Susana Goncalves
email: susana.goncalves@univ-brest.fr

Philippe Schnürle

Marina Rabineau

A Afilhado

Daniel Aslanian

Maryline Moulin

Mikael Evain

A Loureiro

N Dias

S Gonçalves

Susana Gonçalves -Phd

Deep crustal structures with reverse time migration applied to offshore wide-angle seismic data: Equatorial and North-West Brazilian margins

Keywords: Wide-Angle Seismic data, Reverse Time migration, Offshore Brazil, Refraction imaging, Deep crustal structures

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Introduction

The Reverse Time Migration method (RTM) was first developed and applied around the 1980's decade. The purpose of the method is to image the sub-surface by having the correlation between the forward and backward wavefields that propagate according to the two-way acoustic wave equation and the boundary condition (Baysal et al., 1984(Baysal et al., , 1983;;McMechan, 1983;Whitmore, 1983).

RTM has been largely applied to reflection datasets of different sources and geometry acquisitions where the instruments have short distances between them [START_REF] Chang | Elastic reverse-time migration[END_REF][START_REF] Liu | Reverse time migration of multiples for subsalt imaging[END_REF]. The application of the method to wide-angle seismic (WAS) data is uncommon due to low folds in Ocean Bottom Seismometers (OBS) deployment with wide spacing [START_REF] Górszczyk | Toward a robust workflow for deep crustal imaging by FWI of OBS data: The eastern Nankai Trough revisited: FULL-WAVEFORM INVERSION OF OBS DATA[END_REF][START_REF] Kamei | Waveform tomography imaging of a megasplay fault system in the seismogenic Nankai subduction zone[END_REF][START_REF] Nakanishi | Detailed structural image around splay-fault branching in the Nankai subduction seismogenic zone: Results from a high-density ocean bottom seismic survey[END_REF][START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF].

Imaging shallow subsurface structures is usually done in high-resolution reflection profiles with multichannel seismic streamer data (MCS) surveys. However, this kind of surveys frequently fail to image the deep crustal structures due to the limited length of the streamer. Also, these surveys are not always available due to restrictions of using streamer cables, mitigations related to mammals or protected areas on the survey locations or even weather conditions. Being able to image the deep crustal layers through RTM method from WAS data can be a valuable addition to seismic data processing and imaging.

The velocity structures required to perform RTM can be estimated from several processes.

In this study, we use RayINVR from [START_REF] Zelt | Seismic traveltime inversion for 2-D crustal velocity structure[END_REF] which is an iterative procedure of twodimensional forward ray-tracing followed by a damped least-squares travel time inversion.

The two wide-angle seismic profiles presented in this study are part of two different seismic experiments, acquired in collaboration between the Department of Marine Geosciences (IFREMER:

Institut Français de Recherche pour l'Exploitation de la MER, France), the Laboratory of "Oceanic Geosciences" (IUEM: Institut Universitaire et Européen de la Mer, France), the Instituto Dom Luiz -Faculdade de Ciências de Lisboa (IDL-FCUL, Portugal), the Universidade de Brasília (UnB, Brazil), and PETROBRAS (Brazil): (i) MAGIC -Margins of brAzil, Ghana and Ivory Coast, described in [START_REF] Aslanian | Wide-Angle and Multi-Channel Seismic Experiment in the Maranhão-Barreirinhas-Ceará Basins (Brazil)[END_REF]; (ii) SALSA -Sergipe Alagoas Seismic Acquisition, described in (Aslanian et al., 2016).

During the MAGIC survey, five combined wide-angle, and reflection seismic profiles were acquired in the Pará-Maranhão-Barreirinhas-Ceará basins northern Brazil (figure 1). Their location is in the southward second 600-800-km-wide segment of the Equatorial Atlantic Ocean, between the São Paulo Fracture Zone to the north, and the Chain Fracture Zone to the south. The system can be described as a pull-apart passive margin, with two strike slip borders.

A pool of OBS belonging to IFREMER's Marine Geosciences Department [START_REF] Auffret | MicrOBS: A new generation of ocean bottom seismometer[END_REF] was used for the offshore wide-angle acquisition and 3 profiles were extended onshore by using portable seismic stations from the Brazilian Geophysics instrument pool (Observatório Nacional, Rio de Janeiro). The seismic source consisted of a 7589 in 3 array of 18 airguns, towed 25 m below the sea level and fired every 60 s. Shots were also recorded by a 4.5 km long, 360-channel solid streamer towed at 12-15 m depth, 275 m behind the ship [START_REF] Aslanian | Deep structure of the Pará-Maranhão/Barreirinhas passive margin in the equatorial Atlantic (NE Brazil)[END_REF].

Forward modelling of these wide-angle data sets [START_REF] Aslanian | Deep structure of the Pará-Maranhão/Barreirinhas passive margin in the equatorial Atlantic (NE Brazil)[END_REF]Moulin et al, 2021;Schnürle et al., this issue) reveals an E-W lateral evolution of the oceanic crust spreading initiation with: (1) an unthinned continental crust below the São Luís Craton, where the crust is 33 km thick, (2) a 60 km wide necking domain below the Ilha de Santana Platform; (3) offshore, east of the continental slope, a 10 km-thick deep sedimentary basin resting on a 5 km thick crust interpret as exhumed lower continental origin on the top of an Anomalous Velocity Layer (AVL) probably made of intrusions of mantle-derived melts into the lower continental crust, or a mixture of them; (4) eastwards, the limit of the previous domain is marked by NWSE aligned volcanoes and the disappearance of the AVL. The sedimentary succession becomes thinner (6 km) overlaying a protooceanic crust characterized by seismic velocities higher than "normal" oceanic crust in its upper part, but in continuity with the velocity described in the previous domain; The second experiment, SALSA , is composed by 12 profiles -9 perpendicular to the coast with NW-SE orientation and 3 parallel to the coast with SW-NE orientation -acquired in the Jequitinhonha, Camamú-Almada, Jacuípe, and Sergipe-Alagoas basins, northeast Brazil. This experiment aimed to constrain the crustal structure, the segmentation, and the geodynamical setting of the different segments and of the Camamu triple junction, where the aborted Reconcavo-Tucano-Jatoba rift system connects with the Jequitinhonha-Camamu-Almada and Jacuípe-Sergipe-Alagoas rifts [START_REF] Loureiro | Imaging exhumed lower continental crust in the distal Jequitinhonha basin, Brazil[END_REF]Pinheiro et al., 2018;Loureiro et al., this issue, Evian et al., this issue).

In this experiment, 222 OBS instruments were deployed offshore and 124 LSS (Land Seismic Stations from ON) to extend onshore 5 of the profiles -SL02, SL04, SL09 and SL12.

The SL04 profile (figure 1) is located in the far Northeast portion of the experiment, within the Sergipe-Alagoas basin. The area within the profile is composed by 3 main domains (NW to SE):

(1) Onshore, continental slope and offshore part of the Alagoas basin with a 30 km thick crust of continental origin, thinning seawards up to 15 km; (2)In the double Ascension Fracture Zone, the continental crust further thins to 10 km and is underlain by a lens-shaped Anomalous Velocity Layer (AVL) up to 5 km thick. A volcanic edifice that belongs to the Pernambuco seamounts fills the fracture zone; (3) deep sea basin composed by a 6-7 km thick oceanic crust (Aslanian et al., 2016;[START_REF] Neves | The transition zone between the Pernambuco-Alagoas Domain and the Sergipano Belt (Borborema Province, NE Brazil): Geochronological constraints on the ages of deposition, tectonic setting and metamorphism of metasedimentary rocks[END_REF]Pinheiro et al., 2018;[START_REF] Loureiro | Imaging exhumed lower continental crust in the distal Jequitinhonha basin, Brazil[END_REF] In order to investigate the potential of RTM, we selected one NW-SE profile from each survey on both sides of the Pernambuco-Borborema area and in prolongation of each other (figure 1). Both of these profiles have coincident MCS streamer data and for SL04, there is an ION-GXT line previously acquired. Then, we are able to compare the results of the RTM migration with the PSDM migration done for that MCS streamer data. Thus we can validate the usefulness of the RTM method for refractions recorded with wide-spaced OBS to image deep crustal layers, such as, the Moho discontinuity.

Data

The wide-angle seismic data used in this study consists of two different profiles from two wide-angle seismic acquisition projects on the North-West and South-East offshore, Brazil. One of the profiles -MC5 -is located in the Equatorial margin and the other -SL04 -is located in the North-West Brazilian margin (figure 1).

The offshore part of the MC5 profile is composed by 44 OBS stations and has a length of 528 km. The chosen SALSA project profile is composed by 14 OBS stations and has a length of 158 km. The spacing between each OBS station is 12.5 km and the airguns were fired each 60s or 150m, approximately. MCS streamer data acquisition were simultaneously conducted.

The shooting on MC5 profile started at MC5OBS44 and ended to MC5OBS05. Due to shallow water on the shelf, it was not possible to continue the shooting up to the position of MC5OBS01. Also, all the OBS stations were retrieved, but MC5OBS43 did not register any data.

For profile SL04, all the OBS stations were retrieved and the shooting was done from SL04OBS14 to SL04OBS01.

All OBS stations were composed by three-component geophones and a hydrophone sensor. Moho refractions were clearly observed in most of the vertical component of the geophone records.

Method

The term that contemplates the time of propagation in the acoustic seismic equation, does not have a sense of positive or negative values. This means that the path taken by a particular ray can be traced back to the source by simply reverse the time to zero.

First we compute the forward propagating wavefield for each defined time step. Then, we restore the energy back to the respective sources by backpropagating the wavefield imposing the recorded signal as boundary condition for the same time steps. By correlating the forward and backward propagating wavefield for each saved time step, we image the horizons at their true vertical and horizontal positions.

In the case of pre-stack experiments, the shot profile reverse-time migration consists of a non-reflective two-way wave equation modeled with a finite difference (FD) method of the scalar acoustic wave equation. The method implemented is described in steps (Baysal et al., 1984;[START_REF] Nolet | Imaging the Earth's Interior[END_REF][START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF]. By adopting the source-receiver reciprocity on the relation between airgun shots and OBS's for each spacial coordinate in the model (x in equations ( 1), ( 2) and ( 3)), the downgoing wavefields -Fi(x,t), equation ( 1) -are extrapolated forward in time from OBS locations (XOBSi (i=1,2,…,M), equation ( 1)).The upgoing wavefields -Bi(t,x), equation(2) -are extrapolated backwards in time from airgun shot locations (Xshotj, equation ( 2)) (e.g. [START_REF] Schnurle | Acoustic and Shear-Wave Velocities in Hydrate-Bearing Sediments Offshore Southwestern Taiwan: Tomography, Converted Waves Analysis and Reverse-Time Migration of OBS Records[END_REF][START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF]):

1. We forward propagate a shot wavefield -Fi(t,x) -in time (t: 0 → T) to out past all horizons (2) 3. Imaging -I(x) -by adding through all time steps the two wave field's product for each grid point. The imaging condition for the zero instance in the time domain can be represented by:

(3) 4. Finally we obtain the subsurface image along the entire profile by stacking the individual image sections from all OBS records. (Baysal et al., 1984;[START_REF] Nolet | Imaging the Earth's Interior[END_REF][START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF] The processing sequence consisted of 5 steps:

. Data processing and Imaging

1) A wide butter-worth filter was applied in different intervals of lower frequencies -0.5-4 Hz and high frequencies -32-48 Hz, followed by spiking predictive deconvolution. To prevent noise from the water and other layer multiples, they were removed by applying mute. Finally, a narrower butter-worth filter of 1-4-12-18 Hz was applied(figure 3a).

