Katia Oliver-Quelennec

François Bouchet

Thibault Carron

Claire Pinçon

Thibault

Evaluating the Transposition of a Learning Analytics Dashboard Co-design Tangible Tool to a Digital Tool

Keywords: Learning analytics dashboard, co-design, participatory design, cards. 1

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INTRODUCTION

Faced with the massification of higher education, traditional teaching is not always suitable for training an increasingly larger and more heterogeneous student audience. One of the solutions to answer this development is the use of digital technology for (1) training and (2) personalization of training based on the collection of learning data and on their analysis (learning analytics). The dashboard, a classic decision-making aid tool, can support learning and is developing constantly in the field of Technology Enhanced Learning (TEL), mainly for teachers and students [START_REF] Belbin | Review of Research on Student-Facing Learning Analytics Dashboards and Educational Recommender Systems[END_REF]. The problem remains to be able to provide appropriate Learning Analytics Dashboard (LAD) to this heterogeneous public, meeting their needs.

In the field of human computer interface, but also more broadly, usercentered design is a design philosophy which aims at really satisfying users' self-expressed needs [START_REF] Sanders | From user-centered to participatory design approaches[END_REF]. Concerning the conception of LAD, several research studies have shown the importance of explaining clearly the pedagogical objectives [START_REF] Ifenthaler | The measurement of change: Learning-dependent progression of mental models[END_REF] and of choosing a relevant method [START_REF] Jivet | Awareness Is Not Enough: Pitfalls of Learning Analytics Dashboards in the Educational Practice[END_REF]. To build LADs, participatory design [START_REF] Ruiz | Participatory design method: Co-Creating user interfaces for an educational interactive system[END_REF] is a relevant method which has already been often used in the design of TEL tools. However, according to Prieto [START_REF] Prieto Alvarez | LA-DECK: A Card-Based Learning Analytics Co-Design Tool[END_REF] students are usually not involved in the participatory design of TEL, which could explain why some LADs are not always adapted to the learning target. Our first goal was thus to rely on such an existing co-design method for a higher education student context.

Moreover, co-design sessions usually involve an in-person session with participants sitting around a table, which is challenging when social distancing is mandatory, or simply when it is hard to schedule a moment for all stakeholders to be available in a given location. There are reasons to question whether an online version with remote participants would be as efficient, as virtual collaboration can act as a brake on the success of the collaboration by limiting exchanges through text and voice, without facial expressions or body language. [START_REF] Mcnair | Towards a Pedagogy of Relational Space and Trust: Analyzing Distributed Collaboration Using Discourse and Speech Act Analysis[END_REF] identified the importance for participants to establish a sense of trust, which can be challenging in an online context. Therefore, our second goal is to verify whether an online codesign approach of dashboard for and by students can lead to successful results by adapting an existing method to an online context.

Scheduling co-design sessions can be difficult, and even impossible in a global pandemic context. Moreover, even when in-person sessions can # -will be assigned by editors. EVALUATING THE TRANSPOSITION OF A LEARNING ANALYTICS DASHBOARD CO-DESIGN TANGIBLE TOOL TO A DIGITAL TOOL 3 happen, it is harder to collect traces of activity when tangible objects are manipulated. If it can complicate human collaboration, the use of online tools facilitates another important aspect in studying interactions which is tracing participants' activity. Although recording and annotating video and audio of participants' interactions is possible, a digital tool can considerably help in tracking some of these. In a co-design context, the traces that can be collected are made of (1) observational data of how the method is being used, which analysis can help in proposing evolutions to the method (e.g. reformulating instructions, adding human assistance in some critical steps), (2) intermediate data to be able to understand the conditions of effective collaboration (e.g. contributions from each participant and intermediate choices sometimes not retained by the group at the end), and (3) production results (the learning dashboards). We will present here the data collected and the results of several experiments showing that this approach might indeed be an efficient replacement for face-to-face sessions. We also explore the new possibilities that the traces offer in order to assess the quality of the interactions and outcomes.

Deriving from these observations, we can formulate two research questions that will guide us in this chapter:  (RQ1) Can the transposition of a tangible tool to design LAD using participatory design into a digital tool be evaluated at least as well as the original tool? Which can be split into 2 sub-questions:  (RQ1.1): Is the adaptation of a tangible co-design tool used in face-toface to a digital tool used online as effective?  (RQ1.2): Is a digital co-design tool perceived in the same way in face-toface and online?  (RQ2) How can the digital transposition of a tangible participatory design tool be used to provide better insight into its usage in order to improve the method?

The remainder of this chapter is organized as follows. In the next section, we start by presenting previous works on participatory design leading to the conception of LAD. Then in section 3 we provide a first answer to RQ1.1 by proposing the transposition of a tangible tool to a digital tool, by presenting the face-to-face method we used, called PADDLE (PArticipative Design of Dashboard for Learning in Education), the properties to transpose, and our proposal for a digital version, before describing the experiments carried out, the data collected, our results with a discussion the pros and cons of this digital transposition. Throughout this section, we also show how to enrich the digital transposition in order to answer to RQ2. In section 4, we present material and method of a second experiment using the same digital tool in face-to-face sessions to answer RQ1.2, our results with a discussion to try to understand differences in perception. Finally, we conclude by presenting the perspectives opened by this work.

PREVIOUS WORKS

Participatory design

Work by [START_REF] Schneider | Benefits of a Tangible Interface for Collaborative Learning and Interaction[END_REF] has shown that the use of tangible objects (such as cards) can facilitate collaboration and could explain the recurrent use of this format for co-design. However, other works focused on collaboration have also shown that the use of digital technology engages participants in productive processes and in a co-construction framework [START_REF] Jeong | Seven Affordances of Computer-Supported Collaborative Learning: How to Support Collaborative Learning? How Can Technologies Help? 20[END_REF]. It is therefore unclear a priori how a digital adaptation of an existing tangible co-design approach will be perceived. On the one hand, the tool can compel users to guide them and help them stay focused on their main task, but on the other hand, it can also limit creativity if it is too direct. Thus, there is a need to find the right balance in its design.

With participatory design, "the user becomes a critical component of the process" [START_REF] Sanders | From user-centered to participatory design approaches[END_REF], and they can be involved using the appropriate tools, such as card decks [START_REF] Roy | Card-based design tools: A review and analysis of 155 card decks for designers and designing[END_REF]. For learning analytics applications, some card decks-based approaches such as LA-DECK [START_REF] Prieto Alvarez | LA-DECK: A Card-Based Learning Analytics Co-Design Tool[END_REF] have led to successful outcomes in terms of design: "the cards succeeded in playing very similar roles to those documented in the literature on successful card-based design tools". But LA-DECK focuses more on establishing a dialogue between designers, data scientists and users than purely on letting users express their needs.

A literature review of 155 card-based design tools [START_REF] Roy | Card-based design tools: A review and analysis of 155 card decks for designers and designing[END_REF] shows that this format is widely used: their tangible form combines several ideas, with a limited amount of information, thus providing a good intermediary between structureless tools (post-it) and complete tools (instruction manual). However, this review also points out that only "some of the tools are [...] also available as apps or online." Moreover, the existence of a digital version does not guarantee that traces are recorded, as most methods are more interested in final production than in an analysis of the processes used to obtain them. Finally, when the information was explicitly provided by the authors, it appears that none of these tools was used with remote participants: participants were always in a face-to-face context around a table. These sessions are often accompanied by a facilitator who introduces the session, presents the cards, answers any questions and concludes the session [START_REF] Prieto Alvarez | LA-DECK: A Card-Based Learning Analytics Co-Design Tool[END_REF]. Some studies about co-# -will be assigned by editors. EVALUATING THE TRANSPOSITION OF A LEARNING ANALYTICS DASHBOARD CO-DESIGN TANGIBLE TOOL TO A DIGITAL TOOL 5 design [START_REF] Goldman | Technology-mediated teacher-researcher collaborations: Professional learning through codesign[END_REF] uses both online activities and face-to-face time, and recent studies have analyzed the transposition of tangible tools into digital tools in other contexts [START_REF] Jost | From Paper to Online: Digitizing Card Based Cocreation of Games for Privacy Education[END_REF].

