Oriane Vetier

Marie-Alice Yanni

Linda Lassel

Helene Isly

Alain Beuchée

Nyangoh Krystel

Vincent Timoh

Rémi Lavoué

Maela Béranger

Le Lous

H Él Ène Isly

Alain Beuchee

Krystel Nyangoh-Timoh

Vincent Lavoue

R Émi Beranger

MD Maela Le Lous
email: maela.le.lous@chu-rennes.fr

Oriane Vetier¹

Marie-Alice Yanni¹

Linda Lassel¹

Hélène Isly¹

Rémi Beranger

Assessment of compliance with a color code protocol for non-elective cesarean section and its impact on time to delivery interval and neonatal outcomes

Keywords: 2985, Figures count : 2, Tables count : 4 Cesarean section, color code protocol, decision-to-delivery interval, timeframe, maternal outcomes, neonatal outcomes

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Cesarean section is one of the most frequent surgical procedures performed in the world and represents 21.4% of all births in France in 2021 [1,2]. Emergency cesarean sections may occur in different clinical situations with varying degrees of emergency [START_REF] Lucas | Urgency of caesarean section: a new classification[END_REF]. Many studies have tried to find the acceptable time frame for an emergency cesarean section, but there is no international consensus to date [START_REF] Grobman | The Association of Decision-to-Incision Time for Cesarean Delivery with Maternal and Neonatal Outcomes[END_REF]. Some national multidisciplinary guidelines advocate an acceptable decision-delivery interval, such as in the United Kingdom or Germany [START_REF] Overview | Caesarean birth | Guidance[END_REF][START_REF] Hillemanns | Emergency cesarean section--organization and decision-delivery time[END_REF].

In France, Dupuis et al. developed a tool to classify emergency cesarean sections in 2000 [START_REF] Dupuis | Red, orange and green Caesarean sections: a new communication tool for on-call obstetricians[END_REF]. This tool is based on medical indications identified by Lucas et al and includes three color code categories [START_REF] Lucas | Urgency of caesarean section: a new classification[END_REF][START_REF] Rudigoz | Non elective cesarean section: use of a color code to optimize management of obstetric emergencies[END_REF]:

-Green: Non-urgent cesarean section with a decision-delivery interval ≤1 hour.

-Orange: Urgent cesarean section with a decision-delivery interval ≤30 minutes.

-Red: Cesarean section to be performed in extreme emergency with a decision-delivery ≤15 minutes.

The aim of this study was to evaluate compliance with the color code protocol in terms of indication and decision-delivery intervals since its implementation in our maternity ward in 2014, and its impact on maternal and fetal outcomes.

Methods

Design of the study

This was a single-center retrospective study conducted in the maternity unit of Rennes University Hospital, France. This maternity unit is a tertiary maternofetal center with neonatal intensive care facilities and performs around 3700 deliveries per year, 19% of which are cesarean deliveries, and 13.5% non-elective cesarean sections.

Population

The patient inclusion period was from January 1, 2015 to December 31, 2018. The inclusion criteria were: women who underwent a non-elective cesarean section at >24 weeks of gestation, with no documented opposition to participate in research. Patients received a letter to inform them that their data would be collected and if they wanted, they could oppose to the data collection. The exclusion criteria were: patients undergoing elective cesarean section, women who were under legal protection. "A sample size of 200 patients per year was estimated to be enough to draw conclusions about our adherence to the protocol, considering a compliance from 20% in 2015 to 80% in 2018, and considering there were 4 groups (2015, 2016, 2017 and 2018). A random-draw was conducted to select 201 patients per year".

Protocol

The obstetric team consists of five delivery room midwives, one obstetrician, two obstetric interns, one anesthetist and one anesthetist intern on site, and a pediatrician. The labor ward is composed of 14 delivery rooms and three operating theatres specifically designated for cesarean sections.

A written color code protocol according to Dupuis et al was introduced in our maternity ward during year 2014 [START_REF] Rudigoz | Non elective cesarean section: use of a color code to optimize management of obstetric emergencies[END_REF]. It defines indications for each color code, the decision-delivery interval for each color, and the role per color code of each member of the team. The green code corresponds to non-urgent cesarean section with a decision-delivery interval ≤1 hour (labor arrest ; labor induction failure) ; orange corresponds to urgent cesarean sections with a decisiondelivery interval ≤30 minutes (failed instrumental delivery, fetal heart rate abnormalities) and red code is used only when cesarean sections have to be performed in extreme emergency with a decision-delivery interval ≤15 minutes (cord prolapse, fetal bradycardia ; suspicion of placental abruption or uterine rupture, or profuse placental hemorrhage). If another issue come out, not included in the protocol, the obstetrician is free to grade the color according to his beliefs and deliver the baby in the corresponding time.