2) To ensure sufficient resolution with limited dispersion and spacial aliasing, the optimal grid-spacing needs to be established. This grid-spacing was implemented in the 10 th order 2D finite difference acoustic modeling. Given the acquisition footprint, the horizontal grid spacing chosen is that of the shot spacing, i.e. dx=15 m. The recorded OBS data is sampled at 4 ms, and provided ample sampling for a vertical grid spacing dz=25 m. A grid with of 100 km (+/-50 km offset) was selected in order to reach a depth of 25 km of imaging.

3) The layered RayINVR velocity models was converted into regular grids, the grids are cut in order to fit the section where the individual RTM OBS stations are placed and a damped least squares smoothing was applied. Applying the smoothing to the velocity model is essential in order for the migration technique to work and avoid artifacts generated by sharp variations of velocity for neighboring points.

4) The RTM migration was performed for each OBS station (figure 3b). 5)All individual RTM images were stacked in order to get the image for the entire set of stations within the entire profile (figure 3b). In order to enhance the migrated reflectors and refractors and avoid the artifacts generated by the large spacing between the OBS stations, prior to stacking, a dip filter was applied to each OBS obtained results , between -1.75 and 1.75and a final image was obtained (figure 3c).

Results

The input data to perform the RTM for each OBS station contains reflected and refracted waves as we can observe from figure 2 (highlighted by the blue arrows).

The RTM result for station MC5OBS22 with the overlaid ray tracing -figure 4 -shows that we retrieve reflectors/refractors to offset distances of 60 km to each side of the OBS position. Also, the contribution of the refracted wave content is quite significant. For example, the Moho discontinuity is almost only illuminated by refracted waves -dark blue rays in figure 4. For MC5 profile (figure 3), the basement of the basin refractor can be identified, between 10 and 12 km depth, for almost the entire length of the profile. It is less clear between 210 to 260 km distance (MC5OBS24 to MC5OBS28). The Moho discontinuity refractors can be identified between 14 to 17 km depth. In spite of their strength, they are not as continuous along the profile.

The U-unit refractors can also be identified at 14 km depth between 250 to 300 km distance and 400 to 475 km distance. At 5-6 km depth, within the basin -between 275 to 450 km distance -the higher velocity volcanic layer refractors are present. The refractors under the volcanic structures between 25 and 140 km are strong but the connection with the interfaces given by the velocity model is hard to do.

For SL04 profile (figure 5a), the base of the basin refractor at 5 km depth, is continuous and strong for the entire profile. Also, between 6 and 8 km depth, the refractor that corresponds to the base of the middle crust is also strong and continuous between 40 and 175 km distance. The Moho discontinuity refractor is at 14 km depth, visible between 130 and 175 km distance. From figure 5b, where the contours of the velocity model layer are presented (red dashed lines), the mentioned refractors match the velocity layers described. The refractors under the volcanic structure present in this profile are also strong. It is not possible to distinguish refractors that correspond to the layers that are within the basin and present in the velocity model.

Discussion

From the results presented in figure 4, the contribution of the refracted wavefield is essential for the imaging of several refractors, in particular the deeper ones. The basement, the ALV-unit and the Moho discontinuity are imaged almost fully by refracted waves. Imaging the horizontal extent of the interfaces is also mostly supported by the refracted content. This large contribution becomes very important for the success of the RTM method and, although unexpected, highlights their importance for the quality of the seismic imaging. Since the refracted waves contribution are a large part of the energy of the wavefield traveling within the earth we can name the obtained interfaces as refractors.

From the stacked RTM results for each profile (figures 3d and 5 -MC5 and SL04, respectively), we obtained several refractors for different depths that match the layers given by the velocity models. The Moho discontinuity refractors -18 km depth for MC5 profile -are the deeper ones that the method is able to retrieve, for the studied profiles. Not all the obtained refractors have a continuous behavior for the entire distance of the profiles but it is possible to interpolate between them.

For SL04 (figure 5), the basement, the upper crust, middle crust and the Moho discontinuity refractors are continuous and strong for the most offshore part. However, from 115 km model distance (SL04OBS05) and moving landwards, the refractors the correspond to the Moho discontinuity lose amplitude and eventually disappear. The Moho discontinuity seems to deepen abruptly with possible occurrence of an approximately 5 km thick additional ALV-layer. The presence of refractor at the end of the profile -25 km to 40 km model distance (SL04OBS12 to SL04OBS13) -just above ALV-Unit/Moho discontinuity depth, reinforce the structure present in the velocity model for a layered crust and the depth of the Moho discontinuity.

In MC5 (figure 3d), between 250 to 500 km distance, the presence of an ALV-unit (Schnürle et al., this issue), that introduces a slower vertical velocity gradient when compared with the remaining offshore profile, seem to affect the resulting refractors that match the Moho discontinuity [START_REF] Aslanian | Deep structure of the Pará-Maranhão/Barreirinhas passive margin in the equatorial Atlantic (NE Brazil)[END_REF].

Both profiles have the presence of volcanic structures and they have an influence on the obtained results. In SL04 (figure 5a) the refractors under the volcano structure seem to be affected just until the upper crust depth (5 to 6 km depth, at 75 km distance). While the refractor within the volcanic structure seem to give continuity to the top of the upper crust, the refractors of the basement and other at shallower depths seem to be interrupted in the lateral of the volcano structure.

For MC5 (figure 3d) the volcano structure is bigger and wider. All the obtained refractors located between 25 to 125 km seem to be affected by the structure and is hard to follow the refractors that correspond to the different layers. The volcanic structure seem to extend in depth up until the Moho discontinuity, at 14 km depth. Also, the strong oblique refractors present between 100 to 200 km distance and 8 to 14 km depth, suggest that the deeper layers may have played an important role upon the formation of those volcanic structures.

There is a significant difference in the strength and continuity of the obtained refractors between the two studied profiles. They have quite similar acquisition and processing parameters.

The main difference between the profiles is their length and the velocity model used. The amplitude absorption and phase distortion linked with the specific composition of each layer, are the two main factors that affect the structure imaging and interface interpretation and, consequently, the RTM result [START_REF] Wang | Adaptive stabilization for Q -compensated reverse time migration[END_REF][START_REF] Zhang | Compensation for absorption and dispersion in prestack migration: An effective Q approach[END_REF][START_REF] Zhu | Q -compensated reverse-time migration[END_REF]. Comparing both profiles, the number and composition of the sedimentary layers, present on each basin, and an additional lithospheric crust layer on SL04 profile, are the main differences. For example, on the sedimentary basin of MC5, the presence of a thin volcanic ashes layer [START_REF] Aslanian | Deep structure of the Pará-Maranhão/Barreirinhas passive margin in the equatorial Atlantic (NE Brazil)[END_REF][START_REF] Schnurle | Acoustic and Shear-Wave Velocities in Hydrate-Bearing Sediments Offshore Southwestern Taiwan: Tomography, Converted Waves Analysis and Reverse-Time Migration of OBS Records[END_REF] this issue)faster, denser, and very clear on the migration result -may act as an attenuation zone, dissipating seismic energy.

The pertinence of WAS RTM and its efficiency when compared to pre-stack depth migration (PSDM) of multi-channel seismic reflection data needs to be investigated. On figure 6, we present the comparison for SL04 between the PSDM GTX-2400 (an industrial survey conducted by ION with a ~12 km long streamer at the same location), the MCS streamer PSDM, and the RTM results for the same profile. On top of each result, we overlaid the interpreted line-drawing of GTX-2400.

the results are trustworthy, but also that we can easily obtain an image of the subsurface with only WAS data, as previously done by [START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF] .

The used velocity model to perform the RTM is one of the essential elements of the method.

Therefore, an evaluation on how changes in the velocity model grid affect the obtained RTM results was performed for both profiles -figures 7 and 8. We preformed the RTM for overall slower velocity models --4% (dark blue line in figure 7a to 7e) and -2% (cyan line in figure 7a to 7e) of the original (red line in figure 7a to 7e) -and faster velocity models -+2% (yellow line in figure 7a to 7e) and +4% (orange line in figure 7a to 7e). In figures 7a to 7e, we present the vertical velocity variation for five different model distances along MC5 profile. In figures 7f to 7j, the stacked RTM results are presented, for the each velocity model at five different model distances of MC5 profile.

In figure 8 we present the RTM results for SL04, for each velocity model at two different model distances. We can see that the velocity changing is uniform throughout the MC5 profile (figure 7a to 7e) and does not create any vertical variation that was not present on the original model (red line on figure 7a to 7e). Also, the quality of the RTM results is quite similar trough out the profile, being coherent with the previous point. On the other hand, the major feature that we observe is the different strengths of the refractors depending on the velocity model used. In the case of the MC5 profile (figure 7f to 7j), we observe that the basement and Moho refractors are quite good for the original velocity model but seem stronger for a velocity model that has 98% of the velocities of the original one. For the other velocity models -96%, 102% and 104% -the same refractors are quite weak or even absent.

We performed the same analysis for SL04 (figure 8). The obtained results are similar to the ones obtained with MC5. However, for this profile, the refractors corresponding to the basement and Moho discontinuity are slightly stronger for the original velocity model but also quite good for the 96% and 98%.

There are a few reasons that can explain the different RTM results depending on the velocity model: (i) in spite of the ratio of velocity scaling is a few percent, the cumulative velocity difference from the seafloor to the target depth may have a strong effect on the focusing of the refractions [START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF]; (ii) the sensitivity to velocity structures could be high because of low folds of wide-angle data obtained with a spacing between OBS stations [START_REF] Shiraishi | Seismic reflection imaging of deep crustal structures via reverse time migration using offshore wide-angle seismic data on the eastern margin of the Sea of Japan[END_REF]; (iii) the uncertainty associated with the velocities of each layer, in particular the deeper ones; (iv) the geometry of the layers may contribute to the obtained results since, for example, for model distance of 250 km and 96% of the velocity model -MC5, figure 7h -and model distance 50 km and 96%

of the velocity model -SL04, figure 7a -we obtain stronger refractors for the basement and Moho, respectively. For both cases, the layers have a stronger dip for those distances.