Learning Analytics Dashboard

Although the research field around learning analytics dashboards (LAD) is quite young [START_REF] Schwendimann | Perceiving Learning at a Glance: A Systematic Literature Review of Learning Dashboard Research[END_REF], several reviews of the literature on the LADs have already been written [START_REF] Verbert | Learning dashboards: An overview and future research opportunities[END_REF]. LADs allow the learners to be aware of their progress, to create meaning and to take decisions that will impact their learning. But [START_REF] Jivet | Awareness Is Not Enough: Pitfalls of Learning Analytics Dashboards in the Educational Practice[END_REF] explains that LADs are not always developed in line with clear educational objectives, and that making people aware of their journey is not enough to improve learning. In addition, LADs can also cause negative effects [START_REF] Tan | Learner Dashboards a Double-Edged Sword? Students' Sense-Making of a Collaborative Critical Reading and Learning Analytics Environment for Fostering 21st Century Literacies[END_REF][START_REF] Teasley | Student Facing Dashboards: One Size Fits All? Technology[END_REF] in particular when they provide comparisons with peers for certain student profiles. It is therefore necessary to create LADs adapted to the learning contexts and according to the students' needs. Some works show students' expectations for personalization and the importance of having an adaptable LAD [START_REF] Roberts | Give Me a Customizable Dashboard: Personalized Learning Analytics Dashboards in Higher Education[END_REF][START_REF] Teasley | Student Facing Dashboards: One Size Fits All? Technology[END_REF]. There are also early works on the design of adaptive LADs, such as those of [START_REF] Burkhardt | An approach to assess the quality of collaboration in technology-mediated design situations[END_REF] on the design and the dynamic generation of contextual LADs for teachers. All these studies highlight the interest of adaptive LADs, but such LADs have not been developed for the learners themselves.

As seen before and in the previous works [START_REF] Lucero | Designing with Cards[END_REF][START_REF] Roy | Card-based design tools: A review and analysis of 155 card decks for designers and designing[END_REF][START_REF] Ruiz | Participatory design method: Co-Creating user interfaces for an educational interactive system[END_REF], this approach is generally implemented using cards. The participatory design kit developed by Dabbebi et al. ( 2019) offers a complete method for designing LADs, the first uses of which were carried out with secondary school teachers. Therefore, it appeared to be the closest to our goals, and we chose to adapt this method to students in the context of higher education.

RQ1.1 -TRANSPOSITION OF A TANGIBLE TOOL TO A DIGITAL TOOL

Material

THE PADDLE METHOD

To design Learning Analytics Dashboards (LAD), Dabbebi et al. ( 2019) developed a participatory-based design tool using card decks which was positively rated by its users. Our adaptation of this method to the context of higher education and focused on co-design by students is called PADDLE. We used an iterative approach to test and propose adaptations of the design kit for our student target. First of all, we practiced with the existing tool by working with its intended audience (teachers) over two sessions, but in a higher education context. This appropriation time validated (1) the relevance of the method in a university context, (2) its suitability to easily collect users' needs, and (3) the positive rating it received from participants. We were thus able to define a first variant of the initial method. This variant for a higher education context required changes in vocabulary, length of time for the student target and the addition of questions for participants. Vocabulary related to secondary education such as "pupil, class, school, department, academy" has been changed to "student, promotion, institution, regional, national". A second set of changes was necessary to adapt the tool to different stakeholders, i.e., students. In order to more easily fit in time slots usually available to them between two classes, we reduced the duration of a session from 150 minutes to 90 minutes, which led to adopting a questionbased approach to better guide them and thus save time. For example, the card entitled "Monitoring" initially described by a definition, has been replaced by "How do you keep track of your work? What do you need to track your work?". The participants take turns answering the questions and thus identify their possible needs. Naturally, these adaptations do not prevent from using PADDLE with the initial targets (teachers) as well. Drawing of the LAD to show how all the visualizations can be associated together in an integrated dashboard PADDLE allows to co-design LADs in small groups of two to four people. The sessions last from 90 minutes (for students) to 120 minutes (for teachers) and consist of five phases presented in table 1. The session is supervised by a facilitator who supports debates and helps participants in formalizing their ideas. Nonetheless, the facilitator intervenes only on request or when he/she detects a group is struggling, in order to give participants autonomy. In particular they refrain from giving examples of indicators in a learning context or to express judgment on participants' proposals, in order not to inhibit nor direct the students' discussions. To facilitate transport, pooling and animation, the board has been transformed into convenient cards: PADDLE comes in the form of laminated cards to be able to reuse them and magnetic cards to manipulate them on a whiteboard (cf. Figure 1). Participants must set a goal and then complete a board to describe their context before identifying the relevant data and their graphic representations. Finally, they assemble these elements to design their LAD.

Traces of the sessions are collected using audio recordings of the groups, photos of intermediate stage results, photos of the LAD produced and a paper-based or online evaluation questionnaire.

Transposition of relevant properties of PADDLE

We identified 8 properties in the PADDLE method (cf. table 2) and considered their possible digital transpositions to improve trace collection. These 8 properties were chosen to be generic enough to assume that they would also be relevant for any other adaptation of a card-based co-design method into an online remote version, as none are intrinsically related to mechanics exclusive to PADDLE. We believe however that the way we chose to translate them are not unique, and it is possible that for other methods, other translations would be more relevant than the ones chosen here.

More precisely, here are the justifications of our choices; we tried not to lose their primary functionality. The first three properties are only associated to one of the five phases:  Initial explanations (phase 1): the use of a video makes it easier to collect traces (time spent listening to the video, number of views), but the absence of a human to initiate the activity could be detrimental to the motivation of the group. So, we chose to keep a human briefing.  Graphic production (phase 5): using digital tools can have potentially more readable results than a handwritten production. In the case of online software use, the link to the productions is saved.  Evaluation of the method and the results obtained (phase 5): the evaluation method initially developed by questionnaire is adapted to the digital format to facilitate the analysis.

The five following properties are more global and associate to the method overall:  Collaboration between participants: one option considered consisted in adding RFID chips to identify manipulated cards, to keep the tangible aspect of PADDLE, but it limits the possibility of remote sessions. So, we preferred to force each member of a group to give their opinion by proposing individual fields for some questions. This approach requires all members of the group to participate, reinforcing the commitment in the production process and allowing to collect each participants' traces.  Scripting collaboration: scripting the digital device reproduces the order of the cards originally proposed and blocks the possibility of inadvertently mixing the cards. The digital format allows collecting information on the time spent on each card, thus allowing to identify for instance the most discussed cards.  Answers to participants' questions: a chatbot could be considered in order to deal with simple questions, to more easily trace recurring problems as well as guarantee that the provided responses are standardized. However,

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9 chatbots can tend to distract participants (who can spend time gaming the system instead of accomplishing the task at hand [START_REF] Bouchet | Characterization of Conversational Activities in a Corpus of Assistance Requests[END_REF]), lead to distrust in the whole approach if the answers are not appropriate, or may over-guide participants in the method. For these reasons, we chose for now to force participants to call the facilitator, even if it may slow down the process.  Regulation of the session: time regulation is possible to force the transition from one phase to another but may limit rich exchanges, and it is recommended that participants be involved in the regulation of their collaborative activities [START_REF] Mcnair | Towards a Pedagogy of Relational Space and Trust: Analyzing Distributed Collaboration Using Discourse and Speech Act Analysis[END_REF]. The digital format allows to trace the time spent in each phase.

