# Eikonal Tomography Using Coherent Surface Waves Extracted From Ambient Noise by Iterative Matched Filtering—Application to the Large-N Maupasacq Array

## Abstract

Standard ambient noise tomography relies on cross-correlation of noise records between pairs of sensors to estimate empirical Green's functions. This approach is challenging if the distribution of noise sources is heterogeneous and can get computationally intensive for large-N seismic arrays. Here, we propose an iterative matched filtering method to isolate and extract coherent wave fronts that travel across a dense array of seismic sensors. The method can separate interfering wave trains coming from different directions, to provide amplitude and travel time fields for each detected wave front. We use the eikonal equation to derive phase velocity maps from the gradient of these travel time fields. Artifacts originating from scattered waves are removed by azimuthal averaging and spatial smoothing. The method is validated on a synthetic test and then applied to the data of the Maupasacq experiment. Rayleigh wave phase velocity maps are obtained for periods between 2 and 9 s. These maps correlate with surface geology at short period (*T*<3 s) and reveal the deep architecture of the Arzacq and Mauleon basins at longer periods (*T*>4 s).

## Key Points

- Coherent surface wave trains can be extracted from ambient noise by matched filtering
- Robust phase velocity maps are obtained by eikonal tomography from the extracted coherent wave trains
- The method is applied on noise recorded by the Maupasacq array to obtain phase velocity maps of the Arzacq-Mauleon basins for periods 2–9 s

## 1 Introduction

Massive deployments of cheap and easy-to-install geophone nodes, which were so far devoted to active source acquisitions for the oil and gas industry, have recently received increasing interest from the academic world for passive imaging studies (e.g., de Ridder & Dellinger, 2011; de Ridder & Biondi, 2015; Hand, 2014; Lin et al., 2013; Mordret et al., 2013). These large-N passive deployments open important new perspectives for the studies of active faults (Ben-Zion et al., 2015; Roux et al., 2016; Taylor et al., 2019; Wang et al., 2019), reservoirs (Vergne et al., 2017), volcanoes (Brenguier et al., 2016; Hansen & Schmandt, 2015; Nakata et al., 2016), glaciers (Roux et al., 2016), or landslides (Wang et al., 2008).

In the period range 1–10 s, that is, in the so-called “secondary microseismic noise” band, the predominant source of noise is the interaction between oceanic waves and the solid earth, which produces surface waves that can be recorded by seismic stations located far away in the middle of continents (Longuet-Higgins, 1950). These surface waves in the ambient noise have been extensively used for passive imaging of the crust (e.g., Shapiro et al., 2005; Lin et al., 2008, 2009; Ritzwoller et al., 2011). The standard approach consists in estimating empirical Green's functions from the correlation of noise recorded by pairs of sensors (Lobkis & Weaver, 2001; Shapiro & Campillo, 2004). This approach has proven especially well suited for dense seismic arrays, because it can be fully automatized and can thus be applied to massive data sets. Several variants of the method have been proposed to handle the case of an imperfectly homogeneous noise distribution (Curtis & Halliday, 2010; Ermert et al., 2017; Roux et al., 2016; Wapenaar et al., 2011) or to jointly invert for the velocity model and the source distribution (Fichtner et al., 2017; Sager et al., 2018; Yao & van der Hilst, 2009).

Alternatively, dense seismic arrays allow seismologists to measure directly the local velocity and propagation direction of a wave front. For example, the Progressive Multichannel Cross-Correlation method (PMCC; Cansi, 1995) estimates these parameters using phase differences computed over triangles of close stations. This method has been later adapted to large aperture arrays such as the USArray Transportable Array (Fan et al., 2018). Local phase velocities can also be estimated by gradiometry (de Ridder & Biondi, 2015) or by local beamforming (Roux & Ben-Zion, 2017). Unlike classical ambient noise tomography, these approaches remain applicable even if the distribution of sources is highly heterogeneous. However, since they rely on a limited subset of stations, they are more vulnerable to the effects of interfering arrivals, which can strongly bias the measurements.

In this study, we introduce a matched filtering method to isolate and extract surface wave fronts from the ambient noise using a dense seismic array. We then exploit the phase of the extracted wave fronts to derive phase velocity maps by eikonal tomography (Lin et al., 2009). We apply the method on the ambient noise field recorded by the large-N Maupasacq (Mauleon Passive Acquisition) seismic array.