Conclusion

The main purpose of this study was to be able to image the deeper crustal layers by applying the RTM method to WAS data. This goal was clearly fulfilled since we were able to image the lithospheric crustal layers and the Moho discontinuity with success and also obtain the refractors that correspond to sedimentary layers at shallower depths. The refractors obtained match the layer based travel-time inversion models of the two studied areas (MC5: Schnürle et al., this issue; SL04: Aslanian et al., 2016).

The contribution of the energy traveling as refraction within the earth is relevant and is key on the obtained seismic depth images. The refracted waves are the main content that allow to image the base of the basin, the crustal layers and the Moho discontinuity in both profiles (figures 3d, 4 and 5). Without this refracted content within the wavefield, the characterization of the deeper layers geometry would not be as efficient or even impossible with the RTM method. This result is unexpected but very important.

The difference in amplitude and continuity of the refractors between the two profiles is quite clear. The number and composition of each layer present in the velocity models should explain the difference. Differences in amplitude absorption due to those characteristics and the depth of the target interfaces may explain the observed differences [START_REF] Wang | Adaptive stabilization for Q -compensated reverse time migration[END_REF][START_REF] Zhang | Compensation for absorption and dispersion in prestack migration: An effective Q approach[END_REF][START_REF] Zhu | Q -compensated reverse-time migration[END_REF]. However, further studies should be done to better understand it.

By comparing the PSDM results with the RTM, we were able to confirm that we can better image the deeper crustal layers by using this method applied to the wide-angle data and also obtain the refractors that correspond to the shallower layers. We showed that the method is trustworthy and quite useful when the MCS streamer data are not available at the target depths, or can not be at all acquired.

By making variations of the overall velocity model between -4% and 4%, we have showed that the method is quite sensitive to velocity changes that could be related with the overall increase/decrease of velocity but may also be explained by the geometry of the target interfaces and, finally, with the uncertainties in the velocity of the deeper layers.

The general results have significance and are an important contribution for the seismic interpretation of the studied areas. For instance, the MC5 profile RTM results, support the NW-SE segmentation in different basins, with different characteristics. In depth, the presence of a anomalous velocity layer just above the Moho discontinuity and the geometry of the basement and Moho discontinuity are also imaged by the RTM. In SL04, the imaging of the basement and the Moho discontinuity are also imaged and the geometry of the correspondent refractors enforce previous interpretations of having a continental crust with a rapid thinning seawards, the AVL under the thinned continental crust and a deep sea basin offshore with a thickness of approximatly 6-7 km.

These results were obtained from a data set where the OBS spacing, for the two profiles, is 12.5 km.

Also, the velocity models used are quite complex in terms of geometry and velocity change. These characteristics contribute to potential amplitude absorption, phase distortion. The velocity uncertainties need to be taken into account. This gives to the RTM imaging method a great potential on diverse applications on wide-angle seismic data to study and explore at a crustal scale.

  (5) followed by a more characteristic but thin oceanic crust. In a SE-NW alignment and within the location of the MC5 profile presented in this study as well as in Schnürle et al. (this issue), 6 main sectors can be distinguished: (1) Medio Coreaù and Ceará Central trust belt; (2) the Basin I composing the continental slope, the Paraniba Platform and associated Piaui-Comocin and Ceará Basins; (3) Basin II; (4) intermediate Basin III; (5) the volcanic line to the SW of the southern São Paulo double Fracture Zone; (6) deep sea Basin in the São Paulo double Fracture Zone. The main goal of the MAGIC survey was to establish the segmentation of the Pará-Maranhão basin and to determine the crustal nature of its domains

figure 1 -

 1 figure 1 -Location of the OBS stations for MC5 and SL04 profiles within Brazil. a) MC5 -green -is located to the North-West and SL04 -red -to the South-East of Borborema massif; b) Zoom on the OBS and LSS location for MC5 profile; c) Zoom of the OBS and LSS location for SL04 profile

(

  backward sorted), based on the scalar wave equation with a migration velocity -C(x) -and a source function -s(t) -from the i th OBS location -xOBSi (i=1,2,…,M). The d(x-xOBSi) is the Dirac delta function: (1) 2. Back propagate the recorded wave field -Bi(t,x) -at the same time interval (t: T → 0) by treating the seismic traces of the i th OBS record -Di,j(t,xshotj) -as a boundary condition at the sea surface:

Figure 2

 2 Figure 2 presents the raw geophone vertical component of three OBS from the MC5 profile, and highlights clear arrivals reflected from the Moho at each station.

figure 2 -

 2 figure 2 -Examples of OBS acquired data for MC5 profile and examples of clear arrivals of the Moho for each station. a) MC5OBS11; b) MC5OBS22; c) MC5OBS44

figure 3 -

 3 figure 3 -RTM imaging process for profile MC5. a) Processed data for MC5OBS22, channel 2; b) RTM image for MC5OBS10, MC5OBS22 and MC5OBS30 without dip filter applied overlaid with velocity model; c) Stacked result of the RTM section for MC5 profile with no dip filter applied; d) Stacked result of the RTM section for MC5 profile with dip filter applied. Vertical exaggeration 1:6

  figure 4 -RTM results for MC5OBS22 overlaid with the ray tracing in our RayINVR velocity model

figure 7 -

 7 figure 7 -Effect of the variation of the velocity grids --4%, -2%, +2% and +4% of the original -on the RTM results of MC5 profile. . Vertical variation of the velocity for different model distance: a) 50 km; b) 150 km; c) 250 km; d) 350 km; e) 450 km; RTM results overlaid by each velocity model for different model distance: f) 50 km ; g) 150 km ; h) 250 km ; i) 350 km ; j) 450 km. Vertical exaggeration 1:6 figure 8 -Effect of the variation of the velocity grids --4%, -2%, +2% and +4% of the original -on the RTM results for SL04 profile. RTM results overlaid by each velocity model for different model distance: a) 50 km ; b) 150 km Vertical exaggeration 1:6

Acknowledgments

The authors would like to thank for the financial support from CAPES-COFECUB. This work was supported by ISblue project, Interdisciplinary graduate school for the blue planet (ANR-17-EURE-0015) and co-funded by a grant from the French government under the program "Investissements d'Avenir" embedded in France 2030.

We would like to thank to the supervisors who helped to develop the research presented in this manuscript and to the researcher that help improve the writing and the quality of this manuscript.

Funding

This Ph.D of S. Gonçalves was funded by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) I.P./MCTES through national funds (PIDDAC) -SFRH/BD/145433/2019. This research was funded by Petrobras (Brazil) and Ifremer (France). The dataset collected during the MAGIC and SALSA experiments are protected under a partnership with Petrobras. Any request has to be addressed to Daniel Aslanian (aslanian@ifremer.fr) and Adriano Viana (aviana@petrobras. com.br).


domain: phys sde spi

text:
Wen-Cheng Gong

Nicolas Jidenko
email: nicolas.jidenko@universite-paris-saclay.fr

Yang-Rei Li

Thi-Cuc Le

Jean-Pascal Borra

Jinn Tsai
email: cjtsai@nycu.edu.tw

PM 0.1 non-bouncing impactor (NBI) for ultrafine particle mass and number measurements

Keywords: ultrafine particle, PM 0.1, cascade impactor, particle loading, particle bounce

This study designed and tested a 30 L/min PM 0.1 non-bouncing impactor (PM 0.1 NBI) for ultrafine particle (UFP) mass concentration measurement. The PM 0.1 NBI uses a wetted glass fiber filter with continuous water injection to maintain a clean surface, preventing particle loading and bounce effects. Lab tests showed the 30 L/min PM 0.1 NBI outperformed the PM 0.1 stage of NCTU micro-orifice cascade impactor (NMCI, non-rotating) with a silicon oil-coated aluminum foil substrate in collecting solid particles, as the particle collection efficiency of the latter decreased obviously with increasing particle aerodynamic diameter for particles larger than ca. 300 nm, an apparent particle bounce phenomenon. The ambient field tests showed very close UFP mass concentrations between the PM 0.1 NBI sampler (the PM 0.1 V° WC du 29/07/2023 post revue 4JAS 2 NBI preceded by 3 stages with 18, 10, and 2.5 micrometer cutoff sizes) and the reference rotating 10-stages NMCI with the difference of 0.5 g/m 3 only. In addition, the 3 L/min PM 0.1 NBI was combined with a condensation particle counter to measure the UFP number concentrations which were shown to be very close to those of the reference with the difference of 5% only in the laboratory tests for loaded particle mass up to 300 µg. Good agreement was also found in the field tests. Therefore, the current 3 L/min PM 0.1 NBI and the future PM NBI with smaller flow rates (0.2-2.1 L/min) and larger cut-sizes (such as 0.4-0.9 m) can be used as viable UFP classifiers for improving UFP measurement accuracy both in mass concentrations and number concentrations and reducing the maintenance needs for the UFP classifiers which are important to long-term sampling and monitoring.

Introduction

Exposure to air pollution is estimated to cause about seven million premature deaths every year and new air quality guidelines were updated in 2021 in which PM 2.5 daily and hourly AQG levels (air quality goal) were further lowered to 15 and 5 g/m 3 from 25 and 10 g/m 3 , respectively, to help reduce PM 2.5 levels and decrease its health burden [START_REF] Who | Who global air quality guidelines: particulate matter (PM 2.5 and PM 10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide: executive summary[END_REF].

Due to health concerns of UFPs (ultrafine particles or PM 0.1 , particles with aerodynamic diameters, D pa , smaller than 0.1 μm) (HEI, 2013;[START_REF] Ohlwein | Health effects of ultrafine particles: a systematic literature review update of epidemiological evidence[END_REF], BC/EC ( black carbon or elemental carbon) (US EPA, 2019) and SDS (particles originating from sand and dust storms) [START_REF] Querol | Monitoring the impact of desert dust outbreaks for air quality for health studies[END_REF], actions to enhance research on the UFP risks and develop the corresponding mitigation methods were summarized in qualitative good practice statements, despite insufficient data to provide recommendations for AQG levels and interim targets for these specific types of PM [START_REF] Who | Who global air quality guidelines: particulate matter (PM 2.5 and PM 10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide: executive summary[END_REF]. Practices to integrate UFP monitoring into the existing air quality monitoring, prioritize UFP source emission control, and advance approaches to the assessment of exposure to UFP for epidemiological studies and UFP management are recommended [START_REF] Who | Who global air quality guidelines: particulate matter (PM 2.5 and PM 10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide: executive summary[END_REF].