Visibility of previous decisions: posting a summary of each phase allows the group to check their choices and change their minds. Access to this screen can be traced to estimate the coordination of decisions with past choices.

3.1.3

The ePADDLE method

We proposed to transform the PADDLE method and cards deck into the application ePADDLE (cf. Figure 2); a digital format of PADDLE improving traces collection. Based on the 8 properties presented in the previous section, table 2 list each digital transposition we chose to collect. To elaborate the digital transposition of PADDLE, at first, we looked for an adapted tool which can quickly prototype and collect traces. We chose an open-source tool called Scenari Topaze 1 which can generate conditioned path Chapter # -will be assigned by editors in a simple format (web html pages and javascript). Then we developed ePADDLE with several iterative phases with several types of users to test and evaluate it before using it with student groups. All this work has been done remotely during the first French lockdown in response to the Covid-19 pandemic.

The ePADDLE application keeps PADDLE's key elements: (1) its original 5 phases (presentation, decision choice, context, data and visualization choice and LAD design), (2) the number of participants (2 to 4 in each group), (3) the facilitator whose role is mostly to introduce the goals of the workshop at first, and then to answer to both technical questions and methodological questions. Among the new elements we had to adapt or introduce to organize a remote online session, we can mention: (1) the fact that groups are asked to work together with a web conferencing tool where they can chat, talk by voice and share their screens, (2) two additional specific roles to take into account that it is harder for the session facilitator to keep track of the progression of each group compared with a session where all groups are in the same room: the scribe (whose role is to connect to the ePADDLE app, share their screen and take note of answers from the group), and the time keeper (whose role is to ensure some groups do not spend too much time on some phases), (3) the fact that activities are tracked using the LMS Moodle, commonly used in higher education, as the ePADDLE module is open source and can be embedded into Moodle2 .

Additional data collected with ePADDLE to evaluation collaboration

To answer RQ2, to provide better insight into ePADDLE usage in order to improve the method, it is important to consider several dimensions as:  the different types of roles adopted and the preferences of each [START_REF] Belbin | Review of Research on Student-Facing Learning Analytics Dashboards and Educational Recommender Systems[END_REF]) (e. g. coordinator, completer-finisher or teamworker),  oral collaboration management [START_REF] Burkhardt | An approach to assess the quality of collaboration in technology-mediated design situations[END_REF] [START_REF] Holton | Building trust and collaboration in a virtual team[END_REF]) through the analysis of potential pre-existing interpersonal links between the participants,  the quality of the collaboration as perceived by the participants in the task themselves,  the quality of the product of the collaboration as assessed by the group and by others.

We tried to list how to trace additional data we need to evaluate collaboration in table 3.

Acts of dialogue

Audio or screen record to allow manual coding in speech acts. We considered offering participants a simple interface with a few smileys to indicate their intentions when they spoke. We did not choose this solution for fear of distracting the participants from the main objective of the co-design session.

Trust level

New questions inside the original questionnaire to rate how well they knew the other participants in their groups Perception of the quality of the collaboration Original questionnaire from PADDLE Perception of the quality of the collective production Original questionnaire from PADDLE and a poll to the participants allowing them to vote for the best LAD. We have reproduced each LAD designed by students results with a common look (same colors, same pictograms) and asked all students to divide 10 points between their favorite LADs

3.2

Method & data collected

Conditions and methodology of the experiment with PADDLE

We carried out with volunteer students three recorded PADDLE sessions followed by a qualitative analysis: (1) two of them with two pairs of 1 st year language students enrolled in a training formation dedicated to mastering the university environment, and (2) one with three 5 th year pharmacy students in the context of a course using a serious game based on professional simulation. For each session, we recorded the interactions between students, we listed the cards selected, the data they chose to display on their LAD, the final display of the LAD they defined and we asked participants to complete the original evaluation questionnaire [START_REF] Burkhardt | An approach to assess the quality of collaboration in technology-mediated design situations[END_REF]. This evaluation consists in 7 statements to rate using 5-point Likert scale to evaluate their satisfaction both with the process and its outcome (the dashboard they designed). This data collection was led after declaring it to the university data protection officer (DPO).

Conditions and methodology of the experiment with ePADDLE

To validate the claim that ePADDLE supports LAD co-design, 8 sessions using ePADDLE were organized, involving overall n=177 students, composed of first year university students in multimedia design (n=58) and second year university students in pharmacy (n=119), randomly assigned to 52 groups of 2 to 4 students. The experiment was carried out in 2020 in two different universities. With students in multimedia design, we organized four sessions of fifteen students with their teacher. The students were from 18 to 21 years old and familiar with computer use. In the groups, there was a distribution between male and female of 40/58. With students in pharmacy, the experiment was carried with four sessions of approximately thirty students with a PhD student. The students were predominantly female and in an initial study program without specific computer use for their studies.

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Each student accessed the virtual environment through his/her workstation. All students used the environment for approximately one hour and half. They were explicitly allowed to communicate through the tool provided with the system and were warned that they would be observed concerning the use of the system. During two first sessions with students in multimedia design, there was one facilitator for each group, whereas all other sessions involved only one facilitator who was virtually moving from one group to another to check progress or when being called by a group through a personal message. For all the sessions with pharmacy students, there was one facilitator for eight groups.

The audio interactions of each group were recorded. Each participant was asked to fill the same post-session questionnaire used with PADDLE.

Method

For each property of the PADDLE method, data are described as median [interquartile range] since their distribution is asymmetric. Means were compared with Mann-Whitney-Wilcoxon tests or Student's t-tests as appropriate, depending on the normality of the variable as tested by a Shapiro-Wilk test. No adjustment was done for multiple comparisons. The two-sided type I error rate was set at alpha=0.05.

RESULTS OF THE EXPERIMENTS

Each PADDLE property implementation has either been retained as they originally were or transposed through an implementation that allows for better tracing. The ePADDLE sessions made it possible to successfully design 52 LADs (one per group -cf. Figure 3), as no group failed to propose a dashboard at the end of the session. Moreover, it allowed to easily collect the data captured during the session, in addition to the traces usually collected with PADDLE. The follow-up of the questions was successfully managed with only one facilitator per session. The regulation can be considered adapted because the duration of the workshops remained mostly in the expected time (from 81 to 147 min, M -108 min, SD -18 min). Finally, the visibility of previous decisions and graphic production can be validated by the productions made, which are in line with the choices of the participants. By reusing the original evaluation questionnaire [START_REF] Burkhardt | An approach to assess the quality of collaboration in technology-mediated design situations[END_REF], according to users' evaluation (see table 4), ePADDLE was rated a bit lower than PADDLE used in in-person sessions, significantly so regarding help to specify needs and creativity. Then, we worked on the comparison of the results obtained with pharmacy students and multimedia design students, results are presented in table 5. There are significant differences in the perception of the group dynamics and the relevance of the solution:  group dynamic: mean difference of 0.4 point CI95% [0.12;0.68], p=0.005  relevance of the solution: mean difference of 0.3 points CI95% [0.02;0.59], p=0.04

Discussion

Our transposition of the tangible co-design tool into a digital version has achieved its primary objectives: to allow remote co-design sessions, to define LADs and to collect useful traces for our research work. The evaluation of this new tool by the users shows some limits. On the creativity aspect, the tool could not compete with a real paper whiteboard. On the aspect of needs definition, it is possible that the scripting of the digital version guides the participants too much and limits their expression of needs compared to the tangible version. There was one facilitator per group for the PADDLE sessions compared to one facilitator for several groups for the majority of ePADDLE sessions. It may have an important role in developing the expression of needs.