Data collected

The data were collected from medical digital files via DxCare® software, using the keywords "cesarean section during labor -laparotomy" and "emergency cesarean section except labor-laparotomy" and, if necessary, from paper files including the partogram.

The clinical data collected were: maternal age, pre-pregnancy body mass index (BMI)

[weight in kg/size² in metres], gravidity, parity, uni-or multi-scarred uterus. Obstetric data collected were: gestational complications and their type, type of pregnancy (single or multiple), occurrence of fetal death in utero or therapeutic termination of pregnancy, gestational age at which cesarean section was performed, occurrence during labor, and labor induction. Peroperative data comprised: incision time, the surgical technique used, possible presence of surgical difficulties, the occurrence of postpartum hemorrhage (defined by the presence of blood loss >500 mL), total peroperative blood loss (quantitative measurement), and surgery duration.

The following data on anesthesia were also collected: epidural anesthesia administered prior to cesarean section, type of anesthesia performed during the cesarean section, any changes in anesthesia during cesarean section and their reasons.

Neonatal data collected included: birth weight, sex of child, arterial pH and arterial lactates collected from the cord after birth, Apgar score at 1, 5 and 10 minutes, the need for neonatal resuscitation, the need for hospitalization in the neonatal unit including the reason and duration, and the occurrence of a neonatal death. Post-operative maternal data collected were: length of stay, maternal postpartum anemia (defined by hemoglobinemia below 11 g/dL), the need for transfusion, maternal complications and their type (venous thromboembolic event, surgical site infection, hemorrhagic complication, digestive or bladder), and the need for surgery.

To assess protocol compliance the color code indicated by the on-call obstetrician was noted for each patient, as well as the indication for the cesarean section mentioned in the cesarean section report. Based on this information, we checked that the color code was in line with the indication according to the protocol. We also noted any lack of mention of a color code in the file. In the event of non-compliance with the protocol or the absence of mention of a color code, we allocated a code according to the indication noted on the operational report. The decision-delivery interval was calculated by calculating the time between the decision to perform a cesarean section and the time of delivery. Compliance with the decision-delivery interval was verified according to the color code used by the on-call team.

Primary outcome

The primary outcome was compliance with the protocol, i.e. the use of the appropriate color code for the indication of cesarean section and compliance with the decision-delivery interval imposed by the protocol.

Four situations were identified in the event of non-compliance with the protocol:

-Color code used did not correspond to that proposed by the protocol for a given indication.

-Decision-delivery interval greater than that indicated in the protocol.

-Simultaneous presence of the two situations mentioned above (total non-compliance with protocol)

-No mention of a color code or time of decision in the medical file, whether computerized or paper ("missing data" group).

Based on these five situations, we categorized patients into five categories to make it easier to read the results:

-

Results

A total of 1 971 patients underwent a non-elective cesarean section between January 1, 2015 and December 31, 2018. Of these, 201 patients were randomly selected for each year, corresponding to 800 patients included in the study (four patients excluded due to missing files). The details of patient selection can be seen in the patient flow chart (Figure 1).

Population Characteristics

Table 1 presents the characteristics of the overall population and per year. There was no significant difference between the years except for primiparity, a history of scarred uterus, and cesarean section during labor. Overall, 250 of the 800 cesarean sections were coded green (31.3%), 263 orange (32.9%), and 85 red (10.6%). For 202 patients (25.3%), the color code was missing from the medical record, whether computerized or paper. Between 2015 and 2018, the number of patients for whom a color code was not mentioned in the file decreased significantly (p<0.0001). These were mainly for green and orange code cesarean sections, for which the number increased significantly over the years (p < 0.0001), as presented in Table 1. Conversely, there was no significant difference over time in the number of red code cesarean sections.

Results on the primary outcome

Between 2015 and 2018, there was a significant decrease in patients with missing data (p < 0.0001) and a significant improvement in full compliance with the protocol (p < 0.0001).

For patients for whom the color code was inappropriate (patients belonging to categories 3 and 4, i.e. 69 patients in total), 15.9% were under-evaluated according to the clinical situation (reassessed color code required faster management). Figure 2 shows how compliance with the protocol changed from 2015 to 2018. The color chosen by the obstetrician was correct in 96.0%

of the green codes, 82.5% of the orange codes, and 80.2% of the red codes. There was significant agreement between the initial color code and the re-evaluated color code for each of the 3 color codes with a global Kappa match test of 0.82 (0.79 -0.87).