Exposure assessment for UFPs is typically based on particle number concentrations (NCs) [START_REF] Ohlwein | Health effects of ultrafine particles: a systematic literature review update of epidemiological evidence[END_REF], particle mass concentrations (MCs) [START_REF] Kumar | An overview of methods of fine and ultrafine particle collection for physicochemical characterisation and toxicity assessments[END_REF], or lung-deposited surface area [START_REF] Geiss | Lung-deposited surface area concentration measurements in selected occupational and non-occupational environments[END_REF]. Among them, NC is the most common choice because the related measurement technologies are well-established [START_REF] Who | Who global air quality guidelines: particulate matter (PM 2.5 and PM 10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide: executive summary[END_REF], and UFPs are the main contributors to the total number of particles in the atmosphere [START_REF] Morawska | Ambient nano and ultrafine particles from motor vehicle emissions: Characteristics, ambient processing and implications on human exposure[END_REF]Chen et al., 2010a). For the size distribution measurement of submicron particles including UFPs, a scanning mobility particle sizer (SMPS) incorporating a single-stage inlet impactor, an electrostatic classifier and a condensation particle counter (CPC), is the most commonly used instrument. The impactor removes particles larger than a known D pa which sets the upper limit of the SMPS, thereby easing the multiple charge correction in the data inversion program [START_REF] He | A multiple charging correction algorithm for scanning electrical mobility spectrometer data[END_REF]. However, the high cost and complexity of the SMPS limit its widespread use in large-scale UFP monitoring networks (Abdillah and Wang, 2023). In addition, the inlet impactor without a coated impaction substrate or with a silicone oil-coated substrate is known to be affected by particle bounce and loading effects [START_REF] Le | Novel non-bouncing PM 2.5 impactor modified from well impactor ninety-six[END_REF][START_REF] Who | Who global air quality guidelines: particulate matter (PM 2.5 and PM 10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide: executive summary[END_REF]. Therefore, regular maintenance is needed to keep its size-classifying performance accuracy during long-term monitoring and when particle concentration is high, such as in a highway tunnel (Chen et al., 2010a and[START_REF] Chen | Chemical mass closure and chemical characteristics of ambient ultrafine particles and other PM fractions[END_REF] or welding booth (Chang et al., 2013), where PM 2.5 and UFP MCs can be as high as 78 and 33.2 g/m 3 , or 1,500 and 430 g/m 3 , respectively.

For physicochemical and toxicity assessment of UFPs [START_REF] Chen | Chemical mass closure and chemical characteristics of ambient ultrafine particles and other PM fractions[END_REF][START_REF] Tsai | Exposure assessment of nano-sized and respirable particles at different workplaces[END_REF][START_REF] Kumar | An overview of methods of fine and ultrafine particle collection for physicochemical characterisation and toxicity assessments[END_REF], mass-based measurement is required with a minimum sample mass of 100 g and 1000 g for the former and latter, respectively [START_REF] Kumar | An overview of methods of fine and ultrafine particle collection for physicochemical characterisation and toxicity assessments[END_REF]. This amount of UFP sampling can be achieved in the high-concentration tunnels and workplace environments mentioned above, but it is a challenge in ambient settings where UFP concentrations are typically low, e.g. 2.2 g/m 3 in roadside [START_REF] Chen | Chemical mass closure and chemical characteristics of ambient ultrafine particles and other PM fractions[END_REF], 0.7 g/m 3 in forest [START_REF] Chen | Chemical mass closure and chemical characteristics of ambient ultrafine particles and other PM fractions[END_REF], and <0.5 g/m 3 in California city [START_REF] Xue | Comparison of size-resolved PM elements measured using aluminum foil and Teflon impaction substrates: Implications for ultrafine particle source apportionment and future sampling networks in California[END_REF], unless extended periods up to a few days or at high flow rates are used [START_REF] Kumar | An overview of methods of fine and ultrafine particle collection for physicochemical characterisation and toxicity assessments[END_REF][START_REF] Xue | Positive matrix factorization of ultrafine particle mass (PM 0.1 ) at three sites in California[END_REF]. Most UFP samplers with high flow rates are cascade impactors that operate at flow rates ranging from several hundreds to 1100 liters per minute, and the PM 0.1 stage in these samplers is usually preceded by two to three stages, such as the high-volume ultrafine particle sampler (550 L/min, 2 stages: 2.5 and 0.15 m) [START_REF] Misra | A high flow rate, very low pressure drop impactor for inertial separation of ultrafine from accumulation mode particles[END_REF], the harvard high-volume cascade impactor (850 L/min, 3 stages: 2.4, 0.9 and 0.2 m) (Sillanpaa et al., 2003), and the high-volume impactor Sampler (400 L/min, 2 stages: 2.5 and 0.18 m) [START_REF] Saleh | Exposure to atmospheric ultrafine particles induces severe lung inflammatory response and tissue remodeling in mice[END_REF]. However, the D pa50 of the PM 0.1 stage in these samplers is 0.15, 0.2, and 0.18 μm only, respectively, which are considered quasi-UFPs but not true UFPs [START_REF] Xue | Comparison of size-resolved PM elements measured using aluminum foil and Teflon impaction substrates: Implications for ultrafine particle source apportionment and future sampling networks in California[END_REF][START_REF] Kumar | An overview of methods of fine and ultrafine particle collection for physicochemical characterisation and toxicity assessments[END_REF][START_REF] Sotty | Toxicological effects of ambient fine (PM 2.5-0.18 ) and ultrafine (PM 0.18 ) particles in healthy and diseased 3D organo-typic mucocilary-phenotype models[END_REF]. Quartz fiber substrate used in the PM 0.1 stage of high-volume ultrafine particle sampler eliminates initial particle bounce, but the maximum loaded particle mass (M L ) is limited to 60 mg, while the polyurethane foam substrate in harvard high-volume cascade impactor can increase the M L but the particle collection efficiency curve is less steep than that of the flat substrate, as the air can penetrate into the porous substrate leading to increased collection of large particles due to inertia impaction and UFPs due to diffusion. [START_REF] Huang | Particle collection efficiency of an inertial impactor with porous metal substrates[END_REF]Sillanpaa et al., 2003;[START_REF] Huang | Use of porous foam as the substrate of an impactor for respirable aerosol sampling[END_REF].

Therefore, a silicon oil-coated smooth impaction surface is a better choice to achieve a more accurate measurement, especially for the classification of nanoparticles [START_REF] Chen | Design and evaluation of a low flow personal cascade impactor[END_REF], but particle bounce and loading effects still need to be overcome [START_REF] Le | Novel non-bouncing PM 2.5 impactor modified from well impactor ninety-six[END_REF][START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF].

The UFPs measurement can be achieved using samplers that operate at a medium flow rate of 9 to 40 L/min (Chen et al., 2010a and[START_REF] Chen | Chemical mass closure and chemical characteristics of ambient ultrafine particles and other PM fractions[END_REF][START_REF] Kumar | An overview of methods of fine and ultrafine particle collection for physicochemical characterisation and toxicity assessments[END_REF], such as the micro-orifice uniform deposit impactor (MOUDI, 30 L/min, [START_REF] Marple | A microorifice uniform deposit impactor (MOUDI): description, calibration, and use[END_REF], the NCTU micro-orifice cascade impactor (NMCI, 30 L/min, [START_REF] Liu | Collection efficiency and interstage loss of nanoparticles in micro-orifice-based cascade impactors[END_REF][START_REF] Chien | Design and testing of the NCTU micro-orifice cascade impactor (the NMCI) for the measurement of nanoparticle size distributions[END_REF], and the nanosampler (40L/min, [START_REF] Furuuchi | Development and performance evaluation of air sampler with inertial filter for nanoparticle sampling[END_REF]). The PM 0.1 stage in the former two devices is preceded by a 0.18 m-stage while nanosampler is preceded by a 0.5 m-stage.

MOUDI and NMCI employ rotating stages and silicon oil-coated substrates to increase the M L , but the rotating feature does not exist in both high-volume UFP samplers and nanosampler. The mass collected on each stage of the MOUDI is limited to 3 mg [START_REF] Marple | A microorifice uniform deposit impactor (MOUDI): description, calibration, and use[END_REF] because the coating layer becomes ineffective with particle accumulation and particle bounce may occur from particle mounds [START_REF] Tsai | Solid particle collection characteristics on impaction surfaces of different designs[END_REF][START_REF] Misra | A high flow rate, very low pressure drop impactor for inertial separation of ultrafine from accumulation mode particles[END_REF].

For personal sampling of UFPs in workplaces, our group has developed a personal nanoparticle sampler (PENS, Tsai et al., 2012) which consists of a PM 4.0 cyclone-inlet and a micro-orifice impactor with D pa50 of 100 nm. Nevertheless, there is a M L limit of 1.78 mg. To eliminate the particle loading effect, a 3.0 L/min NIC (Nanoparticle Inertial Classifier, [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF] which is based on the non-bouncing feature of 16.7 L/min PM 2.5 M-WINS (modified well impactor ninety-six, [START_REF] Le | Novel non-bouncing PM 2.5 impactor modified from well impactor ninety-six[END_REF][START_REF] Le | The performance of the PM 2.5 VSCC and oil-wetted M-WINS in long-term field sampling studies[END_REF], was developed in which clean water is injected continuously at 0.3 mL/min flow rate (or vacuum oil is applied once per day for one minute at 3 mL/min each time) upward through a small drilled hole (1 mm diameter) located at the center of the glass fiber filter (GFF) impaction surface to wash off the deposited particles. The spent water/oil is then drained off from the hole at the edge of the impaction surface. The impaction substrate is thus free from loaded particle accumulation.

In this study, the non-bouncing impactor technique of our group was employed to modify the 9 th stage of the NMCI [START_REF] Liu | Collection efficiency and interstage loss of nanoparticles in micro-orifice-based cascade impactors[END_REF] as the 30 L/min PM 0.1 Non-Bouncing Impactor (30 L/min PM 0.1 NBI) for UFP MC measurement, in particular for long-term sampling if enough UFP mass is desired. The NIC developed previously (hereafter called as 3 L/min PM 0.1 NBI) was used to replace the traditional impactor at the inlet of CPC or SMPS for long-term UFP NC measurement. The performance of these PM 0.1 NBIs was tested for the particle loading effect both in the laboratory and in an ambient environment using the 10-stage NMCI and SMPS as the references for MC and NC measurements, respectively.

Experimental methods

UFP MC measurement

Design of 30 L/min PM 0.1 NBI and sampling system

The 30 L/min PM 0.1 NBI is designed by modifying the 9 th stage (PM 0.1 stage) of the NMCI, which consists of a nozzle plate having 2000 nozzles with a nozzle diameter of 55 m and an impaction plate covered by a 37-mm GFF (Model TE-G653-37, TISCH) as shown in Fig. 1a. De-ionized water is injected by a peristaltic pump continuously upward via a 1-mm hole (internal diameter) drilled through the impactor plate and GFF with a flow rate of 0.5 mL/min to wet the GFF and remove deposited particles. Spent water then flows into the annular cavity around the impaction plate and is drained by another peristaltic pump. The 30 L/min PM 0.1 NBI was used for the particle collection efficiency test in the laboratory test while a complete 30 L/min PM 0.1 NBI sampler (NBIS) shown in Fig. 1b was used for the particle loading and field tests. The 30 L/min PM 0.1 NBIS consists of the 30 L/min PM 0.1 NBI, preceded by 3 non-rotating impaction stages: the inlet stage (D pa50 of 18 m), the first stage (D pa50 of 10 m), and the second stage (D pa50 of 2.5 m) followed by an after filter (47-mm Teflon filter, Model R2PL047, Pall) to collect UFP. The three preceding stages are used to remove coarse particles to avoid nozzle clogging in the PM 0.1 stage. The first two stages are the same as those of the NMCI while the diameter of 10 nozzles of the 2 nd stage was reduced to 2.1 mm and re-calibrated to be 2.5 m as will be shown in a later publication.