When we look deeper evaluation of users with different profiles: multimedia design and pharmacy. Indeed, the study contexts of the cohorts are very different and can bring an important bias. Due to the nature of their studies, multimedia design students are probably more comfortable with digital tools, and they are probably used to collaboration. Second year of pharmacy students come out of a competition from a very individual first year during which there are no group activities. These differences could explain the differences in perception, the pharmacy students felt that the tool helped them to have a good group dynamic and were more satisfied with their result.

Naturally, these results will have to be confirmed with larger samples but also with other contexts.

RQ1.2: DIGITAL TOOL USED IN FACE-TO-FACE

The digital transposition of our tool seems to be less adapted when used online, we can ask ourselves how this digital transposition is perceived in face-to-face. The digital version would retain its trace collection capabilities and could be as effective as the tangible version.

Material and method

In addition to the experiment presented in part 3, we kept the same approach and we organized 3 sessions using ePADDLE in face-to-face, involving n=78 second year pharmacy students, randomly assigned to 23 groups of 2 to 4 students.

We collected the same data as those collected in the online experiment:  data to evaluate the tool: each participant was asked to fill the same postsession questionnaire used previously  data for our future work: the audio interactions of each group were recorded and the Belbin team roles questionnaire.

For each property of the PADDLE method, data are described as median [interquartile range] since their distribution is asymmetric. Means were compared with Student's t-tests. No adjustment was done for multiple comparisons. The two-sided type I error rate was set at alpha=0.05.

Results

During the ePADDLE sessions in face-to-face, students designed 23 LADs of which 20 groups used paper and pencil for phase 5 drawing. During the online sessions, they produced 34 LADs of which 7 designed with paper and pencil. Students made similar choices of tools, although the face-to-face session made it easier to use pencil and paper for collaboration.

The comparison of the perception of ePADDLE properties between online and face-to-face sessions of the same cohort are presented in table 6. Significant differences were found for some properties, for which remote users are more satisfied:  Group dynamics: mean difference of 0.5 points CI95% [0.2;0.7], p=0.0003  Convergence towards a solution: mean difference of 0.5 point CI95% [0.2;0.7], p=0.0003  Easy-to-handle card: mean difference of 0.5 point IC95% [0.2;0.8], p=0.001  Requirements specification: mean difference of 0.4 point CI95% [0.01;0.6], p=0.02  Relevant solution: mean difference of 0.5 point CI95% [0.2;0.7],

p=0.0008

Discussion

Against all expectations, ePADDLE receives better evaluations for the online sessions. We would have thought that the face-to-face sessions would be better perceived by the participants (especially on the creativity part) or at least evaluated in an equivalent way. We can imagine several reasons for this result. Management by a face-to-face scribe may be less conducive to collaboration because he or she is the only one who interacts with the tool. Indeed, the screens used during the face-to-face sessions were small (tablet or student computer) and may not have allowed all participants to see the scribe's screen well. The arrangement of the tables may be an additional barrier to collaborating with a single screen. Offering the broadcast on a larger screen might have had a different result or using adapted furniture as learning labs can offer. We can therefore ask ourselves if the collection of traces during a face-to-face co-design session with a digital tool remains as interesting if we lose the quality of the tool. For face-to-face sessions, digital tables would be an interesting way to study, as they can combine the advantages of the different methods, such as making all the participant actors, while collecting digital traces easily.

CONCLUSION AND PERSPECTIVES

Our results with students are encouraging and show the possibility of developing online co-design sessions to achieve our main goal consisting in co-designing LADs. Indeed, if the main advantage of this digital transposition is to obtain pre-formatted data that allows a rapid processing of these, we can see other benefits, such as allowing remote use. Moreover, this transposition has led to enrichment to the initial method, such as the definition of multiple roles originally all under the responsibility of the session facilitator.

However, there are still limits with this transposition which leave room for potential future improvements. One particular limit is the lack of traces during the final dashboard design phase. Adding an embedded graphic production tool would not only facilitate this activity for participants and standardize the dashboard produced by different groups, but also help in collecting traces still poor for this phase (only the final dashboard is collected but not the design process of this dashboard). Another limit is revealed by the second experiment, namely the fact that the digital transposition seems only partially adapted for face-to-face sessions. Potential improvements could involve testing digital co-design tools in adapted spaces such as the Learning Lab where collaboration using digital tool is more optimal. Another limit relies on the validity of the properties in another context: although we made an effort to identify property that appear to be generic, only transpositions of the same properties in other contexts would confirm it. This initial work should be further developed by testing ePADDLE in other contexts (using different target groups, considering the impact of how participants are recruited) and by comparing with adaptations of other co-design methods. These additional studies will help to determine rules to follow for such transpositions to be successful.

Through this study, and in particular with the additional traces, we open perspectives such as improving the quality of group dynamics, an important point to enable remote collaborative work and fully validate this tool. We also have been able to focus on using post-session questionnaires to understand group dynamics and identify potential favourable conditions for successful collaboration through (1) an analysis of speech acts based on [START_REF] Mcnair | Towards a Pedagogy of Relational Space and Trust: Analyzing Distributed Collaboration Using Discourse and Speech Act Analysis[END_REF], and (2) finding links with Belbin's collaboration profile [START_REF] Oliver-Quelennec | Understanding online collaboration through speech acts associated to Belbin profiles[END_REF]. Such analyses could help in enhancing initial group formation or during a session to identify clues indicating a less productive collaboration. In parallel, we contribute to a collaborative work to develop a new version called PaDLAD V23 . Future work will focus on defining adaptative LADs for students by identifying indicators and visualizations expected by students depending on their objectives and learning contexts

Figure 1 .

 1 Figure 1. PADDLE cards presented in table 1

Figure 2 .

 2 Figure 2. From PADDLE with tangible cards to ePADDLE for remote online codesign sessions.

Figure 3 .

 3 Figure 3. Examples of LAD designed with PADDLE and ePADDLE

Table 1 .

 1 PADDLE phases

	Phase	Description	Cards
	Phase 1	Introduction of the session with icebreaker
		activity
	Phase 2	Choice of the LAD goal between	6 objectives cards
		monitoring, planning, communication,
		evaluation, evolution and remediation
	Phase 3	Definition of the context by answering the	7 questions cards
		questions: who, where, what, how, for
		when, when
	Phase 4	Definition of the data to track, the Data (open cards) and

Table 2 .

 2 Translating the different properties of PADDLE into ePADDLE

	Properties	PADDLE	ePADDLE	Additional
				traces
	Initial	Slideshow	Slideshow presented by the	-
	explanations	presented by the	facilitator
		facilitator
	Collaboration between participants	Card selection and card annotations by participants	Participating with scribe role and fields to be filled either individually or collectively	Individual and group responses from participants
	Scripting collaboration	Ordered cards and regular interventions by	Online interface for scripted collaboration	Time spent by phase
		the facilitator
	Answers to questions	Session facilitator role	Group facilitator or facilitator for the session	Trace questions in the chat
	the session Time regulation of role Session facilitator	the session facilitator master role and follow-up of Participating with time	-
	Visibility of previous	Magnetic cards on the whiteboard	Summary of the choices made between each phase	Summary previous choices of

Table 3 .

