Quentin Marre

Nathalie Huet

Elodie Labeye

Embodied Mental Imagery Improves Memory

Keywords: simulation, memory strategies, word retention, embodied cognition

According to embodied cognition theory, cognitive processes are grounded in sensory, motor and emotional systems. This theory supports the idea that language comprehension and access to memory are based on sensorimotor mental simulations, which does indeed explain experimental results for visual imagery. These results show that word memorization is improved when the individual actively simulates the visual characteristics of the object to be learned. Very few studies, however, have investigated the effectiveness of more embodied mental simulations, that is, simulating both the sensory and motor aspects of the object (i.e., motor imagery) from a first-person perspective. The recall performances of 83 adults were analysed in four different conditions: mental rehearsal, visual imagery, third-person motor imagery, and first-person motor imagery. Results revealed a memory efficiency gradient running from low-embodiment strategies (i.e., involving poor perceptual and/or motor simulation) to high-embodiment strategies (i.e., rich simulation in the sensory and motor systems involved in interactions with the object). However, the benefit of engaging in motor imagery, as opposed to purely visual imagery, was only observed when participants adopted the first-person perspective. Surprisingly, visual and motor imagery vividness seemed to play a negligible role in this effect of the sensorimotor grounding of mental imagery on memory efficiency.

Embodied Mental Imagery Improves Memory

Mental imagery can be defined as a "quasi-perceptual experience" that "resembles perceptual experience, but occurs in the absence of appropriate external stimuli" (Thomas, 2014, p. 1). It occurs constantly in everyday life, be it when remembering past events, projecting ourselves into the future, or representing the route someone is describing to us. It should be noted that the term imagery does not only concern images. Visual imagery can be either object imagery, which consists in visualizing the details of individual objects and scenes in terms of shape, color, brightness and texture or spatial imagery when this visualization concerns spatial relations, movements of objects and their parts, and spatial transformations such as mental rotation [START_REF] Blazhenkova | Vividness of object and spatial imagery[END_REF]. Visual imagery relies on the manipulation of representations that share the same attributes as percepts [START_REF] Borst | Visual mental imagery and visual perception: Structural equivalence revealed by scanning processes[END_REF][START_REF] Kosslyn | Visual images preserve metric spatial information: Evidence from studies of image scanning[END_REF][START_REF] Shepard | Mental rotation of three-dimensional objects[END_REF], and requires the activation of the same brain systems that are involved in visual perception [START_REF] Albers | Shared representations for working memory and mental imagery in early visual cortex[END_REF][START_REF] Kosslyn | When is early visual cortex activated during visual mental imagery[END_REF]. [START_REF] Shepard | Mental rotation of three-dimensional objects[END_REF], for example, showed that the time taken to resolve visuo-spatial tasks correlates linearly with the difference between the angle of the starting figure and the target figure, which suggests that there is an actual rotation of the image that is operated mentally. Kosslyn highlighted the properties of mental scanning, showing that it takes more time for participants to mentally move between two nearby elements than between two distant ones (Kosslyn, Ball & Reiter, 1978).

Imagery may involve not only other sensory modalities, like olfaction and audition, but also the motor modality. In this case, motor imagery is defined as a mental reproduction of physical activity without any actual movement [START_REF] Driskell | Does mental practice enhance performance[END_REF]. The visual sense is involved: actions can be imagined either from an internal/first-person perspective, such as being inside one's body or having a camera on one's head, or from an external perspective, either observing oneself performing an action or observing someone else perform an action [START_REF] Guillot | Brain activity during visual versus kinaesthetic imagery: An fMRI study[END_REF][START_REF] Roberts | Movement imagery ability: Development and assessment of a revised version of the Vividness of Movement Imagery Questionnaire[END_REF]. In motor imagery, the kinaesthetic sense is generally involved, that is, the sensation of executing a movement, feeling the contraction and stretching of the muscles and the position of the limbs relative to others [START_REF] Cumming | The role of imagery in performance[END_REF][START_REF] Guillot | Brain activity during visual versus kinaesthetic imagery: An fMRI study[END_REF]. This kinaesthetic imagery can be performed in either external or internal motor imagery [START_REF] Glisky | Internal and external mental imagery perspectives and performance on two tasks[END_REF]Robert et al., 2008). Just as visual imagery shares attributes with visual perception, motor imagery involves the same neural networks (e.g., primary motor cortex, premotor cortex, cerebellum or somatosensory cortex) as the actual physical actions [START_REF] Cumming | The role of imagery in performance[END_REF]. This explains several features of motor imagery such as the activation of the limb muscles affected by the action in question [START_REF] Lebon | Modulation of EMG power spectrum frequency during motor imagery[END_REF]. There are also identical temporal characteristics between the duration of the imagery and the duration of the movement, suggesting an actual motor simulation during imagery [START_REF] Guillot | Duration of mentally simulated movement: A review[END_REF]. Motor imagery is grounded in the body of the individual with all its specificities. In a task where left-handers and right-handers had to imagine actions designated by verbs, some manual others not, a difference in the lateralization of the motor cortex was found between right-handers and left-handers for the imagery of manual action verbs [START_REF] Willems | Body-specific motor imagery of hand actions: Neural evidence from right-and left-handers[END_REF]. Similarly, [START_REF] Schwoebel | Pain and the body schema : Evidence for peripheral effects on mental representations of movement[END_REF] showed that for patients with chronic pain in one of their arms, the duration of motor imagery involving the painful arm was longer than when they imagined doing the movement with their unaffected arm, once again indicating that motor imagery is a simulation grounded in the body of the individual. Motor imagery can also be influenced by the perspective that is taken [START_REF] Lorey | The embodied nature of motor imagery: The influence of posture and perspective[END_REF][START_REF] Sigiru | Motor and visual imagery as two complementary but neurally dissociable mental processes[END_REF]. For example, Lorey and her colleagues (2009) found that imagining a hand movement was influenced by the current position of the participant's hand, in that it was facilitated if the actual position of the hand was the same as that of the imagined hand. This facilitation was observed if participants imagined the movement from a first-person perspective (i.e., imagining it from their own point of view), but not if they imagined it from a third-person perspective (i.e., imagining it from the outside, out of their body).

One interesting property of mental imagery is its positive impact on memory performances when people processing stimuli are compared according to whether they have been given a mental imagery instruction or not. Participants who have been given a visual imagery instruction remember verbal material better, especially words of high imageability (e.g., [START_REF] Bower | Mental imagery and associative learning[END_REF][START_REF] Gupton | Imagery, mediational instructions, and noun position in free recall of noun-verb pairs[END_REF][START_REF] Mccauley | The effect of imagery on explicit and implicit tests of memory in young and old people: a double dissociation[END_REF][START_REF] Mueller | Instructions, noun imagery, and priority in free recall[END_REF][START_REF] Paivio | Imagery and verbal processes[END_REF][START_REF] Pressley | Imaginal elaboration of illustrations to facilitate fact learning: Creating memories of Prince Edward Island[END_REF]. In [START_REF] Bower | Mental imagery and associative learning[END_REF], for instance, participants were instructed to memorize 20 concrete-noun pairs either by imagining a visual scene in which the two objects of the pair interacted, or by just memorizing the relation between the two words. In this typical example, participants in the imagery group performed about 30% better than controls on both immediate and delayed cued recall tests.