Particle collection efficiency test

The experimental setup used for testing the particle collection efficiency of the 30 L/min PM 0.1 NBI is depicted in Fig. S1 (Section B) of the supplementary information (SI) and is similar to the one described in [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF]. Liquid dioctyl sebacate (DOS) and solid NaCl particles were generated by the evaporation-condensation method and by an atomizer followed by a diffusion dryer, respectively. The generated particles were charge neutralized and classified into monodisperse particles by a differential mobility analyzer (Model 3081, TSI). The particle concentrations were measured upstream and downstream of the NBI by Water Micro-orifices GFF-covered impaction plate using a home-made faraday-cup with an electrometer (Model 6514, Keithley) to determine the particle collection efficiency (, %) calculated by [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF]:

(1)

where I up and I down is the upstream and downstream particle currents (A), respectively. Then, the particle collection efficiency curve and D pa50 were determined by fitting the measured data using the following equation [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF][START_REF] Le | Novel non-bouncing PM 2.5 impactor modified from well impactor ninety-six[END_REF]:

(2) where a, b, c, d, and e are the fitting parameters. The classification curve sharpness () was also calculated as the square root of the ratio of D pa84 and D pa16 which correspond to the particle collection efficiency of 84% and 16%, respectively. In addition, a single 9 th stage of the NMCI was also tested for comparison, where the impaction substrate is the silicone oil (Model KF96SP, Shin-Etsu Chem. Co., Ltd., Japan)-coated aluminum foil substrate (47mm, Allfield Ltd., Taiwan).

Particle loading test in the laboratory

The experimental setup of the particle loading test of the 30 L/min PM 0.1 NBIS is depicted in Fig. S2 (Section B) of the SI. For comparison, a 30 L/min traditional cascade impactor-R (TCI-R)) consisting of rotating stages 0, 1, 2 and 9 (the cut-sizes of 18, 10, 2.5 and 0.1 m, respectively) of the NMCI and an after filter (47-mm Teflon filter, Model R2PL047, Pall) was also tested. All 4 stages of the TCI-R use rotating and silicon oil-coated aluminum foil substrates. Similar to the 30 L/min PM 0.1 NBIS, the PM 0.1 stage of the TCI-R was preceded by the PM 2.5 stage to examine the possible particle loading effect which may also occur in High-Volume UFP samplers described earlier. The quasi-UFP stages of these samplers are all preceded by an upper stage with 0.9 to 2.5 m as the cutoff size.

The particle loading tests were conducted using nano-TiO 2 particles (AERODISP P25, Degussa, Germany) which were dried in an oven at 105°C for 2 hours before use. Particles were dispersed using a small-scale powder disperser (SSPD, Model 3433, TSI) and then introduced to the NBIS and TCI-R for PM 0.1 MC measurement by weighing the particle masses on the after filters before and after each test. Based on experimental data of the SSPD-dispersed nano-TiO 2 particles, which showed UFP and TSP mass concentrations to be 92 and 3,427 g/cm 3 , respectively [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF], the UFP/TSP fraction is calculated to be 2.68%. As these particles were reported to have stable mass and number size distributions (Tsai et al., 2012;[START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF], the UFP/TSP fraction of 2.68% is assumed to remain constant in this study and is used for comparison with measurements from the NBIS and TCI-R in this loading test.

The M L of the PM 0.1 stage of the TCI-R was obtained by weighing the silicone oil-coated aluminum foil substrates before and after the tests. The M L of the NBIS-PM 0.1 stage was calculated using the formula ((TSP × PM 2.5 /TSP ratio) -PM 0.1 ) (unit: mg). Note that the TSP value was obtained from a 5 L/min filter cassette containing a 47-mm Teflon filter, which was collocated with the NBIS and TCI-R. The particle loading effect of the NBIS and TCI-R was checked by the relationship of the measured UFP MCs with different M L and compared with the reference UFP values.

Field test in ambient conditions

The field comparison tests were performed on the roof of the Institute of Environmental Engineering at National Yang Ming Chiao Tung University. The roof is situated 20 meters above the ground and is close to the Hsinchu Science Industrial Park and the main roads of Hsinchu City, where there is heavy traffic flow during the morning and evening rush hours.

The 30 L/min PM 0.1 NBIS, 10-stage rotating NMCI, and TCI-R were used in the test as shown in Fig. S3 (Section B) of the SI. In addition, the TCI-NR (i.e., the TCI with non-rotating silicon oil-coated aluminum foil substrate) instead of TCI-R was also tested for comparison purposes. Two comparison tests were conducted, test-1 was to compare the NBIS, NMCI, and TCI-R, while test-2 was to compare the NBIS, NMCI, and TCI-NR. Four and five 24-hr average UFP samples were collected for test-1 and test-2, respectively from December 2021 to March 2022, when daily average PM 2.5 concentration varied from 10 to 40 g/m 3 , temperature varied from 14 to 24 C, and relative humidity varied from 62 to 75%.

The M L on the PM 0.1 stage of the TCI-R or -NR was obtained by weight gain on the stage, while the M L on the PM 0.1 stage of the NBIS was calculated using the formula (PM 2.5 mass in the NMCI -PM 0.1 mass in NBIS). It is worth noting that the relative percent differences (RPD) of the PM 2.5 MCs measured by the NMCI, TCI-R, and -NR average 6.2% as shown in Table S1 (Section A), implying the accuracy of the comparison tests. The accuracy of the PM 0.1 measurement was evaluated based on comparing the PM 0.1 MCs measured by the tested devices with those of the NMCI as the reference.

UFP NC measurement

The UFP NC or size distribution monitoring system, shown in Fig. S4 (Section B

Particle loading test in the laboratory

The effect of loaded particle mass (M L ) of the 3 L/min NBI is examined by the relationship of the ratio of the UFP NCs of the NBI-CPC to those of the reference SMPS with various M L . Here the SMPS is used as the reference instrument where a TSI inlet impactor (nozzle diameter: 0.0457 cm) was first tested for the particle loading effect to determine the acceptable M L of 150 g before use. The inlet impactor was cleaned before the M L exceeded the acceptable value to maintain good classification performance.

The experimental setup of the particle loading test for the SMPS's TSI inlet impactor is shown in Fig S5 (Section B) of the SI. The SMPS equipped with a 0.0457 cm-nozzle inlet impactor (D pa50 : 410 nm) was operated at an aerosol flow of 0.6 L/min and a sheath flow of 3 L/min. The polydisperse NaCl particles were introduced into the SMPS to measure the particle number distribution, which was recorded over time. The particle loading effect of the SMPS inlet impactor was evaluated based on the variation of the particle number distribution with loaded particle mass (M L ) which was obtained by determining the mass difference of the impaction substrate by weighing before and after each loading test.

The experimental setup of the particle loading test of the NBI coupled with the CPC is shown in Fig. S6 (Section B) of the SI. Similar to the particle loading test of the SMPS inlet impactor, the generated NaCl particles were introduced simultaneously into the collocated NBI-CPC and SMPS to measure the UFP NC and number size distribution, respectively. The SMPS used in this test applies a 0.3 L/min CPC (Model 3776, TSI), in which the SMPS inlet impactor (nozzle size of 0.0457 cm) has a D pa50 of 615 nm. As the D pa50 is much larger than 100 nm, the UFP measurement in SMPS is not affected [START_REF] He | A multiple charging correction algorithm for scanning electrical mobility spectrometer data[END_REF]. The effective density used for the conversion of the electrical mobility diameter (D pe )-based SMPS data to the D pa -based values using the conversion equation Eq. S1 in Section C of the SI, is 1.7 g/cm 3 for NaCl particles. The M L was determined by integrating the mass distribution converted from the number distribution with the details provided in Section D of the SI. A traditional impactor (TI, i.e., the 3 L/min PM 0.1 NBI used a silicone oil-coated aluminum substrate instead of the water-wetted GFF) used as the inlet of the CPC was also tested for comparison.

Field comparison test

The field comparison test of the 3.0 L/min NBI-CPC versus the SMPS as the reference was carried out at the same location as that of 30 L/min PM 0.1 NBIS test, and lasted for five days (08-13 Jan 2023). Fig. S7 (Section B) of the SI shows the test setup which consists of a PM 10 inlet and a Very Sharp Cut Cyclone PM 2.5 inlet [START_REF] Le | The performance of the PM 2.5 VSCC and oil-wetted M-WINS in long-term field sampling studies[END_REF] followed by NBI-CPC and SMPS. After PM 2.5 inlet, the 16.7 L/min air flow was split into three streams: 3 L/min for the NBI-CPC, 0.3 L/min for the SMPS, and 13.4 L/min for the bypass flow. The UFP NCs were measured by the NBI-CPC and compared with the reference values (i.e. NCs of D pa smaller than 100 nm) determined from the particle number distribution (D pe of 14-700 nm) monitored by the SMPS. The effective density used for the size conversion is chosen to be 1.2 g/cm 3 , which is typical in an urban environment [START_REF] Liao | A mass correction method for the aerosol particle mass analyzer to measure the particle mass of sub-50 nm nanoparticles[END_REF].