 3 Additional trace data to evaluate collaboration

	Dimension	Solutions adopted in ePADDLE
	Collaborative	Belbin profile test for collaboration evaluation
	roles

Table 4 .

 4 Translating the different properties of PADDLE into ePADDLE

	Properties	Statements to rate using 5-	PADDLE	ePADDLE	p*
		point Likert scale	(n=8)	(n=177)
	Collaboration	The tool helped you to have a	M=5 [4;5]	M=5 [4;5]	0.60
		good group dynamic.
		The tool helped you to converge	M=4 [4;5]	M=4 [4;5]	0.95
		towards a solution.
	Scripting	The tool is easy to handle.	M=5 [4.5;5] M=4 [4;5]	0.11
		Cards are easily understandable. M=4.5	M=4 [3;4]	0.08
			[3.5;5]
		The tool has enabled you to	M=5 [4;5]	M=4 [3;4]	0.005
		better specify your needs.
		The tool has enabled you to find	M=5 [4.5;5] M=4 [3;4]	0.002
		original solutions.
		And this solution seems	M=5 [4;5]	M=4 [4;5]	0.10
		relevant to you.

* The degree of significance of the Mann-Whitney test after Bonferroni correction

Table 5 .

 5 Evaluation of ePADDLE properties used in remote sessions by pharmacy students and multimedia design students

	Properties	Statements to rate using 5-	MMI (n=58)	Pharma 2A	p
		point Likert scale		(n=119)
	Collaboration	The tool helped you to have a	M=4 [4;5]	M=5 [4;5]	0.005
		good group dynamic.
		The tool helped you to converge	M=4 [4;5]	M=4 [4;5]	0.27
		towards a solution.
	Scripting	The tool is easy to handle.	M=4 [4;5]	M=4 [4;5]	0.69

Table 6 .

 6 Evaluation of ePADDLE properties by second year pharmacy students in face-to-face sessions and online sessions

	Properties	Statements to rate using 5-point	Face-to-	Online	p
		Likert scale	face (n=78)	(n=119)
	Collaboration	The tool helped you to have a	M=4 [4;5]	M=5 [4;5] 0.0003
		good group dynamic.
		The tool helped you to converge	M=4 [3;5]	M=4 [4;5] 0.0003
		towards a solution.
	Scripting	The tool is easy to handle.	M=4 [3;5]	M=4 [4;5] 0.001
		Cards are easily understandable.	M=3 [3;4]	M=4 [3;4] 0.09
		The tool has enabled you to better	M=3 [3;4]	M=4 [3;4] 0.02
		specify your needs.
		The tool has enabled you to find	M=4 [3;4]	M=4 [3;4] 0.26
		original solutions.
		And this solution seems relevant	M=4 [3;4]	M=4 [4;5] 0.00008
		to you.

https://download.scenari.software/Topaze/

https://padlad.github.io/productions

https://padlad.github.io/productions

ACKNOWLEDGEMENTS

This work is included in the P3 project, developed by Université de Lille and co-financed by the iSite Université Lille Nord-Europe.


V Giardini

Philippe Lekić

C Lognonné

É Beghein

S Beucler

C Carrasco

Charalambous

D Kim

W B Banerdt

S Ceylan

D Giardini

V Lekic

P Lognonné

C Beghein

É Beucler

S Carrasco

C Charalambous

J Clinton

M Drilleau

C Durán

M Golombek

R Joshi

A Khan

B Knapmeyer-Endrun

J Li

R Maguire

W T Pike

H Samuel

M Schimmel

N Schmerr

S C Stähler

E Stutzmann

M Wieczorek

Z Xu

A Batov

E Bozdag

N Dahmen

P Davis

T Gudkova

A Horleston

Q Huang

T Kawamura

S King

S M Mclennan

F Nimmo

M Plasman

A C Plesa

I E Stepanova

E Weidner

G Zenhäusern

I J Daubar

B Fernando

R Garcia

L V Posiolova

M P Panning

Surface Waves and Crustal Structure on Mars

  L'archive ouverte pluridisciplinaire

The InSight mission to Mars [START_REF] Banerdt | Initial results from the InSight mission on Mars[END_REF] has provided direct constraints on the layering of Mars' crust at the landing site [START_REF] Lognonné | Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data[END_REF]. Analyses of body wave conversions and ambient noise wavefield have constrained the crustal thickness beneath the InSight lander in Elysium Planitia to be 39±8 km [START_REF] Knapmeyer-Endrun | Thickness and structure of the martian crust from InSight seismic data[END_REF][START_REF] Durán | Seismology on Mars: An analysis of direct, reflected, and converted seismic body waves with implications for interior structure[END_REF][START_REF] Kim | Improving constraints on planetary interiors with PPs receiver functions[END_REF], providing a key anchoring-point for global models of crustal thickness and density variations. Looking deeper, travel times of body waves from several marsquakes have enabled the determination of seismic velocity profiles of the upper mantle [START_REF] Khan | Upper mantle structure of Mars from InSight seismic data[END_REF] and core radius [START_REF] Durán | Seismology on Mars: An analysis of direct, reflected, and converted seismic body waves with implications for interior structure[END_REF][START_REF] Stähler | Seismic detection of the martian core[END_REF] and mean density [START_REF] Khan | Geophysical and cosmochemical evidence for a volatile-rich Mars[END_REF]. Despite these achievements, competing effects of epicentral distance, source depth, and radial structure on body wave travel times (13), have stymied efforts to constrain lateral variations in structure using a single seismometer on Mars.

The velocity of surface waves, unlike that of body waves, depends on frequency, with lower-frequency waves sensitive to greater depths. The measurement of surface wave dispersion therefore provides a direct observation of the depth-dependent variation of seismic velocities averaged along the path from source to receiver [START_REF] Toksöz | Phase velocities of long-period surface waves and structure of the upper mantle: 1. Great-Circle Love and Rayleigh wave data[END_REF]. Until now surface waves had not been observed on any marsquake records. Their absence could be due to the relatively small magnitude of the recorded seismic events [START_REF] Böse | Magnitude scales for Marsquakes calibrated from InSight data[END_REF], large source depths [START_REF] Durán | Seismology on Mars: An analysis of direct, reflected, and converted seismic body waves with implications for interior structure[END_REF] and/or contamination of seismic data by long-period wind noise as well as atmospheric pressure waves [START_REF] Stutzmann | The polarization of ambient noise on Mars[END_REF]. Strong crustal scattering on Mars [START_REF] Lognonné | Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data[END_REF][START_REF] Van Driel | High-frequency seismic events on Mars observed by InSight[END_REF] can also impede the propagation and affect the visibility of surface waves, as was the case on the Moon [START_REF] Dainty | Seismic scattering and shallow structure of the Moon in Oceanus Procellarum[END_REF].