Recent studies have yielded similar patterns of results, with participants who were given an imagery instruction (compared with others who were told not to use imagery) correctly recalling or recognizing more items [START_REF] Oliver | False memories and the DRM paradigm: Effect of imagery, list, and test type[END_REF] and producing fewer false memories [START_REF] Foley | Imagery encoding and false recognition errors: Exploring boundary conditions of imagery's enhancing effects[END_REF][START_REF] Foley | Imagery encoding effects on memory in the DRM paradigm: A test of competing predictions[END_REF][START_REF] Foley | Imagination and false memory inductions: Investigating the role of process, content and source of imaginations[END_REF][START_REF] Robin | Effects of Image and Verbal Generation on False Memory[END_REF]. Furthermore, motor imagery can facilitate motor learning. A meta-analysis by Driskell (1997) measured the effect of mental practice on performance against a 100 scientifically tested hypotheses, and found a significant effect of mental practice on performance (albeit weaker than actual practice). A literature review focusing mainly on athletes in laboratory studies and follow-up of athletes by [START_REF] Weinberg | Does imagery work? Effects on performance and mental skills[END_REF] also went in this direction, its results seemingly attesting to the effectiveness of motor imagery. [START_REF] Holmes | The PETTLEP approach to motor imagery: A functional equivalence model for sport psychologists[END_REF] developed the Physical, Environment, Task, Timing, Learning, Emotion and Perspective (PETTLEP) model to condense the important variables for effective motor imagery. These authors advise maximizing resemblance to the actual physical performance (e.g., posture, sports clothes), physical environment, content of the pictorial task, timing, emotions felt, and perspective (i.e. first-person).

The scientific literature has frequently provided theoretical frameworks for explaining the nature and properties of mental imagery. However, few of these have given a coherent explanation that integrates neuroscience observations and allows the positive effects of mental imagery on memorization to be easily described. The embodied cognition paradigm takes up this challenge by offering a framework that fits well with the features of mental imagery described above. It states that cognitive processes are grounded in our bodily experiences and that high-level cognitive processes cannot be detached from the peripheral brain systems that process input from the outside world. There are several embodied approaches. Simulation theory states that the brain captures modal states during perception, action and introspection and later simulate these states to represent knowledge. Cognition therefore corresponds to the activation of modal states, be they perceptual, motor or emotional, and more particularly to the simulation or partial re-enactment of lived experiences [START_REF] Barsalou | Perceptual symbol systems[END_REF][START_REF] Barsalou | Grounding conceptual knowledge in modality-specific systems[END_REF]. It is supported by neuroscience data which suggest that memory retrieval involves multimodal simulation. For example, word retrieval requires the reactivation of the sensory cortex regions activated at encoding (see [START_REF] Buckner | The cognitive neuroscience of remembering[END_REF], for a review), or put another way, the simulation of the modal operations performed at encoding. This happens to be in line with the encoding specificity principle which states that "specific encoding operations performed on what is perceived determine what is stored, and what is stored determines what retrieval cues are effective in providing access to what is stored" (Tulving & Thomson, 1973, p.369).

Consequently, item retrieval is facilitated when the retrieval context matches the encoding context. This contextual element can be either the physical environment [START_REF] Godden | Context-dependent memory in two natural environments: On land and underwater[END_REF], posture [START_REF] Dijkstra | Body posture facilitates retrieval of autobiographical memories[END_REF] or a previously associated sensory stimulus [START_REF] Brunel | The sensory nature of episodic memory: Sensory priming effects due to memory trace activation[END_REF]. Therefore, memory traces are composed of sensorimotor elements of the encoding context and remembering seems to reactivate sensorimotor cortices involved in encoding.

It is worth mentioning that other embodied approaches in the embodied cognition paradigm deny the existence of representations. According to the enactive approach, perception is a form of active interrogation of the environment that uses the sensory system to search for specific information needed for action at a particular moment [START_REF] Thomas | Are theories of imagery theories of imagination? An active perception approach to conscious mental content[END_REF][START_REF] Thomas | Mental imagery[END_REF]. Mental imagery is therefore a partial re-enactment, a mental rehearsal of the exploratory perceptual acts that are executed during actual perception. According to sensorimotor theory, there is no such mental rehearsal of perceptual acts. The experience of mental imagery would emerges from the activation or exercise of a practical sensorimotor knowledge of possibilities for action. This sensorimotor knowledge concerns how sensory inputs (e.g., visual stimulations) changes as a function of motor outputs (movements). Mental imagery is therefore simply the fact of holding implicit expectations regarding how sensory stimulation changes as a function of movement (Foglia & O'Regan, 2015). Whatever the theory, the embodied cognition paradigm defends the idea that processes like mental imagery, conceptual processing or memory, are based on the reactivation of sensorimotor brain patterns activated during the real experience to which the knowledge refers. In the present study, we adopted the perspective of simulation theory, and hypothesized that mental imagery corresponds to a mental simulation, emphasizing certain visual attributes during visual imagery, or certain motor attributes during motor imagery. Behavioural empirical data and neural activations reported in the mental imagery literature are highly consistent with empirical data defending the simulation view.

The literature shows that memorization is enhanced when the individual actively simulates the visual characteristics of the object to be learned, that is to say when participants are explicitly instructed to perform visual imagery. However, few studies have investigated the effectiveness of more embodied imagery (i.e., instructions that promotes mental simulation of both sensory and motor aspects of the object) or else have failed to distinguish between the influence of motor versus visual components of imagery on memory performance. Motor imagery presumably promotes the re-enactment not only of visual experiences, but also of motor (and potentially kinaesthetic and tactile) ones, thus increasing the number of modalities by which the memory trace can be retrieved. Motor imagery may also induce a higher degree of self-involvement than a nondynamic mental image that does not involve any mental action on the part of the individual, and personal involvement is known to be a factor favouring retention [START_REF] Rogers | Self-reference in memory: Recognition of personality items[END_REF]. In addition, first-person motor imagery may be more efficient than third-person motor imagery, as the degree of selfinvolvement is greater in the first person [START_REF] Bagri | The role of first person perspective and vivid imagery in memory for written narratives[END_REF] and the level of embodiment is higher, as third-person imagery preferentially recruits nonmotor structures [START_REF] Lorey | The embodied nature of motor imagery: The influence of posture and perspective[END_REF][START_REF] Sigiru | Motor and visual imagery as two complementary but neurally dissociable mental processes[END_REF]. We therefore postulated that memory strategies lie on a continuum running from low embodiment strategies (e.g., mental rehearsal) to high embodiment strategies involving first-person motor imagery. This continuum is based on the idea that sensorimotor elements are privileged cues for retrieval. The more the memorization consciously calls for a sensorimotor mental elaboration about an object, the more sensorimotor cues are available during retrieval, thus facilitating the retrieval of the memory trace.

Overview of the Present Study

The present study was design to distinguish between the influence of visual imagery and the influence of motor imagery and compare the two, in order to test the idea of an embodiment continuum in imagery that results in varying efficiency depending on the memorization strategy adopted. In our study, participants were asked to memorize a 30-word list using either mental rehearsal, visual imagery, third-person motor imagery, or first-person motor imagery. For each group, we analysed the numbers of correct and incorrect responses at immediate and delayed (48 hours later) recall. We expected the continuum of memory embodiment strategies to be reflected in memory performances. In other words, the recall rate would improve as the embodiment level of memory strategies increased. More specifically, recall performance would be better when learning was based on first-person motor imagery rather than on third-person motor imagery. These performances would also be better than those resulting from learning with visual imagery, which in turn would be better than memorization based on mental rehearsal. According to several authors, the level of imagery skills influences the cognitive benefits of imagery. Thus, visual imagery can decrease false memories, but only for individuals with high visual imagery abilities [START_REF] Marmurek | Imagery effects in false recall and false recognition[END_REF]. In addition, vividness plays a key role in the retrieval of sensory traces [START_REF] Palmiero | The format of mental imagery: From a critical review to an integrated embodied representation approach[END_REF] as individuals who are able to create vivid images activate their brain more selectively than low-vividness imagers [START_REF] Fulford | The neural correlates of visual imagery vividness -An fMRI study and literature review[END_REF]. We therefore predicted that visual and motor imagery vividness would moderate the effect of memory strategy on recall performance.

Method

Participants

Participants were 85 adults (59 women and 26 men), who were randomly divided into four groups corresponding to the encoding conditions: mental rehearsal group (MR), visual imagery group (VI), third-person motor imagery group (TPI), and first-person motor imagery group (FPI). Persons under 18 and over 50 years were excluded, as were individuals who did not speak French fluently. The participants were mostly psychology students recruited on the campus of Toulouse Jean Jaurès University. Their mean age was 23 years (SD = 5.27, range = 18-45). They all volunteered to take part in the research, and gave their written informed consent.

