seismic velocities at depth and does not require a perfect match between the CCF waveform and the true Green's function. This technique is expected to provide information about changes that could occur inside the reservoir due to geothermal activities (relative displacement of scatterers induced by pressure variations, thermal fluctuations, variations of the fluid content, etc.). We show that high-frequency noise (0.2 to 0.5 s) due to anthropogenic activity is more stable/repeatable at night. The nocturnal noise sources, although non-uniformly distributed, seem to be more stable in space and time, making nocturnal CCFs more suited for temporal analysis. With a time resolution of 30 days, we estimate the smallest detectable relative phase speed variation to be about 0.05% to 0.1%. Future work will focus on the temporal variations of the medium induced by the operations conducted at the geothermal sites (drilling, injection/production tests, etc.).

## Declarations

### Acknowledgements

This work has been published under the framework of the LABEX ANR-11-LABX-0050_G-EAU-THERMIE-PROFONDE and benefits from a funding from the state managed by the French National Research Agency as part of the Investments for the future program. ML is funded by Groupe Electricité de Strasbourg. We thank GEIE EMC, ECOGI and EOST for providing the data of the permanent network. The array equipment (ARIT and AKUL) was supplied by the SisMob component of the RESIF National Research Infrastructure. We thank the Geophysical Instrument Pool Potsdam (GFZ) for providing temporary stations, as well as E. Gaucher (KIT), V. Maurer (ES-G), H. Wodling, H. Jund, and M. Grunberg (EOST) who deployed the stations and collected the data. We are grateful to the three anonymous reviewers for their constructive criticisms that greatly helped improve the content of this manuscript.