We report here the first detection of surface waves on Mars, in the seismic waveforms of events S1094b and S1000a. S1094b, which occurred on December 24 th , 2021, is the third-largest seismic event (MW = 4.0±0.2) and has the longest-duration seismic signal recorded to date by InSight [START_REF]Materials and Methods are available as supplementary materials[END_REF], with coda energy persisting for more than 135 minutes. Based on the differential travel time of the direct P and S arrivals, and measured P-wave polarization, the initial distance and back azimuth estimates provided by the Marsquake Service were 59.7±6° and 40° (-9°, +18°), corresponding to a source region in Amazonis Planitia, ~3460 km northeast from InSight (Fig. 1). The Mars Reconnaissance Orbiter (MRO) images taken between December 24-25, 2021 reveal a large impact crater in Amazonis Planitia, 3532 km away from the lander and consistent with the source location estimated for S1094b [START_REF] Posiolova | [END_REF]. With similar broad frequency content and moment magnitude of S1094b, event S1000a has also been identified as atypical based on its seismic characteristics [START_REF]Materials and Methods are available as supplementary materials[END_REF] and was recently associated with an impact crater near the Tharsis province, ~7460 km away from the InSight lander [START_REF] Posiolova | [END_REF]. The ground-truth identification of the two events as impacts removes all uncertainties related to hypocentral depth.

We apply standard marsquake data processing methodologies [START_REF]Materials and Methods are available as supplementary materials[END_REF] to the S1094b waveform data. An unusually large amplitude seismic arrival is observed 800 s after the P-wave in the Swave coda in the vertical-component spectrogram (Fig. 2). The arrival's frequency content is considerably lower than typical of P-and S-wave arrivals in low-frequency (LF) family marsquakes [START_REF] Durán | Seismology on Mars: An analysis of direct, reflected, and converted seismic body waves with implications for interior structure[END_REF][START_REF] Khan | Upper mantle structure of Mars from InSight seismic data[END_REF]. Narrow-band filter banks of the raw vertical-component data show dispersion in the 6-18 s period range (Fig. 2). Frequency-dependent polarization analysis confirms that particle motion is strongly elliptically-polarized in the vertical plane (fig. S1E). The systematic phase shift between the vertical and horizontal components suggests that the arrival has a predominantly retrograde particle motion and arrives from 51° due northeast, consistent with the polarization of the direct P-wave (fig. S5).

Taken together, these characteristics allow the positive identification of this phase as the minor-arc Rayleigh wave (R1). Although strong elliptical polarization has been previously observed in the 3-30 s period range of the ambient seismic noise recordings, they were strictly polarized in the horizontal plane [START_REF] Van Driel | High-frequency seismic events on Mars observed by InSight[END_REF] and correlated with daytime wind direction on Mars. Despite heavy late afternoon winds, a comodulation analysis of the potential wind injection during the R1 arrival documents excess seismic energy over that generated by wind between 8-15 s at the time of the observation (fig. S3). Moreover, we confirm that the seismic data recorded during the surface wave arrival is not contaminated by any known electro-mechanical artifacts associated with the seismic sensor or the InSight spacecraft system [START_REF] Kim | Potential pitfalls in the analysis and structural interpretation of seismic data from the Mars InSight mission[END_REF]. We find no evidence for Love waves in the S1094b records. This observation is consistent with an impact origin for S1094b, as an isotropic source would primarily excite Rayleigh waves. The detection of Rayleigh waves from this impact source, but not from other LF marsquakes, supports the argument that marsquakes recorded to date are generally too deep to effectively excite surface waves [START_REF] Giardini | The seismicity of Mars[END_REF]. Our waveform simulation confirms that surface waves from shallow seismic sources are far more likely to be detectable, given the diurnal ambient noise level on Mars (fig.

S14).

We observed an additional anomalous seismic arrival approximately 75 minutes after the identified R1 (fig. S2). Like for the R1 observation, the time of this arrival is far outside the time window for a potential direct or ground-coupled infrasound wave originating from the impact source region [START_REF] Posiolova | [END_REF][START_REF] Garcia | Search for infrasound signals in InSight data using coupled pressure/ground deformation methods[END_REF]. However, the timing is consistent with that expected for the major-arc Rayleigh wave (R2), that propagated in the opposite direction around Mars. Dispersion and enhanced elliptical polarization in the vertical plane in the 6-11 s period range supports the R2 interpretation. While the frequency content of this arrival is comparable to that of R1, broadband environmental injection in the analysis window is also evident (fig. S4). Due to low signal-to-noise ratio, the direction of propagation and particle motion of this phase are unclear and thus the identification of R2 is not definitive. We find no evidence for the arrival of surface wave overtones, nor multi-orbiting Rayleigh waves in the S1094b waveforms [START_REF]Materials and Methods are available as supplementary materials[END_REF]. Surface wave data on Earth are typically interpreted assuming that propagation occurs along the great circle path from source to receiver, and that it can be related to the average flat-layer structure along that path [START_REF] Moulik | Global reference seismological data sets: multimode surface wave dispersion[END_REF]. Using a number of crustal thickness models constructed based on gravimetric data and the extrapolated crustal thickness estimates from the InSight location [START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF], our kinematic ray tracing predicts negligible deviations from great circle paths for R1 and R2, less than 0.2% of the total travel time [START_REF]Materials and Methods are available as supplementary materials[END_REF]. We measured the group velocities of R1 and R2 and obtained average values of 2.77 and 3.14 km/s, respectively, which imply structural differences along their propagation paths (fig. S6). Indeed, while the R1 path traverses only the northern lowlands, a large fraction of the R2 path crosses the southern highlands and between 12% and 17% of the path passes through the Hellas impact basin, where the crust has been largely removed and replaced by uplifted mantle [START_REF] Wieczorek | Lunar multiring basins and the cratering process[END_REF]. Consequently, the crustal thickness within the Hellas impact basin could be as low as a few kilometers [START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF] and R2 would travel at seismic velocities characteristic of the uppermost mantle (VS 4-4.5 km/s) at periods of 10-16 s. The observed higher value in the average group velocity of R2 with respect to R1 could then be accounted for by Hellas alone and as a result the average crustal velocity of the southern and northern hemispheres would be very similar (fig. S18). Notably, both phases show little dispersion in the observed frequency range, which is primarily sensitive to crustal structure between ~5-30 km depth (Fig. 2C). We inverted for pathaveraged radial P-and S-wave velocity profiles using the R1 measurements with multiple approaches (Fig. 2C, and figs. S8-S10) and regardless of the parameterization strategies considered [START_REF]Materials and Methods are available as supplementary materials[END_REF], we obtained a uniform VS of about 3.2 km/s, with a slight linear increase down to 30 km depth. At greater depths, we lose sensitivity due to lack of dispersion measurements at long periods (Fig. 2). At shallowest depths, we cannot rule out a thin slow layer, though due to the non-linear relationship between VS profiles and surface wave sensitivity kernels (Fig. 2C), the greatest permissible thickness of such a layer depends on its VS. The uniform VS in the 5-30 km crustal depth range is different from the three-layer crustal structure observed beneath InSight [START_REF] Knapmeyer-Endrun | Thickness and structure of the martian crust from InSight seismic data[END_REF][START_REF] Durán | Seismology on Mars: An analysis of direct, reflected, and converted seismic body waves with implications for interior structure[END_REF][START_REF] Kim | Improving constraints on planetary interiors with PPs receiver functions[END_REF]. The obtained VS is substantially higher in the upper 10 km and is similar to the average velocities of the second and third layers beneath the lander (Fig. 2D), but does not show the same velocity jump around 20 km depth. From the comparison of the local and the R1 path-average velocity structures, we conclude that the low-velocity observed down to 8-10 km depth below the lander is a local feature and if present in other parts along the path it must be restricted to only few kilometers below the surface. We cannot exclude the presence of deeper layering in the crust, but this would have to occur at varying depths along the path, to be averaged in the observed linear VS increase with depth.