Table 2 presents the mean decision-delivery interval based on the color code and year. There was no significant difference between the years on the decision-delivery interval regardless of the color code used. The rate of compliance of red code cesarean sections (with a decision-delivery interval of ≤15 mins) was 85.9% and increased significantly over the years to 100% in 2018 (p = 0.0020).

Most of the missing data was for color code only (83.6% of patients). For these patients, the decision-delivery interval was met for 73.7% after re-evaluation of the color code (using the indication noted on the operating report). When the decision-delivery interval was missing but the color code present, the color code was in line with the indication for 69.2% of the patients.

Outcomes of red code cesarean sections

Over the study period, 86 patients received a red code cesarean section for the following Most of the red code cesarean sections were therefore performed for actual red code indications. However, 17 patients (19.8%) received a red code cesarean section while the indication corresponded to a different code: 16 patients with an indication corresponding to an orange code, and one patient with an indication corresponding to a green code (forehead presentation for a first twin). One patient had an indication not mentioned in the protocol (cervical retraction after birth of first twin).

Data on red code cesarean sections are presented in Table 3. The mean decision-delivery interval decreased over the years without reaching significance (from 13.6 ±5 min to 11.0±2.2 min, p=0.05). There was a significant improvement in the compliance with the 15minutes decision-delivery interval imposed by the protocol, reaching a 100% compliance in 2018 (p = 0.0020).

Neonatal Results

Neonatal results are presented in Table 4. Arterial pH was missing for 54 newborns and therefore not included in the arterial pH results.

There was a significant increase in mean pH at birth over the years (p = 0.0114) but no significant difference in the number of infants with an arterial pH <7. Eight neonatal deaths were recorded: five newborns died from severe complications linked to prematurity (necrotizing enterocolitis or severe bronchopulmonary dysplasia); three of complications related to neonatal acidosis; two of complications related to severe sepsis due to an intrauterine infection; and one of malformations in relation to maternal type 1 diabetes.

Maternal Complications

Maternal complications are presented in Table 4. Total operating blood loss was 434.7 ± 322 mL. The mean surgery duration was 41.2 ± 14.1 minutes. The overall postpartum hemorrhage rate was 36.4%, and 9.1% cases of postpartum hemorrhage over 1L were noted. There was no significant difference over the years in the rate of postpartum hemorrhage, whether severe or not. Five per cent of patients received a transfusion (globular or platelet). The mean length of hospitalization was 6.3 ± 2.7 nights. The rate of post-operative infection was 3% with no significant difference between years. The surgical revision rate was 1.5%. Only one patient had a venous thromboembolic complication consisting of a pulmonary embolism.

Anesthesia Results

Red codes were mostly done under general anesthesia (n=57, 66.2%) or epidural anesthesia when it was already on the patient (n=28, 32.6%) and spinal anesthesia were sparse (n=1, 1.2%). On the contrary, green and orange codes were mostly under locoregional anesthesia, and rarely under general anesthesia (n=6 (2.4%) and n=14 (5.3%) respectively).

There was no significant difference in the number of conversions to general anesthesia in the color code groups (from 8.4% for green codes to 10.5% for red codes, p=0.3). Lack of analgesia was the main reason for conversion to general anesthesia (61 patients, i.e.

85.9%

). Four patients received general anesthesia due to hemodynamic instability during cesarean section (occurrence of a uterine artery injury). Four patients developed a complication of epidural anesthesia requiring general anesthesia. Two patients underwent general anesthesia after failure of epidural anesthesia.

Discussion

Principal findings

Full compliance with a color code protocol for non-elective cesarean sections improved significantly between 2015 and 2018 in our maternity ward to reach a rate of 76.5% in 2018 (p < 0.0001) and 100% for red codes. There was also a significant decrease in the number patients with missing data in their medical records, with only 3.5% of data missing in 2018 compared to almost 27% in 2015 (p < 0.0001).

Results in the context of what is known

Several studies have studied the clinical impact of this color code protocol on the decision-delivery interval since its introduction in 2014. They have shown that color coding optimizes the organization and communication in the team regardless of the type of structure [START_REF] Linck | Emergency caesarean sections in primary care maternity: Impact of a color code[END_REF][START_REF] Benazza | Impact of establishment of a color code in emergency caesareans in secondary health care maternity[END_REF][START_REF] Mitouard | Decisiondelivery intervals: Impact of a colour code protocol for emergency caesareans[END_REF][START_REF] Bidon | Retrospective cohort study of decision-to-delivery interval and neonatal outcomes according to the type of anaesthesia for code-red emergency caesarean sections in a tertiary care obstetric unit in France[END_REF][START_REF] Deltombe-Bodart | Compliance to the color codes protocol according to the indication of cesarean and to the decision-to-delivery interval[END_REF]. Indeed, in the absence of a protocol, it is difficult to meet the recommended decisiondelivery intervals.