The paper is organized as follows. In section 2, we describe the Maupasacq experiment and characterize the ambient noise field recorded in the 1–10 s period band. We find evidence for highly directive and energetic surface wave trains that are generated in the oceans. Section 3 details the matched filtering method that can isolate these coherent wave fronts. We determine phase velocity maps from the phase gradient of these surface wave fields with the eikonal equation. In section 4, the method is tested and validated on a synthetic data set that mimics the Maupasacq acquisition. In section 5, it is applied to the Maupasacq data set to obtain phase velocity maps of the area for periods between 2 and 9 s. After a preliminary geological interpretation of our results, we discuss some perspectives opened by this new way to exploit data from dense seismic arrays.

## 2 Characterization of Ambient Noise Recorded During the Maupasacq Experiment

### 2.1 The Maupasacq Experiment

The Maupasacq array (presented in Polychronopoulou et al., 2018) operated from March to October 2017 in the Mauleon basin (western Pyrenees, France). It includes a total of 442 temporary three-component sensors (Figure 1): 48 broadband stations (BB) with a cutoff period of 20 s in complement to the 6 permanent broad band stations (PBB, cutoff period 100 s) available in the area, 197 short period stations (SP, cutoff period 1 s), and 191 geophone nodes (GN, cutoff period 0.1 s). The sampling rates are 100 samples per second for the BB and SP stations and 250 samples per second for the GN. The inner part of the network forms a regular 50 × 30 km grid with an inter station spacing of about 7 km for the BB and 3 km for the SP. The GN were installed along five lines in the WNW-ESE direction with a spacing of 1 km, and along three lines in the SSW-NNE direction with a spacing of 1.5 km. The dense part of the array is surrounded by two circles of BB and SP stations extending the total aperture to about 120 × 130 km.

### 2.2 Characterization of the Ambient Noise Field

In this work, we focus on the ambient wave field in the 1–10 s period band, which roughly corresponds to the period band of secondary microseismic noise. We first characterize the noise recorded by the Maupasacq array in the spectral, spatial, and temporal domains.

#### 2.2.1 Power Spectral Density and Noise Polarization

A spectrogram of the vertical component record at permanent station ATE during the Maupasacq experiment is shown in Figure 2a. Several higher-energy patches emerge in the period band of the secondary microseismic peak (Figure 2a, contoured patterns). The upper period bound of these patches extends to about 10 s at the beginning and end of the recording period (e.g., Days 95 or 255) and decreases to 6–7 s during summer (e.g., Day 180). This change in noise amplitude and frequency content reflects the seasonal decline in the intensity and number of oceanic storms during summer in the Northern Hemisphere (Stutzmann et al., 2000).

*β*

_{j}is the back azimuth estimated at station

*j*, in radians, and denotes the complex argument.

The highly energetic patterns observed in the vertical component spectrogram (Figure 2a) are characterized by higher average ellipticity (Figure 2c), which confirms the predominance of Rayleigh waves. As can be seen in Figure 2b, these waves originate mostly from a few specific directions in good agreement with the dominant noise directions previously reported by Chevrot et al. (2007) in the nearby Quercy region: N275° (Galicia), N340° (Northern Atlantic), and N130° (Mediterranean sea; see, e.g., Day 206).

#### 2.2.2 Beamforming Analysis

**s**is the horizontal slowness vector,

*ω*the angular frequency,

*N*the number of stations,

*U*(

**r**

_{j},

*ω*) the Fourier transform of the wave field observed at station

*j*located in

**r**

_{j}, and the reference location, taken here as the center of the array. To account for the dispersive nature of surface waves, we evaluate the beam power near a center pulsation using spectral integration of the band-pass filtered traces:

*G*denotes the Fourier domain Gaussian band-pass filter centered on pulsation with a bandwidth controlled by a coefficient

*α*(e.g., Bensen et al., 2007):