To know if the number of participants was sufficient for the desired statistical power, we ran a G*Power [START_REF] Faul | Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses[END_REF][START_REF] Faul | G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences[END_REF]; Version 3.1.9.6) analysis. The effect size was often not available in the literature so we were forced to base our expected effect size on the most recent researches on memory and imagery [START_REF] Foley | Imagery encoding and false recognition errors: Exploring boundary conditions of imagery's enhancing effects[END_REF][START_REF] Foley | Imagination and false memory inductions: Investigating the role of process, content and source of imaginations[END_REF][START_REF] Foley | Imagery encoding effects on memory in the DRM paradigm: A test of competing predictions[END_REF][START_REF] Oliver | False memories and the DRM paradigm: Effect of imagery, list, and test type[END_REF].

We took the smallest effect size we found in these articles (ƞ²=.24, Cohen's f =.56). The G*Power analysis yielded a total sample size of 40 (for alpha = .05, power = .80, number of groups = 4). As we recruited more participants (85) than the minimum sample size required according to the G*Power analysis, our sample size was not a problem in terms of statistical power.

Materials

Participants in all four groups heard the same list of 30 nouns to memorize in the form of a recording (one word every 7 s). We only used referents that were nonliving and lent themselves to manual motor imagery. Based on these two criteria, we selected words with the highest sensory experience scores in [START_REF] Bonin | Sensory experience ratings (SERs) for 1,659 French words: Relationships with other psycholinguistic variables and visual word recognition[END_REF]'s study. A sensory experience score refers to the degree to which a word generates sensory and perceptual experiences [START_REF] Juhasz | Sensory experience ratings for over 5,000 mono-and disyllabic words[END_REF]. A list of 10 words was created in the same way for the training phase. Words used in the experiment are available in the Supplemental Material, together with their associated sensory experience score and other psycholinguistic variables: concreteness, context availability, emotional valence, arousal, and imagery value, based on the norms established by Bonin, Meot, and Bugaiska (2018) and [START_REF] Bonin | Normes de concrétude, de valeur d'imagerie, de fréquence subjective et de valence émotionnelle pour 866 mots[END_REF].

Frequency was measured with the GlàffOLI web interface using the FrWAc indicator (Sajous, Hathout, & Calderone, n.d.).

For the immediate free recall test, participants were each given a sheet with 30 spaces in which to write the remembered words. There were also two 6-point scales, one to rate the ease of performing the memorization task, the other to indicate how far retrieval was based on the memory strategy indicated in the instruction. There was also a question about any other strategies that were used.

The delayed free recall test was the same as the immediate one, except that it was sent as an online questionnaire (via Qualtrics) to participants 48 hours later. We used the French Vividness of Visual Imagery Questionnaire (VVIQ; [START_REF] Santarpia | Évaluer la vivacité des images mentales dans différentes populations françaises[END_REF] to measure the level of vividness the participants were able to reach in visual imagery. This questionnaire contains 32 items, each rated on a 5-point vividness scale ranging from 1 (No image is visible) to 5 (The image is perfectly clear, as sharp and precise as a real-life perception). The Vividness of Movement Imagery Questionnaire Version 2 (VMIQ-2; [START_REF] Roberts | Movement imagery ability: Development and assessment of a revised version of the Vividness of Movement Imagery Questionnaire[END_REF] was used to measure their ability to do vivid motor imagery. This questionnaire contains 36 items, each rated on a 5-point vividness scale ranging from 1 (Perfectly clear and as vivid as normal vision or feel of movement) to 5 (No image at all, you only know that you are thinking of the skill).

Procedure

The experiment began with a training phase, where the experimenter explained that the participants would hear a list of 10 words, each separated by a 7-second interval, and would have to respect one of the following instructions for each word: either mentally rehearse the word (MR); create a mental image of the word's referent (VI); imagine taking and throwing the object from an external point of view, in the third person (TPI); or imagine taking and throwing the object from one's own point of view, in the first person (FPI). The action to be imagined was standardized, in order to control for interindividual variability in the imaginary interaction with the object as much as possible. Instructions are available in the Supplemental Material. During the listening phase, participants were asked to close their eyes and lay their hands flat on their knees (to control for the influence of posture on the motor imagery). We also asked them to chunk the information as little as possible and to perform the task for each word independently of the other words. After listening to the list, participants had to fill in the free recall sheet and the two rating scales for each word. The instruction for the experimental phase was exactly the same as for the training phase, but with a 30-word list. After the immediate recall test, participants were asked to complete the VVIQ and then the VMIQ-2.

They were contacted 48 hours later to perform the delayed recall test.

Results

Two participants were excluded because they did not follow the instructions. We therefore analysed the data of 83 participants (20 for MR, 21 for VI, 21 for TPI, and 21 for FPI). These analyses were performed using R software. Tests based on comparisons of means were performed when assumptions were met. Otherwise, nonparametric tests were used.

Immediate Recall

We ran a one-way analysis of variance (ANOVA) for independent samples on the number of correctly recalled words. This revealed a significant effect of type of instruction on the number of correct responses, F(3, 79) = 12.7, p < .001, η²p = .325. A unilateral post hoc test with Bonferroni correction showed that this effect was due to the fact that participants in the FPI group correctly recalled significantly more words (M = 19.6, SD = 4.26) than those in either the TPI (M = 16.2, SD = 3.46, p = .01), VI (M = 16.1, SD = 3.79, p < .01), or MR (M = 12.6, SD = 2.89, p < .001) groups. Participants in the TPI group correctly recalled significantly more words than those in the MR group (p < .01), and there were significantly more correct responses in the VI group than in the MR group (p < .01). However, recall performances did not differ significantly between the VI and TPI groups (p = 1.00). These results are reflected in the sizes of the confidence intervals in Figure 1.

[insert Figure 1]
Regarding the numbers of incorrectly recalled words, the mean was 0.70 (SD = 1.26) for MR, 0.29 (SD = 0.72) for VI, 0.38 (SD = 0.80) for TPI, and 0.24 (SD = 0.54) for FPI. A Kruskal-Wallis test failed to reveal a significant effect of instruction type on the number of incorrectly recalled words, χ 2 (3) = 3.14, p = .37.

For the VVIQ results, the mean was 119.9 (SD = 14.2) for MR, 121 (SD = 19.3) for VI, 125 (SD = 18.0) for TPI, and 131 (SD = 16.4) for FPI. For the VMIQ-2 results, the scale was reversed, such that the minimum degree of vividness was 1, and the maximum 5. The mean was 134 (SD = 20.7) for MR, 136 (SD = 19.5) for VI, 145 (SD = 23.5) for TPI, and 140 (SD = 18.9) for FPI. We had expected to observe a moderating effect of visual imagery and motor imagery vividness on the relation between instruction and memory performances. However, these scores failed to predict immediate recall performance. The regression coefficients for VVIQ scores (b = .011, t(76) = .322, p = .748) and VMIQ scores (b = .017, t(76) = .569, p = .571) were not significant. This regression model did not account for a significant portion of the variance in memory performance, R²adj = -.013, F(2,76) = .497, p = .611. Since no link could be found between imagery vividness and memory performance, no moderation effect of vividness could be revealed on the effect of instructions on immediate memory performances.

Delayed Recall

Of the initial sample of 83 participants, only 79 responded to the delayed recall test (19 for MR, 21 for VI, 20 for TPI, and 19 for FPI).