Results and Discussion

UFP MC measurement

Particle collection efficiency test in the laboratory

Fig. 2 shows the particle collection efficiency curves of the 30 L/min PM 0.1 NBI and 9 th stage of the NMCI for different particle types. The PM 0.1 NBI has D pa50 of 107 nm and  of 1.60 for solid NaCl particles, and D pa50 of 108 nm and  of 1.62 for liquid DOS particles, demonstrating good cut-off performance with the cut-size close to the expected 100 nm [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF]. In comparison, the NMCI-PM 0.1 stage (9 th stage) also shows good classification performance for liquid DOS particles with a cut-size of 108 nm and  of 1.71, which agrees well with the test results for liquid particles in the previous studies [START_REF] Liu | Collection efficiency and interstage loss of nanoparticles in micro-orifice-based cascade impactors[END_REF][START_REF] Chien | Design and testing of the NCTU micro-orifice cascade impactor (the NMCI) for the measurement of nanoparticle size distributions[END_REF]. For solid NaCl particles, D pa50 and  of the NMCI-PM 0.1 stage are also 107 nm and 1.87, respectively, similar to those of the 30 L/min PM 0.1 NBI sampler, but the particle collection efficiencies become lower than those of liquid particles when particles are larger than the cut-size. The decrease in the collection efficiency becomes much more obvious as D pa is larger than 300 nm due to solid particle bounce in the NMCI-PM 0.1 stage with the rotating, silicone oil-coated aluminum foil substrate. In the NMCI-PM 0.1 stage with silicone-oil coated Fig. 2. Particle collection efficiency of the PM 0.1 stage of the NBIS and 9 th stage of the NMCI aluminum substrate, an oil-free spot is formed under each nozzle since the air jet velocity is as high as 144 m/s resulting in particle bounce similar to that observed in the previous study of our group (Tsai et al., 2012) in which a silicone-oil coated Teflon filter (10 m pore size) had to be used to resolve this issue and prevent particle bounce. The Teflon filter has a uniform micro-pore structure, which facilitates capturing and retaining liquid within its pores throughout surface [START_REF] Turner | Greased and oiled substrates as bounce-free impaction surfaces[END_REF]. Similar phenomena have been observed in other substrate materials having micro-porous structure, such as oil-soaked sintered metal disks [START_REF] Reischl | The collection efficiency of impaction surfaces: a new impaction surface. Staub -Reinhalt[END_REF]. Besides, continuous water injection at the center of the substrate helps maintain a steady supply of water to keep the GFF surface wet [START_REF] Le | Novel inertial impactor for nanoparticle classification without particle loading effect[END_REF]. Therefore, the air jet won't push water aside and leave a dry spot beneath each of the nozzles.

However, solid particle bounce does not occur easily in the 10-stage NMCI, in which the PM 0.1 stage is preceded by the 0.18-m stage (8 th stage). Only particles smaller than 180 nm are collected on the PM 0.1 stage thereby eliminating possible particle bounce effect. But if a traditional PM 0.1 impactor is preceded by a upstream stage with a cut-size larger than about 0.2~0.3 m, such as 0.5 m in nanosampler (KANOMAX, Japan) [START_REF] Furuuchi | Development and performance evaluation of air sampler with inertial filter for nanoparticle sampling[END_REF] or 0.9-2.5 m in the high-volume UFP impactors, it is very likely that particle bounce could occur on the PM 0.1 stage leading to overestimation of UFP MCs. This will be demonstrated in the following section where the test results of 4-stage TCIs, whose PM 0.1 stage is preceded by the PM 2.5 stage, are shown.

Particle loading test in the laboratory

Fig. 3 shows the PM 0.1 MCs measured by the NBIS and TCI-R at various nano-TiO 2 M L .

Since the source generating particles was stable during the test, the inlet PM 0.1 concentration can be assumed to be constant and is calculated to be 105.46 g/m 3 (based on the measured TSP concentration of 3.93 mg/m 3 PM 0.1 /TSP ratio of 2.68%). This inlet concentration value is used as the reference, represented as the solid line in Fig. 3, to evaluate the performance of the NBIS and TCI-R. Initially, the TCI-R measures PM 0.1 MC of 244 g/m 3 at an M L as low as 0.44 mg, which is much higher than the reference value of 105.46 g/m 3 . It indicates an over-measurement problem of the TCI-R with the rotating, silicon oil-coated impaction substrate. The initial over-measurement occurs due to the "initial bounce" for particles larger than 300 nm from the PM 0.1 stage, which is explained earlier in the previous section.

Subsequently, the measured PM 0.1 MC of the TCI-R increases slightly to 268 g/m 3 from 244 g/m 3 when the particle mass load is increased to 2.96 mg from 0.44 mg.

The acceptable M L limit of 3.0 mg was suggested by [START_REF] Marple | A microorifice uniform deposit impactor (MOUDI): description, calibration, and use[END_REF]. When the M L is increased from 3.0 to 18.38 mg, the measured PM 0.1 MC is increased to 394 g/m 3 , or 1.6 times the initial value. This indicates particle overloading effect induces more particle bounce in the TCI-R when the M L exceeds 3 mg. Therefore, the use of a preceding stage with D pa < 300 nm is needed for the PM 0.1 TCI-R to prevent initial solid particle bounce and its impaction substrate needs to be cleaned and re-oiled regularly to prevent the over-measurement.

In comparison, NBIS measures the PM 0.1 concentration of 128 g/m 3 at an M L of 0.46 mg, which is close to the reference value of 105.46 g/m 3 . The small difference in MCs is attributed to the experimental uncertainty of the low collected mass (<20 g). It indicates that the NBIS has no initial particle bounce since the water-wetted GFF impaction substrate retains water effectively in the pores to prevent solid particle bounce. When the M L is increased to 20.01 mg, the NBIS PM 0.1 MC still keeps at 94.74 g/m 3 . The average MC is 117±22 μg/m 3 for M L ranging from 0.46 to 20.01 mg, which is within 10% bias compared to reference value. Therefore, the 30 L/min PM 0.1 NBIS has no particle bounce and loading effects, and is capable of sampling PM 0.1 MC at high concentration environments with good accuracy.

Field comparison test

The performance of the NBIS and TCIs (rotating or non-rotating stages) in the ambient air with low particle MCs is also tested. since its PM 0.1 stage is preceded by the stage with 2.5 m cut-size, which is much larger than 300 nm. The average concentration difference is slightly higher at 0.78±0.34 g/m 3 for all sampling days since no severe particle bounce caused by particle overloading effect as the M L on PM 0.1 stage, <1.2 mg, is low.

In contrast, the TCI-NR measures the PM 0.1 MCs of 1.59 to 4.87 g/m 3 when the NMCI PM 0.1 MCs values vary from 0.44 to 2.18 g/m 3 . As shown clearly in Fig. 4, the over-measurement of the TCI-NR is serious with the concentration difference of 0.82 to 2.69 g/m 3 when the M L on the PM 0.1 stage is less than 1.2 mg. This is because the particle bounce in the traditional PM 0.1 impactor with the non-rotating substrate is more severe than that with the rotating substrate, which was found in our previous study (Tsai et al., 2012). In addition, over-measurement becomes more serious with the increase in ambient PM 0.1 concentration due to particle mounds formed underneath the nozzles resulting in a serious particle overloading effect.

The difference in the UFP MC measurement performance between TCI-R and TCI-NR can be explained by the difference in the particle deposited areas on the substrates, which can be calculated as the sum of projection areas of all nozzles (diameter of nozzle=55 m, number of the nozzle=2000) in the TCI-NR and the nozzle distribution area of 25 mm in the TCI-R [START_REF] Feng | A computational study of particle deposition patterns from a circular laminar jet[END_REF]. Without rotating the substrate, the TCI-NR has a particle deposited area of 4.60*10 -6 m 2 while the TCI-R with the rotating substrate has an area of 4.91*10 -4 m 2 , which is approximately 100 times that of the former. Therefore, M L per unit deposition area on the PM 0.1 stage of TCI-R is much smaller than the one of TCI-NR. However, this rotating feature does not exist in all high-volume UFP samplers and Kanomax nanosampler, in addition to the afore-mentioned problems associated with the cut-size much larger than 300 nm for the PM 0.1 preceding stage.

UFP NC measurement

Particle loading test in the laboratory Fig. 5 shows the particle number distribution measured by the SMPS with a 0.0457 cm-nozzle inlet impactor at various M L . Initially, the particle number distribution has the CMAD, GSD, and total NCs of 56 nm, 1.8, and 8.0E06 #/cm 3 , respectively. However, with the increase in M L to 150 and 680 μg, the total NCs are decreased to 7.310 6 and 7.010 6 #/cm 3 , respectively, which is 9 and 14% lower than the initial value. The decrease in particle NC is due to the particle loading effect owing to the particle mound formed on the impaction substrate [START_REF] Le | Novel non-bouncing PM 2.5 impactor modified from well impactor ninety-six[END_REF][START_REF] Who | Who global air quality guidelines: particulate matter (PM 2.5 and PM 10 ), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide: executive summary[END_REF]. Particles smaller than the cut-size are collected as the jet-to-plate distance was shortened. As shown in Fig. 5, the particle mound at the M L of 680 g is larger and higher than the one at the M L of 150 g, indicating particle loading effect becomes worse leading to lower NCs. The present test results for the TSI inlet impactor (data not shown) also confirm that the D pa50 is decreased from the initial value of 410 nm (flow rate:0.6 L/min) to 360 and 348 nm as the M L is increased from 0 to 150 and 480 g, respectively, leading to the NC under-measurement by the SMPS. Therefore, the SMPS inlet impactor with a nozzle size of 0.0457 cm needs to be cleaned regularly when the M L exceeds 150 μg to maintain a good performance with an acceptable bias of 10%. In comparison, the PM 0.1 NBI-CPC with the water-wetted GFF substrate shows good performance for PM 0.1 NC measurement as the ratios of PM 0.1 NC to the SMPS are 0.970.05, 0.990.05, and 0.970.06 with the M L in the range of 0-100, 100-200, and 200-300 μg, respectively. The initial ratio is close to 1 and remains constant despite the increase in the M L , which implies that the NBI-CPC can measure PM 0.1 NC accurately without a particle loading effect. This is due to the effective removal of particle deposits by water washing the GFF-covered substrate. In addition, the constant pressure drop during the particle loading process also supports the finding that there is no particle mound formed on the impaction substrate.

In this study, the 3 L/min PM 0.1 NBI is also used to replace the TSI inlet impactor of the SMPS as the PM 0.1 NBI-SMPS for the UFP size distribution measurement without particle loading effect. The results show that the UFP size distribution measured by the PM 0.1 NBI-SMPS remains stable with the increase in the M L up to 1.1 mg (see in the Fig. S8 (Section B) of the SI). The good cut-off characteristics of the NBI results in a size distribution with a nearly ideal cut-off for particles smaller than 100 nm and the effective removal of particle larger than 100 nm. These results demonstrate that 3.0 L/min PM 0.1 NBI can be a viable classifying device for long-term monitoring for the SMPS with a minimum maintenance need. In the future, the NBI with larger cut-sizes (such as PM 0.4 -PM 0.9 NBI with 0.4-0.9 m cut-sizes similar to those of the SMPS inlet impactors) can be designed to replace the original SMPS inlet impactor to obtain unbiased aerosol size distributions, which otherwise could be affected by particle bounce and loading effects. Note that even higher correlation of the two devices (slope = 0.99) can be achieved by changing the effective density from 1.2 to 1.3 g/cm 3 in the period of mid-noon (11:00 to 14:00) for converting SMPS D pe -data to D pa -data (Lin et al., 2018). It is reported that a higher effective density was found for particles with a high proportion of ammonium sulfate and ammonium nitrate salts formed during mid-noon owing to photochemical reactions [START_REF] Yin | Size-resolved effective density of urban aerosols in Shanghai[END_REF]. That is, the SMPS data can't be used to obtain the actual UFP NC directly due to some uncertainties in effective particle density. In contrast, the PM 0.1 NBI-CPC is a relatively convenient choice for obtaining UFP NC since the measurement is based on D pa .