Figure 3 shows the results of beamforming for two different storms recorded between Days 250 and 260 (a–d) and between Days 205 and 208 (e–h) at different periods. The fundamental mode Rayleigh waves correspond to phase velocities near 2.6 km/s at 2 s period and 3.1 km/s at 9 s period. The propagation directions obtained by beamforming are in excellent agreement with the polarization analysis (Figure 2a). In particular, prominent energetic arrivals are detected from back azimuths N275°, N340°, and N130°. The relative amplitudes of these noise sources vary strongly as a function of the time interval considered and the period. For example, the signal recorded between Days 250 and 260 (Figure 2a) is dominated by noise sources from Galicia for periods between 2 and 6 s (Figures 3b–3d and blueish colors on Figure 2b), while the northern direction dominates at periods near 9 s (Figure 3a and pinkish colors on Figure 2b). Secondary arrivals are also observed from the Mediterranean sea at periods below 3 s (Figures 3c and 3d). These Mediterranean sources are rarely dominant. Most of the time, they are masked by the energetic arrivals coming from the northern and western directions, which explains why they are under represented in the polarization diagram in Figure 2b.

Beamforming analysis also revealed a weak but pervasive noise source with a dominant period around 7 s that produces waves with a very fast apparent phase velocity, indicating a nearly vertical incidence (e.g., Figure 3e). Similar waves have been reported in the literature and attributed to distant oceanic sources (e.g., Landès et al., 2010; Meschede et al., 2017; Pedersen & Colombi, 2018). They could be responsible for the spurious large amplitude arrival near the zero lagtime that is often observed in noise correlation functions (Taylor et al., 2019; Villaseñor et al., 2007).

#### 2.2.3 Coherent Surface Wave Trains From the Oceans

In the time domain, the high-energy patterns detected in the spectrogram (Figure 2a) correspond to coherent wave trains that cross the entire array. Figures 4a and 4c display the waveforms recorded during Day 181 at periods 5.2 and 3 s (see the shaded traces), where the noise comes mostly from the Galicia direction (Figure 2b). To highlight the phase alignments of the waves emitted by the dominant noise source, the seismic traces are sorted as a function of increasing distance measured along the propagation direction determined from beamforming. The black solid lines in Figures 4a and 4c correspond to the reference wavelets obtained at the center of the array, using the iterative matched filtering algorithm detailed below.

#### 2.2.4 Concluding Remarks on the Nature of the Ambient Wave Field

We conclude from these detailed observations that the ambient wave field in the 1–10 s period band is a superposition of coherent quasi plane waves coming from a few well-defined dominant directions and not a purely diffusive wave field. The relative amplitudes of the dominant noise sources strongly vary with the time interval and with the period considered.

## 3 Methods

### 3.1 Extraction of Coherent Wave Trains With an Iterative Matched Filtering Approach

- A beamforming, which allows us to estimate the apparent slowness and back azimuth of the dominant noise source: These beam parameters are used to obtain an initial reference wavelet at the center of the array.
- An iterative matched filter: This step iteratively improves the reference wavelet and the values of time and amplitude fields at each station.
- A subtraction of the matched wave field from each trace.

This algorithm is iterated until all the coherent wave trains are extracted and the remaining wave field is incoherent.

#### 3.1.1 Step 1: Beamforming and Initial Wavelet Estimate

*u*(

**r**

_{j},

*t*) is the wave field observed at station

*j*located in

**r**

_{j}, filtered with a Gaussian filter centered at pulsation (equation (4)); and is the reference location, chosen at the center of the array.

#### 3.1.2 Step 2: Iterative Matched Filtering

*n*the iteration number. The denominator in (6) is a normalization constant that ensures that the amplitude of the MFCF at the maximum lag time is the relative amplitude of the extracted wave at station

*j*relative to the reference location.

The MFCFs verify the wave equation because the correlation of a wave field that verifies the wave equation with any other spatially invariant signal still satisfies the wave equation (Lin et al., 2013, their equation 3). By the linearity of the correlation function, this assertion holds true if *u* is the superposition of several wave fields verifying the wave equation.

*j*and the reference location in the direction of propagation of the dominant coherent wave. We then relax the plane-wave assumption. The traces are realigned with the new time delays and stacked to determine a new reference wavelet:

*n*+1 to recompute the MFCF according to equation (6). The process is iterated until convergence, that is, until the energy of the reference wavelet reaches a plateau, which usually occurs after a few iterations.

*c*

_{f}, we get the travel time and amplitude at each station, measured as the maximum lag time and maximum amplitude of

*c*

_{f}

Figure 5 illustrates the travel time and amplitude of the dominant wave field at 5.2 s period extracted from a 1-hr long noise time window.

#### 3.1.3 Step 3 : Subtraction of the Dominant Wave Field from the Signal

The three-step algorithm is then reapplied to the residual wave field, to search for secondary coherent wave fronts.