A one-way ANOVA for independent samples showed that the effect of instructions on the number of correctly recalled words was still present after 48 hours, F(3, 75) = 8.77, p < .001, η²p = .260. When we investigated this effect more closely, a unilateral post hoc test with Bonferroni correction showed that more words were correctly recalled by participants in the FPI (M = 14.0, SD = 5.89, p < .001), TPI (M = 10.1, SD = 4.49, p < .05) and VI (M = 10.9, SD = 4.99, p < .05) groups than in the MR (M = 5.79, SD = 3.95) group. However, there were no significant differences between the three imagery groups. This is in agreement with the overlapping confidence intervals in the diagram in Figure 2. [insert Figure 2] After 48 hours, the mean number of incorrectly recalled words was 2.00 (SD = 2.21) for MR, 1.19 (SD = 1.54) for VI, 1.95 (SD = 2.35) for TPI, and 2.42 (SD = 2.01) for FPI. Once again, a Kruskal-Wallis test failed to reveal a significant effect of instruction type on the number of incorrectly recalled words, χ 2 (3) = 4.32, p = .23. We had expected to observe a moderating effect of visual imagery and motor imagery vividness on the relation between instruction and delayed correct recalls. The regression coefficients for VVIQ scores (b = .031, t(72) = .653, p = .516) and VMIQ scores (b = .030, t(72) = .739, p = .462) were not significant. This regression model did not account for a significant portion of the variance in memory performance, R²adj = .003, F(2,72) = 1.13, p = .329. Even after 48 hours, no link could be found between imagery vividness and memory performance, therefore no moderation effect of vividness could be revealed on the effect of instructions on delayed memory performances.

Ease of Performing the Memorization Task and Use of Instructed Strategy

Mean ratings for the ease of performing the task in the MR (M = 5.07), VI (M = 5.11), TPI (M = 4.41) and FPI (M = 5.1) groups were all between 4 (Fairly easy) and 6 (Very easy).

A one-way ANOVA for independent samples showed no significant difference between the groups, F(3, 77) = 2.20, p = .095. Participants therefore generally complied with the instructions with relative ease in each experimental condition.

Mean ratings for the extent to which participants used the instructed strategy in the MR (M = 4.58), VI (M = 3.84), TPI (M = 4.24) and FPI (M = 4.39) groups were all between 3 (Medium) and 5 (High). A one-way ANOVA for independent samples failed to reveal any significant difference between groups, F(3, 77) = 1.27, p = .292. Therefore, most of the participants remembered the words using the strategy indicated in the instructions.

Other Memory Strategies

A total of 49 participants (57%) stated that they used another complementary strategy.

They were mainly in the MR group, where 80% of participants declared that they had semantically chunked the words in order to remember them. In the imagery groups, participants mainly used semantic chunking and mental rehearsal: 57% in VI, 38% in TPI, and 52% in FPI.

Controlling the gender effect

Gender differences may be observed in mental imagery (e.g., [START_REF] Campos | Gender differences in imagery[END_REF][START_REF] Richardson | Gender differences in the Vividness of Visual Imagery Questionnaire: A meta-analysis[END_REF] and in the memory benefit of imagery mnemonic instructions (e.g. [START_REF] Lenhart | Tactile perception and the right hemisphere: A masculine superiority for imagery coding[END_REF][START_REF] Metzger | Sex and coding strategy effects on reaction time to hemispheric probes[END_REF]. In order to ensure that gender as no influence on the link between instructions and memory performance, we ran an ANOVA with gender and instructions as independent variables and found that there is no main effect of gender on the number of immediate correct recalls, F(1,75) = .248, p = .620, and no interaction between gender and instructions, F(3,75) = .295, p = .829. The same pattern was observed on delayed correct recalls where no main effect, F(1,71) = .107, p = .745, or interaction effect, F(3,71) = .103, p = .958, was significant. The imager could be a man or a woman, the effect of instructions on memory performance was the same.

Discussion

Our first hypothesis concerned the effect of type of memory strategy (induced by the instructions in the experiment) on recall performance. More specifically, we postulated that memory efficiency increases with the strategies' level of sensorimotor simulation. This hypothesis was generally corroborated.

First, as expected, participants in the VI condition correctly recalled more words than those in the MR condition, which involved little multimodal simulation. This is in agreement with the results of classic studies such as those of [START_REF] Paivio | Imagery and verbal processes[END_REF], as well as more recent ones (e.g., [START_REF] Oliver | False memories and the DRM paradigm: Effect of imagery, list, and test type[END_REF].

Second, as expected, FPI proved to be the most effective strategy of all. Adding the simulation of motor characteristics to purely visual imagery improved its memory benefits. This echoes the embodied cognition literature, which has repeatedly highlighted the fundamental role of action and motor skills in cognition, whether in word recall [START_REF] Engelkamp | Memory for actions: Item and relational information in categorized lists[END_REF][START_REF] Senkfor | Episodic action for real objects: An ERP investigation with perform, watch, and imagine action encoding tasks versus a nonaction encoding task[END_REF] or in conceptual processing [START_REF] Siakaluk | Evidence for the activation of sensorimotor information during visual word recognition: The body-object interaction effect[END_REF].

Regarding TPI, results showed that it did not differ significantly from VI, contrary to predictions. We had expected the performances of participants in the TPI group to lie between those of the VI group and those of the FPI group, but this was not the case. It may be that in the third person, motor imagery is not sufficiently embodied to recruit brain structures that are not directly involved in motor skills [START_REF] Sigiru | Motor and visual imagery as two complementary but neurally dissociable mental processes[END_REF].

Over the longer term, strategies based on imagery (i.e. VI, TPI and FPI) remained more effective than MR. The benefits of motor simulation, however, appeared to fade over time, as the recall performance of participants in the FPI group no longer differed from that of participants in the VI group after 48 hours. This means that the motor motor memory trace had no consolidation advantages over the other conditions.

No particularly salient result pattern was detected for incorrect recall, in contrast to the results of [START_REF] Foley | Imagery encoding and false recognition errors: Exploring boundary conditions of imagery's enhancing effects[END_REF]her colleagues (2006;2009) for imagery instructions. These results are most certainly due to the fact that our experimental protocol was not conducive to the emergence of false memories, unlike the Deese-Roediger-McDermott (DRM) paradigm used by these researchers.

Our second hypothesis concerned the moderation of the association between strategy and recall by visual or motor imagery vividness. Surprisingly, both types of vividness seemed to play only a negligible role. This went against not only our hypothesis, but also what the literature (i.e., [START_REF] Fulford | The neural correlates of visual imagery vividness -An fMRI study and literature review[END_REF][START_REF] Marmurek | Imagery effects in false recall and false recognition[END_REF][START_REF] Palmiero | The format of mental imagery: From a critical review to an integrated embodied representation approach[END_REF] suggests. It may be that the questionnaires we used were not sensitive enough to capture the variability of the vividness level among the participants, thus preventing us from detecting an effect. However, a more likely explanation is that we treated the vividness variables differently. Most researchers studying the role of imagery vividness divide their participants into vividness level groups (high vs. low vividness). In the present study, however, we preferred to leave the vividness variables as continuous variables and not to arbitrarily dichotomize them.

These results point to the existence of a memory efficiency gradient running from lowembodiment (i.e., poor perceptual and/or motor simulation) to high-embodiment (i.e., rich simulation in sensory and motor systems engaged in interactions with the object) strategies. This is a logical follow-on from previous studies (e.g., [START_REF] Engelkamp | Memory for actions: Item and relational information in categorized lists[END_REF][START_REF] Senkfor | Episodic action for real objects: An ERP investigation with perform, watch, and imagine action encoding tasks versus a nonaction encoding task[END_REF] suggesting that there is a gradient of effectiveness in recalling action verbs running from the reading of the verb and then the observation of the action designated by the verb to the actual personal action. More generally, this continuum is in line with embodied and grounded theories (e.g., [START_REF] Barsalou | Perceptual symbol systems[END_REF][START_REF] Barsalou | Grounding conceptual knowledge in modality-specific systems[END_REF]. The recall of concepts related to words requires the simulation of sensorimotor experiences that have contributed to the creation of the meaning of these concepts. In our experiment, mental rehearsal did not favour this type of simulation during encoding. In this case, because there was no explicit perceptual and/or motor simulation instruction, individuals did not intentionally implement this cognitive strategy. The resulting memory trace had few sensory and motor components. By contrast, active visual imagery favoured the emergence of visual experiences, and motor imagery promoted the re-enactment not only of visual experiences, but also of motor (and potentially tactile and kinaesthetic) ones. The intentional cognitive activity of sensorimotor simulation seemed to increase the memory effects of mental imagery compared with other types of imagery.