The high crustal seismic velocities inferred from the S1094b dispersion analysis are supported by S1000a data. Two distinct long-period arrivals, at ~20 s and ~30 s periods, are visible in the vertical-component spectrogram of S1000a in the R1 group arrival time range predicted based on the posterior distribution on VS (fig. S11). While R1 in S1094b shows clear polarization, the comparative strength of the environmental injection during the expected R1 window of S1000a prevents a definitive identification. The inferred VS structure using the S1000a group velocity measurements at ~20 s and ~30 s periods (2.73 km/s and 2.83 km/s) overlaps with our posterior VS distribution based on group velocities of R1 for S1094b down to 30 km depth and provides additional constraints to image a slowly increasing VS in the lower crust down to 45 km depth (Fig. S2E). This agreement suggests a high degree of similarity in the average crustal structure along the two R1 paths Unlike dispersion, the frequency-dependence of Rayleigh wave ellipticity, expressed as the ratio of horizontal-to-vertical amplitude (H/V), is strongly sensitive to the structure directly beneath InSight. We find that the H/V measurements made on R1 are consistent with previous models of crustal layering directly beneath InSight (figs. S15, S16), as are P-to-s conversions in the P-wave coda of S1094b which show prominent arrivals at 2.4 s, 4.8 s, and 7.2 s after the direct P arrival (fig. S19,S20). Even with a single event, we can confirm that the shallow crustal structure at the landing site down to 10 km depth is substantially slower than the average crustal velocity sampled by the R1 path.

The observed surface waves allow us to expand the current understanding of crustal structure on Mars beyond the crustal layering inferred beneath the InSight landing site [START_REF] Knapmeyer-Endrun | Thickness and structure of the martian crust from InSight seismic data[END_REF]. We find that the low VS layer extending down to 10 km depth in the shallow crust of Elysium Planitia does not exist globally on Mars. Instead, the average crustal velocities along the R1 paths of S1000a and S1094b (Fig. 3) are considerably faster and are likely to be more representative of average crustal structure. Large geographic variations in upper crustal structure hold implications for interpreting waveforms of surface-bouncing seismic waves such as PP and SS, and must be explicitly accounted for when constructing models of the spherically-symmetric structure of Mars. Relatedly, these structural variations hold clues for the deeper signature of surface geologic units and for interpretations of gravity data.

A large portion of the R1 paths between Elysium and Amazonis Planitiae passes through the Elysium rise, the largest volcanic province in the northern lowlands (Fig. 1). Its surface geology is characterized by lava flows of Hesperian to Amazonian age, reaching up to several kilometers of thickness and representing a history of major resurfacing [START_REF] Platz | Eruption history of the Elysium volcanic province, Mars[END_REF]. Beyond Elysium, the S1000a R1 path again encounters extensive regions covered by Hesperian and Amazonian volcanics in Amazonis Planitia and north of Alba Patera. Differently, the plains around the InSight lander are composed of Early Hesperian and Early Amazonian lava flows [START_REF] Golombek | Geology and physical properties investigations by the InSight lander[END_REF][START_REF] Golombek | Geology of the InSight landing site on Mars[END_REF] whose limited thickness is insufficient to affect R1 dispersion. Below ~200 m, weaker sedimentary material is suggested to extend in places at least to 5-6 km depth based on the phyllosilicate signatures and layered sedimentary rocks brought up in the central peaks of large impact craters [START_REF] Pan | Crust stratigraphy and heterogeneities of the first kilometers at the dichotomy boundary in western Elysium Planitia and implications for InSight lander[END_REF]. Similar constraints are provided by density inferred from gravity data. The maximum permissible density of the overall crust on Mars (2850-3100 kg/m 3 ) is lower than the density of most martian basaltic materials found at the surface, as estimated by gamma-ray compositional mapping [START_REF] Baratoux | Petrological constraints on the density of the Martian crust[END_REF] and by mineralogical norms for SNC meteorites of predominantly Amazonian age (see summary in 23). The two factors contributing to a layered crustal density structure on a global scale could be a less mafic (less dense) composition and/or an elevated porosity (6, 7, 23) (Fig. 3).

As most of the R1 paths pass through regions resurfaced by relatively young volcanic rocks, this would result in similar, higher densities of the upper and lower crust. Although Elysium volcanic cumulates are only a few kilometers thick [START_REF] Tanaka | The digital global geologic map of Mars: Chronostratigraphic ages, topographic and crater morphologic characteristics, and updated resurfacing history[END_REF] and thus within the uppermost zone of poor seismic sensitivity (Fig. 2), their magmatic history influenced the nature of the whole crust in this region [START_REF] Wilson | Mars: Review and analysis of volcanic eruption theory and relationships to observed landforms[END_REF][START_REF] Christiansen | The origin of magma on planetary bodies[END_REF]. The average ratio of intrusive/extrusive magmatism on Mars [START_REF] Taylor | The bulk composition of Mars[END_REF][START_REF] Black | The eruptibility of magmas at Tharsis and Syrtis Major on Mars[END_REF] implies that intrusives account for >5 km of average crustal thickness integrated over the entire Elysium rise, and even more near the volcanic centers traversed by R1 (Fig. 1). One proposal for Mars is that intrusive rocks (i.e. magma chamber centers) would concentrate at greater depths than on Earth [START_REF] Wilson | Mars: Review and analysis of volcanic eruption theory and relationships to observed landforms[END_REF]. These intrusive magmas represent, at least in part, residues of the partial melting giving rise to surface lavas and so likely are of greater density (38) and elevated seismic wave speeds closer to values typical of basaltic volcanic rocks, consistent with the path-average velocity profiles we observe below 5 km depth (Fig. 2). Substantial porosity is also likely to be present in the upper crustal layers beneath the lander [START_REF] Lognonné | Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data[END_REF][START_REF] Knapmeyer-Endrun | Thickness and structure of the martian crust from InSight seismic data[END_REF][START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF]. Their low VS is compatible with fractured basalt having, for example, 10% porosity, though the exact amount depends strongly on both the aspect ratio of the pore spaces and material contained therein (fig. S21). However, the higher path-averaged velocities we observe in the upper 10 km would require lower porosity, which could result from viscous closure of pore spaces due to thermal annealing expected to accompany volcanic resurfacing processes [START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF]39), partial filling of pore spaces by the deposition of precipitated minerals from a briny ancient aquifer system [START_REF] Manga | No cryosphere-confined aquifer below InSight on Mars[END_REF], or the presence of a deep cryosphere or substantial water table beneath the thick Amazonian lava flows along the R1 path [START_REF]Materials and Methods are available as supplementary materials[END_REF][START_REF] Clifford | Depth of the Martian cryosphere: Revised estimates and implications for the existence and detection of subpermafrost groundwater[END_REF][START_REF] De Toffoli | Rheological and Mechanical Layering of the Crust underneath thumbprint terrains in Arcadia Planitia, Mars[END_REF] (Fig. 3). We note that images from the High Resolution Imaging Science Experiment of the S1094b impact crater show large blocks of pure ice ejected from the shallower layers [START_REF] Posiolova | [END_REF]. This would not be expected to be the case near InSight, because the shallow crust with VS of 1.7-2.1 km/s in the upper 8-11 km [START_REF] Knapmeyer-Endrun | Thickness and structure of the martian crust from InSight seismic data[END_REF] rules out an ice-saturated cryosphere [START_REF] Manga | No cryosphere-confined aquifer below InSight on Mars[END_REF].