#### 3.1.4 Average MFCF

For each 1-hr long time window and each iteration of the three-step matched filtering procedure, we obtain a collection of MFCFs associated to a dominant average wave number vector. The MFCFs obtained for similar wave vectors are averaged in order to increase the signal to noise ratio and minimize the cross-terms due to fortuitous correlations between uncorrelated noise sources (Snieder, 2004).

### 3.2 Regularized Eikonal Tomography

*θ*discretized on a regular Cartesian grid that minimizes the misfit with the observed travel times at each station, and such that its gradient leads to a phase slowness model that is close to an a priori slowness model. The cost function of the problem is

In this expression, *T*(**r**_{j}) is the travel time field observed at each station, **r**_{j} the location of the *j*^{th} station, (*L*.*θ*)_{j} the travel time estimated at station *j* using the bilinear interpolation operator *L*, and *s*_{prior} the vector containing the prior phase slowness model over the same grid as *θ*. The dependency of *θ*, *T*, and *s*_{prior} to the center pulsation
is dropped for the sake of simplicity. The first term in equation (10) quantifies the misfit between the predicted and observed travel times. The second term measures the misfit between the eikonal phase slowness derived from the inverted parameter using the eikonal equation ||∇*θ*|| and the prior slowness model *s*_{prior}. The last two terms are penalty constraints that are introduced in order to minimize the total curvature of the travel time and slowness models, respectively, which are quantified with the norm of the Laplacian (Smith & Wessel, 1990). The parameters *α*, *β*, and *γ* control the penalty constraints that regularize the solution. The inverse problem (10) is solved with a conjugate gradient algorithm. The travel time model *θ* used to initiate the inversion is computed in the prior slowness model *s*_{prior} using the fast marching method (FMM Sethian, 1996). The inversion is first applied to the longest period using a homogeneous prior model. The period is then progressively decreased, using the solution of the inversion at the current period as an a priori for the next period. The regularization terms in equation (10) allow us to smooth the inverted travel time (third term in equation (10)) and the corresponding eikonal tomographic model (fourth term in equation (10)), which mitigates the influence of the outliers and improves the accuracy of the velocity model by canceling the interference between the incident and scattered wave fields. We adjust these regularization parameters by a systematic grid search. The criterion is to obtain smooth travel time and slowness models that provide a good fit of travel time data.

## 4 Validation of the Matched Filtering and Eikonal Tomography Methods on a Synthetic Test

### 4.1 Synthetic Experiment Setup

We now validate our method with a numerical experiment. The objective of this synthetic test is to demonstrate the ability of the matched filtering method to measure travel time and amplitude fields on waves that simultaneously arrive from different directions and interfere in the time domain.

We consider 1 day long synthetic noise time series containing 5 s Rayleigh waves propagating in the structural phase velocity model shown in Figure 6a. The synthetic noise records are built using temporal wavelets obtained by bandpass filtering white noise series around 5 s period. These noise series are then shifted in time and scaled in amplitude to simulate the propagation of the waves across the array. The phase travel time shifts and amplitude corrections at each station are obtained by resolving the scalar wave equation with a finite difference method for each noise source. As a boundary condition, we impose the displacement produced by an incident plane wave coming from the azimuth of the noise source with a phase velocity of 3.0 km/s. We implement Stacey boundary conditions to absorb the outgoing scattered wave field (Stacey, 1988). Figures 6b and 6c show the phase travel time and amplitude fields modeled for an incoming wave with a back azimuth of 280°. We apply independent phase and envelope travel time shifts in the frequency domain. The signal is reformed afterward in the time domain. For the envelope shifts, we use the group travel times estimated with the FMM algorithm in the synthetic group velocity model shown in Figure 7.

We add the two synthetic noise records modeled for back azimuths 280° and 130° to simulate the interference of the Atlantic Ocean and Mediterranean Sea noise sources. The amplitude of the Mediterranean source is taken as one third of the Atlantic source. Additional incoherent noise in the form of random Gaussian noise with an amplitude of 20% of the Atlantic noise source is added to each trace to simulate instrumental noise or local uncorrelated noise sources.