Through the experimental conditions tested in the present study, we were able to elicit an increasingly rich multimodal simulation with greater probability of word retrieval. The positive effects of the FPI condition could predicted by the more radical embodied theories.

From the sensorimotor perspective (Foglia & O'Regan, 2015) practical sensorimotor knowledge was more accessible in the FPI condition than it was in other the conditions, presumably making it easier to exercise knowledge about how the object should look as a function of movement. During retrieval, this knowledge about the object was presumably more accessible (having been more explicitly exercised during encoding), thus facilitating recall. From the enactive perspective [START_REF] Thomas | Are theories of imagery theories of imagination? An active perception approach to conscious mental content[END_REF][START_REF] Thomas | Mental imagery[END_REF], because it was potentially easier to perceptually explore an object in FPI, it may also have been easier to recreate that exploration when recalling the word associated with the object.

In brief, the embodied cognition paradigm allowed us to shed new light on the links between mental imagery and memory. This study also had the merit of providing original data on different types of imagery and their relative efficiency in terms of memorization.

These results could thus be used to optimize memory strategies, especially in the school context, although the effect on abstract concepts has yet to be ascertained. In our experiment, the word list contained quite concrete words. Although the sensorimotor grounding of mental imagery was found to have an effect on the memorization of these concrete words, results might have been different for more abstract ones. According to the language-and-situatedsimulation theory [START_REF] Barsalou | Language and simulation in conceptual processing[END_REF], the implication of modal systems is not exactly the same for abstract concepts, although in categorization tasks, access to these abstract concepts is facilitated by the level of sensory experiences they produce [START_REF] Zdrazilova | Grasping the invisible: Semantic processing of abstract words[END_REF].

Finally, it should be noted that several experimental modifications will have to be made in order to reproduce and confirm our results. First, many of our participants reported verbally that third-person motor imagery was particularly hard to master. Thus, even if there were motor activations, this difficulty may have reduced the memory benefits of the motor simulation-benefits that could be fully manifested in the first person. It is difficult to determine whether the difference between third-and first-person imagery arose because the former is harder to achieve or because it is less embodied. Second, a number of participants, most of them in the mental rehearsal condition, said that they used other strategies to memorize the words. It is possible that this type of memorization spontaneously encourages people to adopt other, more effective strategies. However, the results of our study show that the chunking strategy they favoured did not actually result in higher scores than those resulting from mental imagery strategies. Finally, some of the objects named in the word list may have been linked to one or more prototypical actions (e.g. reading a book, eating an apple) that conflicted to a greater or lesser degree with the action indicated in the motor imagery instructions. Thus, in the case where the action intuitively related to the object was close to the action indicated in the instruction, the recall of certain words may have been

facilitated. It would be advisable to consider complementing the questionnaires with different metrics of visual and motor imagery skills, such as response times or neurophysiological markers, which would provide information on the nature of the participants' subjective experience. These same neurophysiological measures could also prove useful for verifying the correct execution of the imagery tasks.

Declaration of Competing Interests

The authors declare that there are no conflicts of interest.


Hugo Duwiquet
email: hugo.duwiquet@gmail.com

Laurent Guillou-Frottier

Laurent Arbaret

Mathieu Bellanger

Théophile Guillon

Michael J Heap

Crustal Fault Zones (CFZ) as Geothermal Power Systems: 3D Variation of Permeability and Related Processes

Keywords: 3D permeability variations, THM numerical modeling, high-temperature geothermal energy, Crustal Fault Zone (CFZ)

The Pontgibaud Crustal Fault Zone (CFZ) in the French Massif Central provides an opportunity to evaluate the high-temperature geothermal potential of these naturally permeable zones. Previous 2D modeling of heat and mass transfer in a fault zone highlighted that a subvertical CFZ concentrates the highest temperature anomalies at shallow depths. By comparing the results of these large-scale 2D numerical models with field data, the depth of the 150°C isotherm was estimated to be at a depth of 2.5 km. However, these results did not consider 3D effects and interactions between fluids, deformation and temperature. A combined multidisciplinary approach makes it possible to better constrain the variation of permeability in 3D. This variation is then integrated into 3D numerical modeling. Based on a thermo-poroelastic assumption, a preliminary 3D THM numerical model is presented. A first parametric study highlights the role of permeability, stress direction and stress intensity on fluid flow. In particular, three different convective patterns have been identified: finger-like, blob-like and double-like convective patterns. Finally, a large-scale 3D numerical model of the Pontgibaud CFZ, based on THM coupling and the comparison with field data (temperature, heat flux, electrical resistivity), allows us to observe the convective pattern at the origin of the rise of the 150°C isotherm to economically exploitable depths. This result is obtained for values of permeability, intensity and direction of stresses comparable to the parametric study. Although simplified hypotheses have been used, 3D field data have been reproduced. Finally, we tried to understand the observed effects of poroelasticity on fluid flow.

INTRODUCTION

As potential renewable and economical resources, Crustal Fault Zones (CFZ) remain largely unexplored and therefore unexploited. Widely present on Earth (Scibeck, 2020), these naturally permeable zones have all the characteristics of a potential reservoir for high-temperature geothermal energy and therefore offer significant energy potential over the world. Moreover, these naturally permeable and deep zones would limit the use of hydrofracturing and/or hydroshearing that could induce seismic events that have disrupted geothermal projects or suspended operations [START_REF] Deichmann | Earthquakes induced by the stimulation of an enhanced geothermal system below Basel (Switzerland)[END_REF]Giardini 2009, Evans et al., 2005). Since 2014, TLS-Geothermics, a French company involved in geothermal exploration, has been keen to demonstrate the viability of CFZ as a geothermal exploration play for economic power generation.

This kind of reservoir is currently poorly constrained, probably due to a lack of understanding of the primary geological factors controlling the occurrence of this type of geothermal play. In order to facilitate exploration, it seems necessary to be able to dissociate the key parameters favoring the ascent of hot fluid to economically attractive depths. Previous studies have shown that vertical deep deformation zones, could concentrate the most important temperature anomalies at the lowest depths [START_REF] Duwiquet | On the geothermal potential of crustal fault zones: a case study from the Pontgibaud area (French Massif Central, France)[END_REF][START_REF] Guillou-Frottier | On the morphology and amplitude of 2D and 3D thermal anomalies induced by buoyancy-driven flow within and around fault zones[END_REF]. Our recent results suggest that vertical deformation zones oriented at 30 and 70° relative to maximum horizontal stress could correspond to potential targets for high-temperature geothermal energy [START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF]. Permeability variation in crustal domain has been widely discussed since the 1990s [START_REF] Martel | Formation of compound strike-slip fault zones, Mount Abbot quadrangle, California[END_REF]. Overall, the permeability variation of CFZ is primarily controlled by the coupling between Thermal (T), Hydraulic (H), Mechanical (M), and Chemical (C) processes [START_REF] Horne | Three-dimensional natural convection in a confined porous medium heated from below[END_REF][START_REF] Parry | Pore-fluid chemistry and chemical reactions on the Wasatch normal fault, Utah[END_REF][START_REF] Barton | Fluid flow along potentially active faults in crystalline rock[END_REF]. Permeability can be considered as a static and isotropic parameter in space. Different studies have reproduced field data by considering fixed fault permeabilities around 10 -14 m 2 [START_REF] Guillou-Frottier | Structure of hydrothermal convection in the Upper Rhine Graben as inferred from corrected temperature data and basin-scale numerical models[END_REF][START_REF] Magri | 2D and 3D coexisting modes of thermal convection in fractured hydrothermal systems-Implications for transboundary flow in the Lower Yarmouk Gorge[END_REF]. For large-deformation fault zones field data from the Pontgibaud CFZ have been reproduced by considering a static but variable permeability in different space dimensions. [START_REF] Duwiquet | On the geothermal potential of crustal fault zones: a case study from the Pontgibaud area (French Massif Central, France)[END_REF][START_REF] Scibek | Multidisciplinary database of permeability of fault zones and surrounding protolith rocks at world-wide sites[END_REF][START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF]. However, permeability has been recognized as a dynamic parameter evolving in time and space as a result of the various geological processes [START_REF] Sibson | High-angle reverse faults, fluid-pressure cycling, and mesothermal gold-quartz deposits[END_REF][START_REF] Ingebritsen | Introduction to the special issue on crustal permeability[END_REF].