## Authors’ Affiliations

## References

- Bensen GD, Ritzwoller MH, Barmin MP, Levshin AL, Lin F, Moschetti MP, Shapiro NM, Yang Y (2007) Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements. Geophys J Int 169(3):1239–1260, doi:10.1111/j.1365-246X.2007.03374.xView ArticleGoogle Scholar
- Bonnefoy-Claudet S, Cotton F, Pierre-Yves B (2006) The nature of noise wavefield and its applications for site effects studies: a literature review. Earth Sci Rev 79(3–4):205–227, doi:10.1016/j.earscirev.2006.07.004View ArticleGoogle Scholar
- Brenguier F, Shapiro NM, Campillo M, Ferrazzini V, Duputel Z, Coutant O, Nercessian A (2008) Towards forecasting volcanic eruptions using seismic noise. Nat Geosci 1(2):126–130View ArticleGoogle Scholar
- Brenguier F, Clarke D, Aoki Y, Shapiro NM, Campillo M, Ferrazzini V (2011) Monitoring volcanoes using seismic noise correlations. Comptes Rendus Geosci 343(8–9):633–638, doi:10.1016/j.crte.2010.12.010View ArticleGoogle Scholar
- Bussat S, Kugler S (2011) Offshore ambient-noise surface-wave tomography above 0.1 Hz and its applications. Leading Edge 30(5):514–524, doi:10.1190/1.3589107View ArticleGoogle Scholar
- Calò M, Dorbath CC (2013) Different behaviours of the seismic velocity field at Soultz-sous-Forêts revealed by 4-D seismic tomography: case study of GPK3 and GPK2 injection tests. Geophys J Int 194(2):1119–1137View ArticleGoogle Scholar
- Calò M, Dorbath C, Cornet FH, Cuenot N (2011) Large-scale aseismic motion identified through 4-DP-wave tomography. Geophys J Int 186(3):1295–1314View ArticleGoogle Scholar
- Calò M, Kinnaert X, Dorbath C (2013) Procedure to construct three-dimensional models of geothermal areas using seismic noise cross-correlations: application to the Soultz-sous-Forêts enhanced geothermal site. Geophys J Int 194(3):1893–1899, doi:10.1093/gji/ggt205View ArticleGoogle Scholar
- Campillo M, Sato H, Shapiro NM, van der Hilst RD (2011) Nouveaux Développements de L'imagerie et Du Suivi Temporel à Partir Du Bruit Sismique. Comptes Rendus Geosci 343(8–9):487–495, doi:10.1016/j.crte.2011.07.007View ArticleGoogle Scholar
- Derode A, Larose E, Campillo M, Fink M (2003a) How to estimate the Green's function of a heterogeneous medium between two passive sensors? Application to acoustic waves. Appl Phys Lett 83(15):3054–3056, doi:10.1063/1.1617373View ArticleGoogle Scholar
- Derode A, Larose E, Tanter M, de Rosny J, Tourin A, Campillo M, Fink M (2003b) Recovering the Green's function from field-field correlations in an open scattering medium (L). J Acoust Soc Am 113(6):2973–2976, doi:10.1121/1.1570436View ArticleGoogle Scholar
- Dziewonski A, Bloch S, Landisman M (1969) A technique for the analysis of transient seismic signals. Bull Seismol Soc Am 59(1):427–444Google Scholar
- Froment B, Campillo M, Roux P, Gouédard P, Verdel A, Weaver RL (2010) Estimation of the effect of nonisotropically distributed energy on the apparent arrival time in correlations. Geophysics 75(5):SA85–SA93, doi:10.1190/1.3483102View ArticleGoogle Scholar
- Gaucher E, Maurer V, Wodling H, Grunberg M (2013) Towards a dense passive seismic network over Rittershoffen geothermal field. 2nd European Geothermal Workshop. KIT, EOST, Strasbourg, FranceGoogle Scholar
- Gouédard P, Roux P, Campillo M, Verdel A (2008) Convergence of the two-point correlation function toward the Green's function in the context of a seismic-prospecting data set. Geophysics 73(6):V47–V53, doi:10.1190/1.2985822View ArticleGoogle Scholar
- Groos JC, Ritter JRR (2009) Time domain classification and quantification of seismic noise in an urban environment. Geophys J Int 179(2):1213–1231View ArticleGoogle Scholar
- Gutenberg B (1936) On microseisms. Bull Seismol Soc Am 26(2):111–117Google Scholar
- Hadziioannou C, Larose E, Coutant O, Roux P, Campillo M (2009) Stability of monitoring weak changes in multiply scattering media with ambient noise correlation: laboratory experiments. J Acoust Soc Am 125(6):3688–3695View ArticleGoogle Scholar
- Kedar S, Longuet-Higgins M, Webb F, Graham N, Clayton R, Jones C (2008) The origin of deep ocean microseisms in the North Atlantic Ocean. Proc Royal Soc A Math Phys Eng Sci 464(2091):777–793, doi:10.1098/rspa.2007.0277View ArticleGoogle Scholar
- Larose E (2005) Diffusion multiple des ondes sismiques et expériences analogiques en ultrasons. Université Joseph-Fourier - Grenoble I, FranceGoogle Scholar
- Larose E, Roux P, Campillo M (2007) “Reconstruction of Rayleigh-Lamb Dispersion Spectrum Based on Noise Obtained from an Air-Jet Forcing”. The Journal of the Acoustical Society of America 122(6):3437–44. doi:10.1121/1.2799913View ArticleGoogle Scholar