### 4.2 Results

The three-step matched filtering method is applied to the 1 day synthetic noise series, cut into consecutive and nonoverlapping 1 hr time windows. In each window, we recover the azimuth of both the primary and secondary wave fronts after the first two iterations of the three-step procedure (i.e., back azimuths N280° and N130°, not shown). The phase travel times of the average MFCFs obtained at each station for the Atlantic and Mediterranean directions are shown in Figures 8a and 8b. They are in good agreement with the expected travel time fields (Figures 8c and 8d) obtained from the phase of the modeled wave fields for these two directions as in Figure 6b. The lateral distribution of the amplitudes at each station from the average MFCFs also reproduces the expected ones for the two directions imposed (Figure 9).

We invert the travel time fields at each station to obtain the eikonal phase velocity models for the two directions using equation (10) (Figures 10a and 10b). We compare them with the expected eikonal models, determined from the gradient of the expected travel time fields of Figures 8c and 8d. The expected velocity models are smoothed laterally to ensure a fair comparison with the inverted phase velocity maps (Figures 10b and 10d). The differences between the expected phase velocity models for back azimuths 280° and 130° are attributed to the errors introduced by the eikonal approximation, which discards the information carried by the amplitude field. This test validates the ability of our method to separate interfering wave fronts emitted by uncorrelated noise sources. Note that the method is also able to separate coherent wave fronts from incoherent background noise.

Figure 11a shows the velocity model obtained by averaging the Atlantic and Mediterranean sources eikonal models. It is in very good agreement with the true structural model shown in Figure 11c, at least beneath the dense part of the seismic array. The strong similarity between the eikonal model derived from a complete azimuthal coverage (Figure 11b) and the true structural model (Figure 11c) demonstrates that in practice, eikonal tomography is sufficient to obtain accurate and robust phase velocity models provided a good azimuthal coverage.

## 5 Application to the Maupasacq Dataset

### 5.1 Data Preprocessing

We preprocess the vertical component records as for the polarization analysis presented above. After removing the anomalous traces, the seismograms are deconvolved from their instrumental response, detrended, resampled at 2.5 samples per second, and cut into 1-hr nonoverlapping time windows.

### 5.2 Extraction of Coherent Wave Trains by Iterative Matched Filtering

We apply the matched filtering approach at a number of periods spaced logarithmically between 2 and 9 s. To mitigate the instrumental noise level in the seismograms, we use only the broadband stations for periods above 7 s (Figure 1, BB and PBB), the short period and broadband stations for periods between 3 and 7 s (BB, PBB, and SP), and all the stations for periods below 3 s (BB, PBB, SP, and GN). Inside a given time window, we can usually extract several (sometimes up to 10) coherent wave fronts. We only keep the wave fronts whose average phase velocity corresponds to the fundamental mode Rayleigh wave. The phase velocity ranges used to isolate the Rayleigh wave component are 2.8–3.2 km/s at period 5.6 s, 2.6–3.0 km/s at period 3.48 s, and 2.4–2.8 km/s at period 2.34 s (Figure 12). The first detections (dark red dots on Figure 12) are in good agreement with the dominant noise sources previously identified with the polarization and beamforming analyses. Interestingly, the later detections, which correspond to less energetic noise sources, often come from other back azimuths. Thus, by iterating and exploiting all the coherent but less energetic arrivals, we can improve the azimuthal coverage very significantly. However, very few arrivals are detected in the northeast and southwest directions.

### 5.3 Results of Matched Filtering

The MFCFs obtained for similar directions are averaged over 5° azimuthal bins to increase the signal to noise ratio. Further details about the temporal variation and the convergence rate of the MFCF are given in the supporting information. The MFCFs obtained at each station for period 5.2 s for the two back azimuths N280° and N130° are displayed on Figures 13a and 13d. The MFCFs are ordered as a function of their distance from the noise source. The origin time is defined as the onset time at the center of the array. The travel time and amplitude fields derived from the averaged MFCF at each station for the two directions are shown, respectively, on Figures 13b and 13c and Figures 13e and 13f. Movies showing the propagation of the extracted surface wave fronts across the network for several back azimuths and periods are given in the supporting information.