In this study, we first propose additional field observations to better constrain permeability variation in the three dimensions. This variation in permeability will be integrated into a 3D coupled THM numerical modeling where a thermo-poroelastic hypothesis is assumed. These results will be compared with field data. Our multidisciplinary approach will facilitate the understanding of how fluids can circulate within a naturel system. Finally, a 3D numerical study with THM coupling and dynamic permeability will attempt to approach the different processes that can control the fluids circulation within a fault.

GEOLOGICAL SETTING

The "La Sioule" licence area (black contour in Figure 1) is located to the West of the Limagne graben in the Massif Central (France), in a Paleozoic basement domain and is partially covered by the northern part of the Cenozoic volcanic formations (in blue in Figure 1). It is bounded to the West by the Sillon Houiller fault zone, to the South by the volcanic massif of the Monts Dore, and to the North and East by the granitic massif of Saint-Gervais and the Chaîne des Puys volcanic chain, respectively. Variscan metamorphic formations (ortho and para-migmatites, orthogneiss, paragneiss and mica schists) are mainly present in the area (in green in Figure 1). Carboniferous plutonic rocks are characterized by monzogranite and granodiorite (red in Figure 1) and Viseo-Serpukhovian volcano-sedimentary formations (brown in Figure 1). Upper Pennsylvanian and Permian detritic sedimentary formations mark the late Variscan basins emplaced on the major crustal fault zone.

Bounded to the East and West by the Aigueperse-Saint-Sauves fault and the Sillon Houiller fault, the "La Sioule" licence is largely affected by late Variscan tectonics. The Pontgibaud Crustal Fault Zone is a more than 40 km long system pinched between the Sillon Houiller and the Aigueperse-Saint-Sauves fault zones (Figure 1). The evidence of current fluid circulation is indicated by the presence of springs (Ceyssat and Pranal springs, Figure 1).

Several seismological stress-state evaluations were performed around the studied area. [START_REF] Mazabraud | Evidence for short-scale stress field variations within intraplate central-western France[END_REF] determined that the maximum horizontal stress axis is oriented close to NW-SE. More recently local stress-states evaluated by TLS-Geothermics and processed by MAGNITUDE (a Baker Hughes company) indicated that direction of the maximum stress axes are bracketed between N135° and N150° (for more details see [START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF].

OBSERVATIONS AND MEASUREMENTS OF PERMEABILITY SPATIAL VARIATION (X, Y, Z)

Field, thin-section and X-ray microtomography observations for permeability spatial variations (X, Y)

When examining different outcrops of the Pontgibaud Crustal Fault Zone, all lithologies show a large range of facies from unaltered and undeformed rocks to altered and/or fractured rocks. Breccia, fractured zones, cataclasites and mineralized veins are noteworthy (see Figure 2). These mineralizations are markers of the paleo-circulation of fluids. Samples were acquired from the "Peyrouses 1" borehole located within the Pontgibaud fault system (see Figure 1). Microstructural observations made on thin sections of these samples mainly show fractured and altered facies. Voids are located within the fracture networks (present in red, Figure 2). Some of these fractures are totally sealed, and therefore may provide barriers to fluid flow, while others show voids, thus conferring a potential permeability to the system. We therefore observed evidence for potentially high-and low-permeability zones within the fault system.

Secondary mineralization is present at the borders of voids, thus ruling out the possibility of an anthropogenic origin of these voids during the manufacturing process of the thin sections. At this scale of observation, all the fractures seem to form a dendritic network. This type of network is largely detailed in the literature [START_REF] Reis | Constructal theory: from engineering to physics, and how flow systems develop shape and structure[END_REF][START_REF] Lorenzini | Fin shape thermal optimization using Bejan's constructal theory[END_REF] and would be present in systems with intense fluid circulation [START_REF] Bejan | Constructal theory of generation of configuration in nature and engineering[END_REF].

In order for fluids to circulate, it is necessary that these voids are connected in the three dimensions of space. In order to verify this, the same samples were scanned and analyzed by X-Ray computed tomography at the Institute of Earth Sciences in Orleans (ISTO). The 3D observations (see bottom left in Figure 2) show, in yellow, the walls of mineralizations in which some voids are taken into account and in red the mineralization (here galena (PbS)). The presence of voids is marked at the heart of some mineralizations and at the levels of the mineralization walls. Moreover, these planes seem to be connected in the three dimensions, thus potentially facilitating the fluids circulation.

The conceptual model of [START_REF] Faulkner | A review of recent developments concerning the structure, mechanics and fluid flow properties of fault zones[END_REF] describes damage zones (high permeability zone) and fault cores (low permeability zone). Considering the close correspondence between the variations in potential permeability of the different observations made with the conceptual model of [START_REF] Faulkner | A review of recent developments concerning the structure, mechanics and fluid flow properties of fault zones[END_REF], we propose to integrate this permeability variation into our numerical models along the two axes, x and y (see Figure 2). Equations 1 and 2 include a lateral variation of permeability within the fault zone in order to virtually reproduce the high permeability zones (damage zones) and low permeability zones (fault cores). While this model appears consistent with the model of [START_REF] Faulkner | A review of recent developments concerning the structure, mechanics and fluid flow properties of fault zones[END_REF], other conceptual models of permeability variations in a fault zone may exist [START_REF] Mitchell | Towards quantifying the matrix permeability of fault damage zones in low porosity rock[END_REF]. The latter seems to be better suited to our field data. If the variations along the x and y axes could be constrained, variation along the z-axis and quantification of this range of permeability variation would provide additional qualitative and quantitative information.

Borehole observations and permeability measurements for permeability spatial variations (X, Z)

Sampling was made on different lithological facies present in the "Peyrouses 1" borehole. Permeability measurements have been performed at the Strasbourg Institute of Earth and Environment (SITES), in Strasbourg (France). For more details on the protocol used, see Heap and Kennedy 2016. The averages values of the permeability on intact, fractured, altered, fractured and altered facies are of 2.8 × 10 -16 , 3.9 × 10 -15 , 1.5 × 10 -15 , 3.1 × 10 -13 m 2 , respectively. In order to observe these permeability variations according to the different facies and depth, we have transcribed these average values into a permeability/depth profile (Figure 3). This profile provides additional constraints on the variation of permeability from 0 to 250 m. We can then try to incorporate these permeability variations into our numerical model.

Depth-dependence of permeability follows the equation of [START_REF] Garibaldi | Thermal anomalies and geological structures in the Provence basin: Implications for hydrothermal circulations at depth[END_REF]. This equation makes it possible to consider the effect of compaction on permeability. Local variations in permeability are additionally given by equation 2. By zooming in on the first 250 meters, permeability variations in the order of 10 -16 to 10 -13 m 2 can be observed (Figure 3). This variation is of the same order of magnitude as the one measured in the laboratory. It is not surprising that the permeability variation of the numerical models does not exactly follow the variations present in the borehole. Moreover, the figures do not exactly reflect the exact values, since we have inserted the averages of these measured values. Nevertheless, we will keep the assumption that the general trends are respected.