- Lin F-C, Tsai VC (2013) Seismic interferometry with antipodal station pairs. Geophys Res Letts 40(17):4069–4613. doi:10.1002/grl.50907View ArticleGoogle Scholar
- Lin F-C, Tsai VC, Schmandt B, Duputel Z, Zhan Z (2013) Extracting seismic core phases with array interferometry. Geophys Res Lett 40(6):1049–1053, doi:10.1002/grl.50237View ArticleGoogle Scholar
- Lobkis OI, Weaver RL (2001) On the emergence of the Green's function in the correlations of a diffuse field. J Acoust Soc Am 110(6):3011–3017, doi:10.1121/1.1417528View ArticleGoogle Scholar
- Longuet-Higgins MS (1950) A theory of the origin of microseisms. Phil Trans R Soc A 243(857):1–35, doi:10.1098/rsta.1950.0012View ArticleGoogle Scholar
- McNamara DE, Buland RP (2004) Ambient noise levels in the continental United States. Bull Seismol Soc Am 94(4):1517–1527View ArticleGoogle Scholar
- Mordret A, Landés M, Shapiro NM, Singh SC, Roux P, Barkved OI (2013) Near-surface study at the Valhall oil field from ambient noise surface wave tomography. Geophys J Int 193(3):1627–1643, doi:10.1093/gji/ggt061View ArticleGoogle Scholar
- Obermann A, Planès T, Larose E, Campillo M (2013) Imaging preeruptive and coeruptive structural and mechanical changes of a volcano with ambient seismic noise. J Geophys Res Solid Earth 118(12):6285–6294, doi:10.1002/2013JB010399View ArticleGoogle Scholar
- Pedersen HA, Krüger F (2007) Influence of the seismic noise characteristics on noise correlations in the Baltic shield. Geophys J Int 168(1):197–210View ArticleGoogle Scholar
- Poli P, Campillo M, Pedersen H (2012) Body-wave imaging of Earth's mantle discontinuities from ambient seismic noise. Science 338(6110):1063–1065, doi:10.1126/science.1228194View ArticleGoogle Scholar
- Rost S, Thomas eC (2002) Array seismology: methods and applications. Rev Geophys 40(3):1008, doi:10.1029/2000RG000100View ArticleGoogle Scholar
- Roux P, Kuperman WA, and the NPAL Group (2004) Extracting coherent wave fronts from acoustic ambient noise in the ocean. J Acoust Soc Am 116(4):1995–2003, doi:10.1121/1.1797754View ArticleGoogle Scholar
- Roux P, Sabra KG, Kuperman WA, Roux A (2005) Ambient noise cross correlation in free space: theoretical approach. J Acoust Soc Am 117(1):79–84, doi:10.1121/1.1830673View ArticleGoogle Scholar
- Sabra KG, Gerstoft P, Roux P, Kuperman WA, Fehler MC (2005a) Extracting time-domain Green's function estimates from ambient seismic noise. Geophys Res Lett 32(3):L03310View ArticleGoogle Scholar
- Sabra KG, Gerstoft P, Roux P, Kuperman WA, Fehler MC (2005b) Surface wave tomography from microseisms in southern California. Geophys Res Lett 32(14):L14311View ArticleGoogle Scholar
- Sabra KG, Roux P, Kuperman WA (2005c) Arrival-time structure of the time-averaged ambient noise cross-correlation function in an oceanic waveguide. J Acoust Soc Am 117(1):164–174View ArticleGoogle Scholar
- Sens-Schönfelder C, Wegler U (2006) Passive image interferometry and seasonal variations of seismic velocities at Merapi Volcano, Indonesia. Geophys Res Lett 33(21):L21302, doi:10.1029/2006GL027797View ArticleGoogle Scholar
- Sergeant A, Stutzmann E, Maggi A, Schimmel M, Ardhuin F, Obrebski, M (2013) “Frequency-Dependent Noise Sources in the North Atlantic Ocean.” Geochem Geophys Geosyst 14(12):5341–5353, doi:10.1002/2013GC004905View ArticleGoogle Scholar
- Shapiro NM, Campillo M (2004) Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise. Geophys Res Lett 31(7):L07614View ArticleGoogle Scholar
- Shapiro NM, Campillo M, Stehly L, Ritzwoller MH (2005) High-resolution surface-wave tomography from ambient seismic noise. Science 307(5715):1615–1618, doi:10.1126/science.1108339View ArticleGoogle Scholar
- Stehly L, Campillo M, Shapiro NM (2006) A study of the seismic noise from its long-range correlation properties. J Geophys Res 111(B10):B10306View ArticleGoogle Scholar
- Weaver R, Froment B, Campillo M (2009) On the correlation of non-isotropically distributed ballistic scalar diffuse waves. J Acoust Soc Am 126(4):1817–1826, doi:10.1121/1.3203359View ArticleGoogle Scholar
- Weaver RL, Hadziioannou C, Larose E, Campillo M (2011) On the precision of noise correlation interferometry. Geophys J Int 185(3):1384–1392, doi:10.1111/j.1365-246X.2011.05015.xView ArticleGoogle Scholar
- Withers MM, Aster RC, Young CJ, Chael EP (1996) High-frequency analysis of seismic background noise as a function of wind speed and shallow depth. Bull Seismol Soc Am 86(5):1507–1515Google Scholar

## Copyright

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.