Significant distortions of the travel time field can be observed as a result of lateral variations of velocity beneath the array. For example, the wavefront curvature observed for the back azimuth N280° (Figure 13b) in the northeastern part of the array reveals the low-velocity anomaly of the Arzacq basin. We also observe significant amplitude variations within the array, ranging from about 0.25 to 2 at period 5.2 s (Figures 13c and 13f). The lateral distribution of the amplitudes varies with the incoming direction, which suggests that this distribution is first controlled by the heterogeneities that are crossed by the waves, rather than local structural amplifications. For example, the higher amplitudes observed in the Arzacq basin for the N280° direction (Figure 13c) result from the focusing of the wave front produced by the negative velocity anomaly in the northeast corner of the array.

### 5.4 Phase Velocity Maps

We use the regularized interpolation approach to estimate the eikonal phase velocity dispersion map for each back azimuth from the average MFCFs (as exemplified on Figures 13b and 13e). We start the inversion using the wave fronts originating from the Atlantic direction (from the average MFCFs obtained for the back azimuths between N280° and N285°) at the longest period (9 s) assuming a homogeneous 3.1 km/s prior model based on the average slowness measured by beamforming. The regularization parameters (*α*,*β*,*γ*) in equation (10) are adjusted to balance all the terms of the misfit function. The resulting phase slowness model is then used as the prior model for the next period (8.32 s) shifted by a constant slowness value to fit the mean slowness of the detected wave fronts at period 8.32 s. The procedure is repeated for the 20 periods spaced logarithmically down to period 2 s. The phase slowness models obtained at each period for the incoming Atlantic direction are then used as prior models to invert the travel time fields in the other directions. The azimuthal average of the phase velocity models obtained are shown in Figure 14.

## 6 Discussion

### 6.1 Comparison Between Matched Filtering Coherent Wave Field Imaging and Standard Ambient Noise Tomography

The matched filtering method shares many similarities with standard ambient noise tomography. However, while both methods exploit the surface waves present in the ambient noise field for passive imaging, they do differ in several aspects.

First, in contrast to standard ambient noise tomography, the matched filtering approach does not rely on the implicit assumptions of a diffusive ambient noise field (Lobkis & Weaver, 2001) or of a spatially uniform distribution of uncorrelated noise sources (Roux et al., 2005). Instead, it exploits the strong directivity of noise sources to separate and extract coherent wave trains. While ambient noise correlation can usually provide relatively accurate travel time information even with heterogeneous noise source distributions or imperfectly diffuse wave fields, the matched filter approach better exploits the strong directivity of ambient noise fields. We have shown that the matched filtering method remains valid in the case of interfering wave trains originating from different directions, as observed with the Maupasacq array. The iterative extraction of coherent waves allows us to exploit sources from a broad range of azimuths thanks to the secondary noise sources that are most of the time buried beneath the predominant Atlantic and Mediterranean noise sources. Since the azimuthal averaging of eikonal phase velocity map can mitigate the error due to the eikonal approximation (Bodin & Maupin, 2008), we believe that the improved azimuthal coverage will ultimately lead to more robust isotropic tomographic models with less artifacts.

Second, the standard noise correlation method often implies some aggressive nonlinear preprocessing filters like spectral whitening or temporal normalization (Bensen et al., 2007), which annihilate the amplitude information. Although it is usually admitted that those filters should be avoided for applications that try to exploit the amplitude information, no clear consensus can be found in the literature about the optimal preprocessing to simultaneously ensure a good reconstruction of the amplitudes and convergence of the noise correlations (e.g., Bowden et al., 2015, 2017; Liu et al., 2015; Mordret et al., 2013). With the matched filtering approach, since we normalize the correlations by the energy of the reference wavelet, the amplitude information is naturally preserved. The amplitude fields obtained by matched filtering should open important perspectives to better constrain attenuation and seismic anisotropy beneath dense local or regional seismic arrays.

Third, in ambient noise tomography, exploiting the noise correlation functions for interstation distances smaller than a few wavelengths is generally challenging. In that case, surface waves are observed in the near field, which hinders the estimation of phase and group travel times, and errors due to heterogeneous noise source distributions become prominent (Weaver et al., 2009). For these reasons, close station pairs are often discarded (Bensen et al., 2007), which has a detrimental effect on the spatial coverage. The matched filtering approach does not suffer from this limitation.

Fourth, in the matched filtering approach, the separation and extraction of the different coherent wave trains scale with the number of sensors, while noise correlation scales with the square number of sensors when considering all the station pairs. Therefore, matched filtering can be used to obtain a tomographic image with lower computational cost. On the other hand, since noise correlations exploit the redundancy of information between a large number of station pairs, this can reduce the errors in the traveltime estimates.