Field comparison test in the ambient condition

Conclusion

This study designed and tested a 30 L/min PM 0.1 non-bouncing impactor (30 L/min PM 0.1 NBI) and a NBIS (PM 0.1 non-bouncing impactor sampler, the PM 0.1 stage with 3 preceding stages) for accurate UFP MC measurement without the issues of particle loading and bounce.

The NBI uses clean water to wet the GFF continuously, which prevents particle bounce and helps remove deposited particles and provides a clean impaction surface without particle loading effect since particle loaded mass M L on the substrate is essentially zero. In comparison, the impactor with a silicon oil-coated aluminum foil substrate has an obvious decreasing efficiency for particles larger than 300 nm due to particle bounce. The laboratory particle loading tests further show that the NBIS samples accurate UFP MCs with M L on the PM 0.1 stage up to 21 mg with the difference of ca. 10%, while the traditional cascade impactor TCI-R over-measures MC initially due to initial particle bounce for particles larger than 300 nm and the over-estimation increases very much when the M L exceeded 3 mg due to over-loading effect. In the ambient field tests, the UFP MCs of the NBIS differ by only 0.5 g/m 3 as compared to those of the rotating 10-stages NMCI (reference) while TCI-R also shows over-measurement by 0.8 g/m 3 in average due to the bounce for particles larger than 300 nm. Furthermore, the TCI-NR shows higher over-measurement which increases further with increasing ambient concentration.

For the UFP NC measurement, the previously developed 3 L/min NIC (or called as 3 L/min PM 0.1 NBI in this study) is combined with a CPC as NBI-CPC, and it shows stable and accurate performance with M L up to 300 µg, while the impactor with the non-rotating, silicone oil-coated substrate under-measures owing to over-collection for particles smaller than the cut-size when M L exceeds 200 µg. In ambient field tests, the 3 L/min PM 0.1 NBI-CPC measures NCs in good agreement with the SMPS reference values, with a linear regression slope of 0.98 and an R 2 of 0.95, respectively. This study concludes that traditional impactors with silicon oil-coated substrate can over-measure and under-measure the UFP MCs and NCs, respectively, due to particle bounce and loading effects, and the use of the NBI devices developed in this study can eliminate these effects to provide accurate UFP measurements.

In the future, the 30 L/min PM 0.1 NBI can be used to obtain enough UFP mass of over thousands of g/m 3 , or several 30 L/min PM 0.1 NBIs can be arranged in parallel to provide a higher flow rate and longer sampling days when UFP MC is low at several g/m 3 only. For long-term UFP NC measurement, the 3.0 L/min PM 0.1 NBI-CPC is a viable instrument with a minimum maintenance need. In the future, the NBI with smaller flow rate and larger cut-sizes (such as PM 0.4 -PM 0.9 NBI with 0.4-0.9 m cut-sizes similar to those of the SMPS inlet impactors) can be designed to replace the original SMPS inlet impactor to obtain the unbiased aerosol size distributions without particle bounce and loading effects for long-term monitoring applications.

Acknowledgement

The

Fig. 1 .

 1 Fig. 1. Schematic diagram of the (a) 30 L/min PM 0.1 NBI (b) 30 L/min PM 0.1 NBI sampler

  ) of the SI, uses the 3 L/min PM 0.1 NBI as the inlet of a commercial CPC (Model 3788, TSI) or a SMPS (Model 3936, TSI), respectively. The systems for UFP NCs or size distribution measurement are named NBI-CPC or NBI-SMPS. Because the flow rate of the PM 0.1 NBI is 3 L/min, 2.4/2.7 L/min has to be bypassed when the inlet flow rate of CPC/SMPS is 0.6/0.3 L/min.

Fig. 3 .

 3 Fig. 3. UFP MC by the NBIS and TCI-R versus M L .

  Fig. 4. Comparison of the UFP MC by the TCI and NBIS to the NMCI

Fig. 5

 5 Fig.5The particle distribution by the SMPS with the TSI inlet impactor (nozzle: 0.0457 cm)

Fig. 7

 7 Fig. 7 displays the correlation plot for PM 0.1 NCs measured by the 3 L/min PM 0.1

  support of the Taiwan National Science and Technology Council (contracts MOST 108-2221-E-009-076-MY3, MOST 110-2622-8-110-001, MOST 111-2622-8-110-004 and MOST 111-2221-E-A49-057-MY3), the Ministry of Education, and the Higher Education Sprout Project of National Yang Ming Chiao Tung University is gratefully acknowledged. Data curation, Carrying out the experiment, Figure preparation, Writing, Reviewing, Editing and Finalizing the manuscript. Nicolas Jidenko: Rewiewing and Conceptualization Yang-Rei Li: Data curation, Carrying out the experiments, Figure preparation Thi-Cuc Le: Data curation, Writing, Reviewing, Editing the manuscript Jean-Pascal Borra: Conceptualization, Methodology and Rewiewing Chuen-Jinn Tsai: Conceptualization, Reviewing and Editing the final manuscript Reference Abdillah, S. F., & Wang, Y. F. (2022). Ambient ultrafine particle (PM 0.1 ): sources, characteristics, measurements and exposure implications on human health. Environ. Res., 115061. Bateman, A.P., Belassein, H. & Martin, S.T. (2014). Impactor apparatus for the study of particle rebound: relative humidity and capillary forces. Aerosol Sci. Technol., 48(1), 42-52. Chang, C., Demokritou, P., Shafer, M., & Christiani, D. (2013). Physicochemical and toxicological characteristics of welding fume derived particles generated from real time welding processes. Environ. Sci.: Process. Impacts, 15(1), 214-224.


Guglielmo Fernandez

Iris De Gelis

Thomas Corpetti

Sébastien Lefèvre

Arnaud Le Bris

"LOW SUPERVISION" DEEP CLUSTER CHANGE DETECTION (CDCLUSTER) ON REMOTE SENSING RGB DATA: TOWARDS THE UNSUPERVISING CLUSTERING FRAMEWORK

Keywords: Change Detection, Semi-supervised Learning, Unsupervised Learning, Clustering, Multitemporal images, Deep learning

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The availability of advanced remote sensing (RS) imagery has paved the way for a new era of environmental studies [START_REF] Kwok | Ecology's remote-sensing revolution[END_REF] and Earth Observation (EO) studies. In addition to satellite images [START_REF] Yang | The role of satellite remote sensing in climate change studies[END_REF], researchers now have access to unmanned aerial vehicle (UAV) or aerial surveys [START_REF] Alvarez-Vanhard | Can uavs fill the gap between in situ surveys and satellites for habitat mapping?[END_REF], as well as historical archives [START_REF] Bris | Cnn semantic segmentation to retrieve past land cover out of historical orthoimages and dsm: first experiments[END_REF]. These resources offer valuable opportunities for investigating the dynamics of various areas, such as land resource planning, disaster monitoring, and urban expansion, by analyzing dense time series data. A critical aspect in these studies is Change Detection (CD) [START_REF] Khelifi | Deep learning for change detection in remote sensing images: Comprehensive review and meta-analysis[END_REF], which involves understanding the progression of events over time, specifically the analysis of bi-temporal images, to output change maps that identify, and eventually classify, change areas.

Historically, CD has been tackled as an unsupervised problem based on the analysis of differences between the two input images, as in the well-known CVA method [START_REF] Johnson | Change vector analysis: A technique for the multispectral monitoring of land cover and condition[END_REF][START_REF] Bovolo | A theoretical framework for unsupervised change detection based on change vector analysis in the polar domain[END_REF]. These methods, however, are often based on a pixel-wise comparison of images. As RS imagery embed high spatial correlation, such approaches may limit their capability to obtain further information on the nature of the change. More recently, deep learning, specifically Convolutional Neural Networks (CNNs), have captured researchers' interest in developing novel CD methods thanks to their capacity to capture spatial context. However, CD via CNNs remains challenging when This work has been supported by the ANR HIATUS (ANR-18-CE23-0025), financed by the French National Research Agency.

dealing with high-resolution remote sensing data. One of the primary difficulties is the limited availability of labelled data necessary for training. Historical aerial image archives exemplify this issue: although they provide rich time series data with high spatial resolutions (sub-meter) and diverse spectral channels (RGB, infrared, panchromatic, etc.), these parameters vary throughout the time series. Consequently, this heterogeneity results in a notable scarcity of labelled data, necessitating larger-than-usual resources for the labelling process.

To cope this difficulty, unsupervised deep learning approaches have been recently developed with remarkable results (for examples see [START_REF] Bergamasco | Unsupervised change detection using convolutional-autoencoder multi-resolution features[END_REF][START_REF] Sun | Structure consistency-based graph for unsupervised change detection with homogeneous and heterogeneous remote sensing images[END_REF][START_REF] Luppino | Code-aligned autoencoders for unsupervised change detection in multimodal remote sensing images[END_REF]). Nevertheless, depending on applications, these methods are often limited with respect to the diversity and complexity of data. Examples of open problems [START_REF] Jiang | A survey on deep learning-based change detection from high-resolution remote sensing images[END_REF] can be related to multisensor data, multiscale changes, classification or finally the inherent problem of defining what the change is (e.g. a change in the canopy of vegetation or the construction/destruction of a building).

Recent years have seen the development of datasets oriented towards CD, like LEVIR-CD [START_REF] Chen | A spatial-temporal attentionbased method and a new dataset for remote sensing image change detection[END_REF], HRSCD [START_REF] Daudt | Multitask learning for large-scale semantic change detection[END_REF] or SECOND [START_REF] Kunping | Asymmetric siamese networks for semantic change detection[END_REF], creating a common basis for benchmarking methods but also providing data availability that can be exploited for pre-training models. This also enabled the development of novel insights from semisupervised or supervised learning on the issue [START_REF] Daudt | Fully convolutional siamese networks for change detection[END_REF][START_REF] Daudt | Multitask learning for large-scale semantic change detection[END_REF][START_REF] Sun | Semisanet: A semi-supervised high-resolution remote sensing image change detection model using siamese networks with graph attention[END_REF].

Given all these elements, we propose in this paper the first steps for a novel approach for pixel-wise CD, called "low supervision" strategy, that can be a middle-ground between supervised and unsupervised learning. The approach exploits a few labelled training data to bootstrap unsupervised training with a more significant number of unlabelled training samples. To do so, we took inspiration from similar works in the field of visual feature clustering, primarily Deep-Cluster [START_REF] Caron | Deep clustering for unsupervised learning of visual features[END_REF][START_REF] Caron | Unsupervised learning of visual features by contrasting cluster assignments[END_REF], in which an unsupervised clustering method is used to generate pseudo-labels from features extracted via a CNN; these pseudo-labels are then used to optimize the whole network. The method presented, entitled CDCluster (see Figure 1), can be seen as an extension of the latter idea to CD: as in classic siamese networks [START_REF] Chicco | Siamese Neural Networks: An Overview[END_REF][START_REF] Chen | Dasnet: Dual attentive fully convolutional siamese networks for change detection in high-resolution satellite images[END_REF], two encoders generate features per date that are subtracted, followed by a decoder and convolutional layers; such features are then clustered and used as pseudo-labels.