NUMERICAL MODELING

Numerical simulations were run with Comsol Multiphysics TM software. Here we couple the heat and mass transfers with the poroelastic interface. This interface combines the regular fluid flow formulation with linear elastic solid mechanics of the porous medium matrix. Poroelasticity coupling means that the pore volume fraction can be affected by external stress. Voids filled with fluids change in pressure, resulting in fluid movement. The material will deform elastically as a consequence of this stress and the change in void volume. This interface includes an expression of the stress tensor as a function of the strain tensor and the Biot-Willis coefficient. Details on the used equations used can be found in [START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF].

These numerical models will consist of integrating the observations previously made. First, an idealized and simplified case including different parameters such as the intensity and direction of the stress, or the permeability, will be tested. Particular attention will be paid to the convective pattern. Second, a more realistic model including field data issued from the natural Pontgibaud system will be performed. The results of the numerical modeling will be compared with other field data, and this comparison will allow to identify of convective pattern and its comparison with the parametric study. Stress effects will be observed on the fluid flow. A calibration step will be carried out in order to verify the use of version 5.5 of the Comsol Multiphysics TM code with other numerical codes. Finally, in order to approach the processes at the origin of the modifications in the circulation of fluids, a dynamic function of permeability adapted to fractured media will be integrated.

3D permeability variation

Field and laboratory analyses indicate that the Pontgibaud area has a very high fracture density. By keeping the usual depth-decrease of permeability, a lateral variation can be included, by using the following spatial variation:

𝐾 𝐹 (𝑥, 𝑦, 𝑧) = 𝐾 𝐹0 × 𝑓(𝑧) × 𝑓(𝑥, 𝑦 , 𝑧) (1)
Here 𝐾 𝐹 (𝑥, 𝑦, 𝑧) is the fault permeability (in m 2 ) dependent on the three space directions. 𝐾 𝐹0 is the permeability at the surface, 𝑓(𝑧) is the depth-dependent function and 𝑓(𝑥, 𝑦 , 𝑧) makes the permeability alternate along a sinusoid applied to the three axes of the numerical model, such as:

𝐾 𝐹 (𝑥, 𝑦, 𝑧) = 𝐾 𝐹0 × [𝑒𝑥𝑝 𝑧-800 𝛿 ] × [101 + 100 × sin (2 × 𝜋 × (𝑥+𝑦+𝑧) 𝜆 )] (2)
The term 𝜆 corresponds to the wavelength of the sinusoid. To reproduce rather fine alternations of high and low permeability, as suggested by field and laboratory observations (see Figure 2), a low value (10 -5 ) for the term 𝜆 was chosen [START_REF] Duwiquet | On the geothermal potential of crustal fault zones: a case study from the Pontgibaud area (French Massif Central, France)[END_REF][START_REF] Scibek | Multidisciplinary database of permeability of fault zones and surrounding protolith rocks at world-wide sites[END_REF][START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF]. The length 𝛿 (m) characterizes the intensity of the decrease in permeability with depth, taken here at 2500 m.

Parametric study: effect of stress intensity, stress direction and permeability on fluid flow

We will consider two different numerical experiments. The first considered a very simplified and idealized geometry, where a vertical deformation zone is located in the middle of a basement. We will look at the role of stress intensity and direction as well as permeability on fluid flow and their effects on the intensity and depth of temperature anomalies. To do this, the direction of the deformation zone varies from 0 to 90° (with a 10° step), and the intensity of the main stress varies from 0 to 100 MPa (with a 10 MPa step). The permeability KF0 of the fault varies from 1 × 10 -16 to 4 × 10 -14 m 2 (with a 10 -16 m 2 step). The permeability of the basement will be fixed in all our models at Kb0 = 10 -16 m 2 . (for more details on boundary conditions, see [START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF]. In order to account for both permeability of the fault and of the basement, the R ratio is defined by:

𝑅 = 𝐾 𝑓𝑚𝑎𝑥 𝐾 𝑏0
(3)

This ratio compares the maximum permeability of the fault and of the basement. Other 𝐾 𝑏0 values have been tested but higher values are not realistic and lower values do not change the results detailed below. The purpose of this first step is to unbundle different parameters that may influence the fluid flow.

Three convective patterns are observed: blob-like, finger-like and double-like convective pattern (Figure 4). Each of these patterns can be found for ranges of the tested parameters. Looking at the permeability ratio we find two different convective patterns for the lowest ratios tested R . It would seem that for low permeability ratios, the evolution from a blob-like pattern to a finger-like pattern is controlled by the other parameters, such as the intensity and direction of the stress. With higher permeability ratios R [200-400] we observed only one convective double-like pattern. Thus, it would seem that for high permeability ratios, the intensity and direction of the stress have no effect on fluid flow. This does not seem to be the case for the other two convective patterns.The blob-like convective pattern is obtained for stress intensity values between 1 and 39 MPa and directions between 0 and 50°. We observe finger-like convective pattern for stress intensity values between 40 and 100 MPa and directions between 51 and 90°. Therefore, with a thermo-poroelastic hypothesis and for low permeability ratios, the intensity of a stress and its direction in relation to the deformation zone plays a significant role on fluid flow patterns.

Numerical modeling of a natural system: the case of the Pontgibaud CFZ

The second numerical experiments will involve 3D THM numerical modelling of the Pontgibaud crustal fault zone. Each lithology will be assigned its own physical and thermal properties. Concerning the mechanical boundary conditions, we propose to use in situ measurements from the Chassoles borehole (located 60 km South-East of Pontgibaud). The objective of this second step is to integrate the set of observations and properties specific to Pontgibaud. Whether for the first parametric study or the second study on the Pontgibaud hydrothermal system, the Young's moduli chosen for the basement and deformation zone are 60 GPa and 5 GPa, respectively [START_REF] Cappa | Modeling of coupled deformation and permeability evolution during fault reactivation induced by deep underground injection of CO2[END_REF]. For more details on boundary conditions, geometries and physical properties, see [START_REF] Duwiquet | Crustal Fault Zones (CFZ) as geothermal power system: a preliminary 3D THM model constrained by a multidisciplinary approach[END_REF].

The distinction between these three convective figures can be a determining factor in estimating the volume of the geothermal reservoir. For example, the volume occupied by the blob-like isotherms will be larger than the volume occupied by the finger-like convective pattern isotherms. If we were able to parametrically determine three convective patterns, it would be interesting to compare these results with models of natural systems integrating field and laboratory observations and measurements. 2021). The Pontgibaud system is characterized by a large deformation zone comprising different fault families [START_REF] Duwiquet | On the geothermal potential of crustal fault zones: a case study from the Pontgibaud area (French Massif Central, France)[END_REF]. The observations and field measurements point to a system that allow fluids to circulate to great depths. Numerical modeling of this system shows that for a maximum permeability value imposed within the Pontgibaud fault zone of to 1 × 10 - 14 m 2 , the 150°C isotherm would be at a depth of 2.3 km.

The resistivity profiles established by [START_REF] Ars | Joint inversion of gravity and surface wave data constrained by magnetotelluric: application to deep geothermal exploration of crustal fault zone in felsic basement[END_REF] show a negative resistivity anomaly between 3 and 4 km in depth. This anomaly may be related to the presence of metals, clays, or the presence of hot fluid. Compared to the results obtained with numerical modeling a positive temperature anomaly is estimated at a depth between 2 and 3 km. Moreover, these results show a geothermal gradient of 41°C.km - 1 and a heat flux of 110 mW.m -2 , at the location where they were measured and estimated in the field to be 41.5°C.km -1 and 110 mW.m - 2 .

This 150°C rise in the isotherm (Figure 5B) is the consequence of fluid ascending to the center of the Pontgibaud CFZ and descending at its extremities. This convective pattern was defined in the study as the blob-like convective pattern (see Figure 4). This convective pattern was, in the parametric study, obtained for permeability ratios R[1-200], stress intensities below 39 MPa, and an orientation with respect to the main stress between 0 and 50°. When comparing these three parameters, the convective pattern observed in the numerical model of the Pontgibaud area is comparable with the result from the parametric study.