The main limitation of the matched filtering approach comes from the geometry of the acquisition. It first needs to be sufficiently dense to sample the wave field without spatial aliasing. In addition, the aperture of the array must be sufficiently large to be able to separate wave fields originating from nearby directions. In other words, the results of matched filtering will be controlled by the array response function at the periods considered (see the supporting information).

### 6.2 Going from Eikonal to Helmholtz Tomography

Despite the long-term averaging of the MFCFs (over 6 months), the amplitude fields obtained are still noisy (Figures 13c and 13f). A first source of problem is probably due to the use of different types of instruments and from an imperfect knowledge of their responses, especially for the SP sensors. In addition, since the periods considered in this study are well below the cutoff period of the SP and GN sensors, we have to face a significant level of instrumental noise. This will limit our capacity to exploit the amplitudes with Helmholtz tomography (Lin & Ritzwoller, 2011). In any case, amplitude fields still constitute untapped important sources of information that should allow us to further improve over the results of eikonal tomography in the near future.

### 6.3 Lateral Variations of Phase Velocities Beneath the Maupasacq Array

The phase velocity maps show strong lateral variations, revealing the complexity of the structures in the upper 10 km. The main shallow feature is the low-velocity anomaly in the northeastern part of the model, which coincides with the Arzacq basin, a Tertiary unit separated from the Mauleon basin by the North Pyrenean Front Thrust (Figure 1). The Mauleon basin, to the south west, is filled with Cretaceous calcareous and flysch rocks, which are characterized by much higher phase velocities. The low-velocity anomaly observed in the southwestern part of the Mauleon basin for periods shorter than 3.5 s is related to a large syncline approximately oriented along a WNW-ESE direction. It is nicely correlated with shallow post and syn-rift sedimentary deposits visible in the surface geological maps of the area (e.g., Masini et al., 2014). The phase velocity maps at periods longer than 4 s show a different and simpler pattern. In these maps, a sharp transition is observed, which marks the limit between a high-velocity domain in the south and a slower domain in the northernmost part of the Mauleon basin. Interestingly, this high-velocity region is found on the top of the fast velocity anomaly imaged in Wang et al. (2016), which has been interpreted as a mantle body exhumed during the Cretaceous episode of rifting. This would suggest that the top of the basement is at a much shallower depth in the southern part of the Mauleon basin, in good agreement with the geological sections recently published for this area (e.g., Gómez-Romeu et al., 2019; Saspiturry et al., 2019).

## 7 Conclusions

We analyzed the ambient noise recorded during 6 months by the large-N Maupasacq array in the Arzacq-Mauleon basins (Western Pyrenees, France) in the period band 2–9 s. Our study revealed strong coherent sources from several directions corresponding to the Galicia (N275°), the northern Atlantic (N340°), and the Mediterranean sea (N130°), in good agreement with the directions previously identified by Chevrot et al. (2007). This observation motivated the development of an iterative matched filtering method to separate and extract coherent wave fronts from the ambient noise field, which has been validated on a synthetic test case. We have shown that robust phase velocity maps can be obtained with the eikonal approach, after averaging the eikonal phase velocity maps obtained for the different incoming azimuths. The final phase velocity maps at short period (2–3 s) are nicely correlated with surface geology. At longer period (>4 s), they reveal the deep architecture of the Arzacq and Mauleon basins.

## Acknowledgments

This work is part of the OROGEN research project, a tripartite partnership between the French CNRS, Total, and BRGM. We thank the CNRS and Observatoire Midi Pyrénées (OMP) who provided and deployed the broadband temporary stations (BB); CSIC who provided and installed the 191 geophone nodes (GN); Seismotech for the installation, maintenance, and harvesting of the 197 Short Period recorders (SP); and the Maupasacq Team, who settled the stations on the field and collected the data. We are grateful to the two anonymous reviewers for their constructive criticisms that greatly helped improve the content of this manuscript. Data from the permanent broadband (PBB) stations are part of the Resif-RLBP French permanent network and are accessible via the RESIF data center (RESIF, 1995). The data acquired in the framework of the OROGEN project (BB, SP, and GN stations) are not publicly available during the time of the project. Researchers can gain access to the data by contacting the OROGEN project leaders (at this address: http://www.orogen-project.com/contact). The MFCFs are provided in the supporting information.