Another possibility is that a low density, high porosity layer beneath InSight results from ejecta deposited by the Utopia impact [START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF]. Because ejecta thickness is a strong function of radial distance, one would expect the ejecta thickness averaged along the R1 path to be much less than beneath InSight, consistent with the observations. Regardless of the exact origin -composition and/or porosity -variations of crustal seismic structure presented here are likely correlated with density variations, because both temperature and compositional variations increase density together with VS, and our results imply greater crustal densities between Elysium and Amazonis Planitiae than directly beneath the lander. This result is consistent with previous estimates of higher crustal density beneath the Elysium rise of 3100±100 kgm -3 (43) and lower density beneath the lander (44) from gravity-topography measurements. Density variations would also affect inferences of crustal thickness from topographic and gravity signals associated with the crustal dichotomy (4,[START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF]. Currently, both exogenic (i.e., one or more large impacts; 45) and endogenic (i.e., mantle convection) processes [START_REF] Nimmo | Early crustal evolution of Mars[END_REF], or a combination thereof [START_REF] Citron | Timing of oceans on Mars from shoreline deformation[END_REF] continue to be debated as the origin of the dichotomy. Both processes would be expected to generate a basaltic secondary crust in the northern lowlands, consistent with the R1 observations from the two recent impacts. However, if confirmed by further analyses or other events, the S1094b R2 observation of similar group velocities across the southern hemisphere (once corrected for path in the Hellas impact basin) preliminarily indicates that the crustal structure at relevant depths could be substantially similar North and South of the dichotomy (Fig. 3).

Figure 1 .

 1 Figure 1. Locations of two large meteoroid impacts (yellow circles) identified in MRO images[START_REF] Posiolova | [END_REF]. The great circle paths for R1 (solid) and R2 (dashed) in S1094b are in white, while the R1 path for S1000a is in yellow. Background 5 topographic relief is from the Mars Orbiter Laser Altimeter[START_REF] Smith | The global topography of Mars and implications for surface evolution[END_REF]. The distribution and sequence of major geological unit groups of Hesperian and Amazonian age[START_REF] Tanaka | The digital global geologic map of Mars: Chronostratigraphic ages, topographic and crater morphologic characteristics, and updated resurfacing history[END_REF] are overlaid. Global elevation (orange) and the crust-mantle boundary depth profiles[START_REF] Wieczorek | InSight constraints on the global character of the Martian crust[END_REF] along the R1 and R2 paths (dashed blue) are shown at the top.

Figure 2 .

 2 Figure 2. Seismic waveforms and velocity profiles. (A) Vertical-component seismogram of S1094b bandpass filtered between 1-5 s (gray) and 8-15 s (blue) with P and S wave picks (black vertical lines). Narrow-band filter banks and envelopes show dispersed signals 800 s after the P-wave. (B) The vertical component S-transform shows a large amplitude seismic arrival that exhibits dispersion (c.f., 2A). The frequency domain envelope averaged across the 8-15 5 s period range is plotted at the top of the spectrogram. Other characteristics enabling the identification of this dispersive arrival as R1 are shown in the Supplementary Materials (19). (C) Depth sensitivity kernels and data misfit of R1 in S01094b (inset). The mean and standard deviation are drawn from 10 pairs of dispersion measurements (fig. S6). Kernels in dashed lines are computed based on the three-layer crustal model in (7) denoted as KE2021. Note the substantial differences between the kernels due to different velocity profiles. Shaded kernels and predictions are 10 computed using the average model in panel 2D. (D) Posterior distribution of VS structure inverted from the group velocity measurements of S1094b R1 (K1094bR1). Posterior distribution and prediction are based on the best-fitting 10,000 models after one million iterations. Depths where sensitivity is inadequate (<40% in cumulative kernel strength) are muted. The range of V S in the three-layer crustal models beneath the lander (7) are indicated by gray

Figure 3 .

 3 Figure 3. Cross section of the S1094b surface wave path through Mars. Surface topography (21) and crustal thickness (23) with a 20x vertical exaggeration are shown along the path of R1 and R2, with major geological provinces labeled at the surface and potential subsurface structures that affect surface wave velocity. The approximate sampling depth of the observed surface waves is indicated by gray dashed line. The inset context map shows the topography along the surface wave paths. The colored arcs indicate the path length(s) through provinces with surface volcanism (red), ice stability at latitudes > 30º (cyan), and cratered highlands (gray).

Implications for the interpretation of Martian seismic data. Icarus, 330, 11-15.

Acknowledgments:

This paper is InSight contribution number 266. The authors acknowledge the NASA, the CNES, their partner agencies and Institutions (UKSA, SSO, DLR, JPL, IPGP-CNRS, ETHZ, IC, and MPS-MPG) and the flight operations team at JPL, SISMOC, MSDS, IRIS-DMC, and PDS for providing the SEED SEIS data. We acknowledge the thorough and thoughtful reviews from the editor and three anonymous reviewers which greatly improved the manuscript. Fundings: ND, CD, GZ, and SCS would like to acknowledge support from ETH through the ETH+ funding scheme (ETH+02 19-1: \Planet Mars"). NS and VLacknowledge support from NASA PSP grant 80NSSC18K1628. CB and JL were supported by NASA InSight PSP grant #80NSSC18K1679.

The French co-authors acknowledge the funding support provided by Centre national d'études spatiales (CNES) and the Agence Nationale de la Recherche (ANR-19-CE31-0008-08 MAGIS) for SEIS operation and SEIS Science analysis. Numerical computations of McMC Approach 2 were performed on the S-CAPAD/DANTE platform (IPGP, France) and using the HPC resources of IDRIS under the allocation A0110413017 made by GENCI. AH is funded by the UKSA under grant numbers ST/R002096/1 and ST/W002523/1. IJD was supported by NASA InSight PSP grant 80NSSC20K0971. A portion of this work was supported by the InSight Project at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Author contribution: DK, SC, DG, VL, PL, CB, EB, JC, AK, BK, JL, MS, SCS, and ES, analyzed the seismic data and contributed in detection and identification of the surface wave arrivals. DK, VL, CB, MD, RJ, BK, JL, RM, HS, and EW performed the inversions. CC and WTP performed the comulation analysis. SCS performed the analysis on ray tracing. DK performed waveform simulations. SC, BK, and ZX performed the H/V analysis. DK, CD, and BK performed the receiver function analysis. Review of the continuous data and detection of seismic events was done by DK, SC, CC, JC, CD, SCS, ND, AH, TK, MP, and GZ. DK, WBB, SC, DG, VL, PL, CB, JC, MG, AK, BK, JL, RM, NS, SCS, MW, AB, TG, SK, SMM, FN, ACP, IES, and MPP participated and contributed to the interpretation of the results. DK wrote the main paper with contribution from DG, and VL. DK, WBB, SC, VL, CB, JC, MG, AK, BK, JL, WTP, RM, NS, SCS, MS, ES, MW, EB, PD, QH, SK, SMM, FN, ACP, and RG edited the main text and supplementary materials. S1094b and S1000a impact analysis and discussion are contributed from DG, PL, JC, SCS, AH, IJD, BF, RG, and LP. The InSight mission is managed by WBB, and MPP. The SEIS instrument development was led by PL, DG, WTP, and WBB. Competing interests: The authors declare that they have no competing interests. Data and materials availability: The InSight event catalogue [START_REF]Mars Seismic Catalogue, InSight Mission; V[END_REF] and waveform data are available from the IRIS-DMC, NASA-PDS [START_REF]InSight Mars SEIS Data Service[END_REF] and IPGP data center [START_REF]InSight Mars SEIS Data Service[END_REF].

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S21

References