MATERIALS AND METHODS

In this section, the overall pipeline of our CDCluster is given (Figure 1. Then, a detailed description of the training and validation strategy is provided.

Feature extractor

As mentioned, one of the main inspirations behind CDCluster is the capacity of siamese networks [START_REF] Chicco | Siamese Neural Networks: An Overview[END_REF][START_REF] Chen | Dasnet: Dual attentive fully convolutional siamese networks for change detection in high-resolution satellite images[END_REF] to extract a set of features adapted to CD. First, the RGB images are treated with a Sobel filter, and the input vector is formed among these four channels. The idea is to guide the network with realistic solutions. Secondly, the dimensionality of the input vectors (256x256x4) is reduced through two encoders, composed of three blocks, to arrive at two feature spaces of 64x64x64 that are subtracted. Each block consists of a convolution layer, followed by batch normalization, a second convolution layer and a max pooling. A decoder is used to upscale these features up to 256x256x16, the size at which the features are clustered. However, in the unsupervised/"low supervised" settings, there is no guarantee that the extracted features actually contain the right amount of information about the differences between the two inputs to be able to generate pseudo-labels. For this reason at each encoding block, after normalization, features are extracted from each channel and subtracted from each other. Three skip connections, with CBAM attention [START_REF] Woo | Cbam: Convolutional block attention module[END_REF], are used between the encoder's features differences and the decoder. On top of this architecture, two dense layers forming an MLP (Multi-Layer Perceptron), extract the change detection maps. The number of outputs, corresponding to the number of clusters (k), is treated as a hyperparameter (see the following section). During all training, categorical cross-entropy was used as loss and learning rate of 0.001.

Feature clustering and pseudo-label generator

The second core idea of CDCluster is to assign pseudo-labels via clustering the 256x256x16 extracted features. In this work, we focused on the k-Means implementation present in the FAISS package (that allows fast search on GPU devices). As suggested by Caron et al. [START_REF] Caron | Deep clustering for unsupervised learning of visual features[END_REF] and Mustapha et al. [START_REF] Mustapha | A deep dive into deep cluster[END_REF], it is not the specific choice of clustering algorithm that is crucial, but rather the number of clusters, k, and the "clustering halt", that is the frequency of epochs at which the centroids are calculated. Concerning the number of clusters, it has been shown on similar tasks that k needs to be larger than the number of desired classes to ensure the stability of the model. For this reason, we explored a set of k ranging from 2 up to 500 in preliminary studies. A final value of k = 20 has been set. Concerning the clustering halt, no influence has been found after a value of 5 epochs. In order to extract binary change maps from the 20 clusters, the per-pixel maximum value has been taken and binarized. Similarly than DeepCluster, CDCluster is also prone to trivial solutions. Therefore, while training, whenever the population of a cluster drops below a given threshold, the data points assigned to a random abovethreshold cluster are split and reassigned to the below-threshold one. At each epoch of clustering, only 75% of the dataset was used, chosen randomly, in order to limit GPU memory.

Dataset and training strategy

For this work, we decided to use a well-established dataset for CD, namely the LEVIR-CD dataset [START_REF] Chen | A spatial-temporal attentionbased method and a new dataset for remote sensing image change detection[END_REF], in order to be able to validate and test the results with standard evaluation metrics.

In an unsupervised setting, in order for CDCluster to be able to discriminate the change zones between the two images, it is necessary that the features generated by the convolutional filters in the first epochs of the training are consistent with regard to the CD issue. Preliminary tests in this setting did not lead to satisfactory results. A first possible solution, not explored here, might be to encode more efficiently the differences between the images, as suggested in [START_REF] De Gélis | Change detection needs change information: improving deep 3d point cloud change detection[END_REF]. Alternatively, it can be assumed that a small amount of ground truths exists and they can be used to bootstrap the initial signal. For this reason, we divided the training into two phases: a "warm-up phase" and an "unsupervised phase". The former consists in a supervised phase in which only 30% of the dataset is used for training. Since the quantity of True Negative data is not negligible in the dataset, a data sampling based on a minimum quantity (3%) of True Positive pixels has been used, except where noted. Subsequently, in the "unsupervised phase", the model is free to explore the whole LEVIR-CD dataset and the pseudo-labels generated from clustering are used. The term "low supervision" used in this paper, therefore, indicates the sum of the two phases, in which the initial signal given by the random values of the convolutional filters is augmented with the help of a small part of labelled data.

Metrics and validation strategy

Standard metrics such as Accuracy, F1-score, Mean Squared Error (MSE), Cohen's kappa (κ), Specificity and Confusion Matrix have been used to evaluate the results on the test set. Apart from this, we aimed also to explore and understand under which conditions CD-Cluster works. It has been pointed out that the quality of the random filters at the beginning of the training must play a fundamental role, and they can be used as a proxy for the final performances of the training [START_REF] Mustapha | A deep dive into deep cluster[END_REF]. In order to assess this factor for CD, we also used the Initial Alignment (IA) metric, introduced by Mustapha et al. [START_REF] Mustapha | A deep dive into deep cluster[END_REF], defined as:

IA(k, θ) = N M I adj. (L, P ) ( 1
)
where k is the number of clusters, θ is the random filters generated for a given seed at the beginning of the training, L is the set of ground truth labels, P is the set of pseudo-labels generated from the starting θ random filters and N M I adj. is the Adjusted Normalized Mutual Information.

RESULTS AND DISCUSSION

As a first evaluation, we explored the performances of CDCluster on the test set (Table 1). Remarkably, a high level of Accuracy and Specificity was found. As suggested by the F1-score and the κ, it is expected, however the presence of False Negative detections. The Confusion Matrix further confirms this. These results are in line with the state of the art of the literature [START_REF] Chen | A spatial-temporal attentionbased method and a new dataset for remote sensing image change detection[END_REF]. When looking at the graphical results of the detection (Figure 2), it is evident that an absence of constraints in the definition of the contours of the change maps undermines the overall quality of the detection. This is rational, considering that no element is currently provided in the backbone to suggest the definition of more accurate contours. An initial analysis found no correlation between building size and False Negatives.

As far as False Positive pixels are concerned, it should be noted that their evaluation is not trivial: the LEVIR-CD dataset is focused on the detection of buildings, and it cannot be excluded that these False Positives are other types of change (e.g. vegetation) not included in the ground truth.

Accuracy F1 MSE κ Specificity Confusion Matrix 0.98 0.75 0.02 0.74 0.99 0.99 0.30 0.01 0.70 Table 1. Metrics on the test set for CDCluster with k = 20 and 30% of data in the "warm-up" phase.

In order to consolidate this approach, however, it is also necessary to explore under which conditions these results are achievable. As mentioned, k and IA can play a pivotal role in this kind of approach and these hyperparameters depend on the specific model and the dataset. For assessing these factors, we calculated the IA for eight seeds for a range of k from 2 to 500 (Figure 3). First of all, it has to be noted that all values of IA are at least one order of magnitude lower than similar tasks [START_REF] Mustapha | A deep dive into deep cluster[END_REF], suggesting an explanation on the reason why the "low supervision" approach is necessary. Secondly, after approximately k = 10, the average IA is independent of k, supporting the choice of k = 20 to balance accuracy and computational costs. Finally, it should be noted that IA with different clusters, but the same seed, trace a consistent trend with only minor differences. While this suggests that, in our particular case, the choice of seed is not crucial, it also support the idea that, given a seed and a k, the value of IA with another k can be used as proxy for preliminary explorations.

These results raise the question of the amount of data needed in the "warm-up phase", as it is desirable for this phase to be as short as possible during the training but, above all, with as little data as possible. For this reason, we tested different amounts of data in the "warm-up phase", randomly sampled from the full LEVIR-CD dataset. As shown in Table 2, no relevant results can be found up to 20% of the train set, corresponding to 1424 couples of images. On the other hand, when applying a sampling only on data with at least 3% of True Positive pixels (as mentioned in Section 2.3), we were able to recover most of the accuracy with only 6% of the dataset, corresponding to 427 couple of images. Even if it requires further experiments, this result consolidates the idea that a "low supervision" approach, i.e., using a minimal amount of labelled data at the beginning of the training, can be explored as a viable idea to initialise unsupervised learning.

Metric

1% 2% 5% 10% 20% 6% (sampled) Accuracy 0.05 0.05 0.05 0.05 0.84 0.72 MAE 0.94 0.95 0.95 0.95 0.10 0.24 Table 2. Accuracy and MAE with the reduction of data in the "warm-up" phase.

CONCLUSIONS

In this work, we explored a novel pathway to perform CD in a setting that mixes supervised and unsupervised learning, which we called "low supervision": based on the presence of a modest portion of ground truth, an initial supervised ("warm-up") phase gives clues to the model as to what kind of changes are being sought, followed by an unsupervised phase. In doing so, we also presented an extension of DeepCluster to the CD, based on the idea of Siamese networks. From this point of view, one of the fundamental questions of this work can be reformulated as follows: under what conditions is it possible to exploit visual features from a neural network to create pseudo-labels by clustering? Of course, giving an unambiguous and definitive answer is beyond the scope of this preliminary work, but we can already state some elements. For example, it should be noted that CDCluster shows encouraging results for k = 20 and 30% of the dataset (with 3% white pixels), indicating that it is indeed possible to obtain valuable information from change features. The low values of IA corroborates the need of an initial bootstrapping. On the other hand, these results lead to the question of which are the ideal conditions for a backbone to effectively encoding change information, question that is shared also in other fields, as 3D Point Clouds CD [START_REF] De Gélis | Siamese kpconv: 3d multiple change detection from raw point clouds using deep learning[END_REF]. In this sense, this paper aims to take a first step towards a more systematic study of how to create architectures with higher IA. Beyond these considerations, this study shows another interesting possibility. The increase of public datasets for CD can become a good starting point for developing strategy for transfer learning to a specific dataset. Although in this work both training phases involved the same dataset, the prospect to be explored in the future is to perform the unsupervised phase on an unknown dataset (such as the HRSCD dataset). In this regard, it remains to be determined whether the current minimum amount of data to obtain results is sufficient and evaluate the generalization possibilities for features calculated on one dataset to be exported to another.

Fig. 1 .

 1 Fig. 1. Schematic representation of CDCluster model.

Fig. 2 .

 2 Fig. 2. Examples of predictions: couple of images A and B are shown, along with the predicted Change Map and the ground truth (used only for the calculation of metrics during testing). Several cases are reported as example: a True Positive change maps (a), False Positive (b) and False Negative (c).

Fig. 3 .

 3 Fig. 3. Initial Alignment (IA) dependency on the number of clusters (k) for different seeds. The blue line is the average of all seeds.