Hence, in these two first approaches, we distinguished three different convective pattern, which we were able to compare to a natural system constrained by field data. However, no process was demonstrated that could explain for example the origin of the difference between the blob-like and finger-like convective pattern. We will start by checking the code of Comsol Mulitphysics TM version 5.5 with the OpenGeoSys codes [START_REF] Magri | Thermal convection of viscous fluids in a faulted system: 3D benchmark for numerical codes[END_REF] as well as version 3.5a of Comsol Multiphysics TM [START_REF] Guillou-Frottier | On the morphology and amplitude of 2D and 3D thermal anomalies induced by buoyancy-driven flow within and around fault zones[END_REF].

Variation of fault permeability with a thermo-poroelastic assumption

In order to try to understand the processes that can act on the fluids flow (see Figure 4), we will integrate a relationship between porosity and permeability. For this, the Kozeny-Carman relationship in which permeability is proportional to the cube of porosity does not seem appropriate for fractured systems. Based on empirical work, [START_REF] Parisio | The risks of long-term re-injection in supercritical geothermal systems[END_REF] make a link between a permeability of a fully fractured system kf with a permeability of an intact system ki and the porosity n. This relationship is written in the form:

log 𝑘 = (1 -𝜔)𝑙𝑜𝑔𝑘 𝑖 + 𝜔𝑙𝑜𝑔𝑘 𝑓 (4)
With 𝑘 𝑖 = 4.979 × 10 -11 𝑛 3.11 (5) and 𝑘 𝑓 = 1.143 × 10 -11 𝑛 0.64 (6)

In this relation n is the porosity (n = 0.1) and ω is a parameter representing a fully fractured system (ω = 1), or an intact system (ω = 0).

Here ω = 0.8 (for more details see [START_REF] Parisio | The risks of long-term re-injection in supercritical geothermal systems[END_REF].

We will impose an arbitrarily chosen stress of 15 MPa, on the side of the cube. By its application and its intensity, this boundary condition does not transcribe the natural evolution of the constraint with depth. It could nevertheless allow us to consider the first order effects of this stress on permeability. The results of the numerical experiments show no permeability variation within the basement, which remains fixed at 10 -16 m 2 . Within the fault, for a compressive boundary condition, the permeability is 10 -13,005 m 2 at the extremities of the fault and 10 -13,008 m 2 at the center of the fault. For an extensive boundary condition, the permeability at the extremities of the fault is 10 -12,995 m 2 and the permeability at the center of the fault is 10 -12,997 m 2 . The consequence of applying a 15 MPa compressive stress will slightly decrease the permeability.

Conversely, the application of a 15 MPa stress in extension will slightly increase the permeability.

This different response of permeability to the stress application can be explained by the difference in Young's modulus. As in other numerical models, the value of 60 GPa is imposed to the basement and 5 GPa to the fault [START_REF] Cappa | Modeling of coupled deformation and permeability evolution during fault reactivation induced by deep underground injection of CO2[END_REF]. The response to the mechanical effects of permeability may then be greater in the fault than in the basement. In the fault, the results of this variation in permeability may be the consequence of compression or stretching of the porosity.

In a natural case, the variation in permeability in the interseismic phase varies by 25% around 4×10 -14 m 2 (Ma et al., 2019). Here we can see with a thermo-poroelastic hypothesis a variation in permeability of less than 1%. At this stage, the question that can be asked is whether this tiny variation can have a role on fluid circulation. Even if these mechanical boundary conditions are not legitimate in a natural system, where the stress decreases with depth, it does allow a small variation in permeability to be highlighted when a stress is applied.

CONCLUSIONS AND PERSPECTIVES

Observations and measurements, both from the field and the laboratory constrained the permeability variations imposed in the numerical models. These observations highlight succession of high permeability and of low permeability zones. This variation in permeability within CFZ corresponds to the conceptual model of [START_REF] Faulkner | A review of recent developments concerning the structure, mechanics and fluid flow properties of fault zones[END_REF], in which they present a variation in the space of the damage zone (high-permeability) and fault core (low-permeability). These observations, related to a conceptual model, allow us to constrain the lateral variations in permeability. The average values of laboratory permeability measurements made on the different lithologies present in the Peyrouses 1 borehole vary from 2.8×10 -16 to 3.1×10 -13 m 2 . The transcription of these values within the borehole allowed us to constrain the permeability variation with depth. Finally, through observations and measurements, we were able to constrain the permeability variations of a CFZ modelled with Comsol Multiphysics TM in all three spatial dimensions. On the basis of a thermo-poroelastic hypothesis, the first step of the numerical modeling consisted of dissociating the role of permeability, intensity and direction of a stress on fluid flow. After more than 2,500 runs, three convective forms were observed: the blob-like convective pattern, the finger like and the double like convective pattern. The shape of these convective patterns can have an significant impact on the volume of the geothermal reservoir. At this stage, the second step was to model a natural system in order to see if, by integrating values of permeability, intensity and direction of stress, the convective patterns observed by the parametric study could be found. The blob like convective pattern is found on the result of the large-scale numerical modeling, for values of permeability, intensity and direction of stress consistent with the ranges obtained during the parametric study. By an upward movement of the fluids at the center of the system, this convective pattern moves up the 150°C isotherm to a depth of 2.3 km. Although it was possible to reproduce field data from this numerical modeling, it did not allow us to understand the observed effect of the application of a stress on the circulation of fluids.

In order to understand possible processes at work we calibrated our numerical models and then considered that they no longer have a static (even if variable in the three dimensions of space) but dynamic permeability adapted to fractured mediums. When a simplified horizontal stress is applied, we observe a permeability variation of less than 1%. Futher studies will decipher whether this small variation could cause changes in convective patterns.

Figure 1 :

 1 Figure 1: Geological and geothermal features in the "La Sioule" licence area (black contour), French Massif Central (FMC). Heat flow and geothermal gradient (red crosses) are from, Lucazeau and Vasseur (1989), International Heat Flow Commission. Heat production (is from Lucazeau, 1981) and resistivity profile (black dashed line) from Ars et al. (2019). P: Pontgibaud. LG: La Goutelle. V: Villelongue. T: Tortebesse. Coordinate system: WGS84 Pseudo-Mercator EPSG: 3857 (After the 1/50,000 th geological map published by BRGM). Modified after Duwiquet et al. (2019, 2020).

Figure 2 :

 2 Figure 2: Field and laboratory observations (left). Incorporation of the multiple fault core conceptual model (Faulkner et al., 2010) within numerical modelling done with Comsol Multiphysics TM (right). The resolution of the microtomographic image is 10 𝝁𝒎.

Figure 3 :

 3 Figure 3: Variation in permeability along the x and z axes and comparisons with the average permeability value of samples representing different facies taken from the Peyrouses 1 borehole (see location Figure 1).

Figure 4 :

 4 Figure 4: Results of the parametric study. On the whole of the calculations made (n > 2,500) three convective patterns are observable: the blob-like, the finger-like and the double-like patterns. These three patterns depend on parameters such as permeability ratio, direction and intensity of the stress.

Figure 5 :

 5 Figure 5: [A] Synthesis of field observations and numerical experiments. The Pontigbaud CFZ is a large deformation zone whose geophysical data (Ars et al., 2019) show deep rooting. [B] The results of the numerical experiments and the comparison with the geothermal gradient and heat flow show that a blob-like fluid circulation would be effective within the Pontgibaud CFZ.

Figure 6 :

 6 Figure 6 : Benchmarking of our numerical experiments with the OpenGeoSys code (Magri et al., 2017) and Comsol Mulitphysics TM V3.5a (Guillou-Frottier et al., 2020).

Figure 7 :

 7 Figure 7 : Permeability variation within the basement and fault for compressive and extensive boundary conditions (+/-15 MPa).