Clinical implications

Red codes time to delivery delay of 15 minutes might appear very short and is not recommended by other guidelines [START_REF] Overview | Caesarean birth | Guidance[END_REF]. However, we observed a significant increase in compliance with the protocol for red code cesarean sections to reach full compliance in 2018 (p = 0.0020).

The mean decision to delivery interval in 2018 for red codes reached 11 ± 2.2 minutes. Most of the red codes were under general anesthesia (66.2% in the four years). However, it is also possible to perform a red code under epidural, adapting epidural shortly after the decision.

About orange codes, 13 out of 72 (18%) of orange codes in 2018 were out of delay. Three of them are because of surgical difficulties, one because of long patient transportation, two because of anesthesia difficulties. For the seven others, the decision to delivery interval was 31 or 32 minutes. The mean decision to delivery interval for orange code cases with non-compliance was 38+-8 minutes.

Despite better compliance with the decision-delivery interval imposed by the protocol, there was no significant difference in neonatal morbidity over the years. The study was not powered to demonstrate this point. Even if a trend toward improve neonatal outcomes was observed, it is impossible to show it is related to the adherence to the protocol. A literature review by Pierre et al. reported that the pathology leading to emergency cesarean section may outweigh the neonatal prognosis over the adherence to a short decision-delivery interval [START_REF] Pierre | Emergency caesarean delivery: is there an ideal decision-to-delivery interval?[END_REF]. The implementation of this protocol still shows a reduced number of missing data in the operative reports, which is crucial considering the importance of information tracing. Additionally, even if our study was not designed to address this point, no increase in maternal morbidity was noticed due to the rapid DDI in emergency situations.

Our study revealed that some indications of non-elective cesarean sections did not appear in the protocol. These non-protocol indications included preeclampsia, HELLP syndrome, intrauterine infection, and maternal shock, pathologies which do not necessarily require a cesarean section depending on the severity of the pathology. This underlines one of the limitations of the protocol in that a specific color code is not always adequate. It is important thus to remember that while such a protocol assists decision making in current practice, it is crucial to adapt management to each clinical situation for optimal outcome.

Research Implications

This study is a quality care and certification program to evaluate the communication code use in a team, to evaluate the traceability of the strategy and its consequences. It appears that it may be important to do this evaluation daily. Our protocol may enhance discussion with a common language within a multidisciplinary team in an emergency situation, even if it is difficult to establish an ideal decision-to-delivery interval that is applicable to all teams. Communication inside the teams will be investigated in further studies.

Also, to improve protocol compliance, it would be interesting to study the elements that lead to non-compliance and thus improve our decision-delivery interval. In some studies, these elements appear to be the time between the decision to perform a cesarean section and entry into the operating room, organizational deficiencies, or anesthesia difficulties [START_REF] Pierre | Emergency caesarean delivery: is there an ideal decision-to-delivery interval?[END_REF]. Protocol compliance could also be improved by team simulation training which has been shown to be effective in improving the management of many pathologies in obstetrics, especially when requiring coordinated teamwork [START_REF] Siassakos | Retrospective cohort study of diagnosis-delivery interval with umbilical cord prolapse: the effect of team training[END_REF][START_REF] Fuhrmann | Multidisciplinary team training reduces the decision-to-delivery interval for emergency Caesarean section[END_REF][START_REF] Van De Ven | Re-ducing errors in health care: cost-effectiveness of multidisciplinary team training in obstetric emergencies (TOSTI study); a randomised controlled trial[END_REF].

Strengths and limitations

The main strength of our study is the large patient sample which ensures robustness of the results on the main judgment criterion. Our population of 800 patients undergoing nonelective cesarean section is one of the largest series studying color codes in this setting. On the other hand, a higher power would have been required to demonstrate the decrease in the rate of per-partum asphyxia following the implementation of the protocol. The main weakness of our study lies in its retrospective design implying the usual biases inherent to this type of study mainly due to missing data. It is more than possible that some data, such as the color code, were announced orally at the time of the cesarean section decision but not recorded in the medical records. A prospective study would help to overcome this bias and to assess current practices as accurately as possible.

Conclusion

We observed an improvement of full compliance with the color code protocol over the years (appropriate color code and decision-to-delivery interval). The implementation of such a protocol in our maternity also contributed to reduce missing data. The ensuing decrease in the rate of per-partum asphyxia remains to be demonstrated.

Legends tables and figures

 Figures Figure 1.  Tables Table 1. Characteristics of the general population per year. Table 2. Mean decision-delivery interval per year and color code. Table 3. Outcomes for red code cesarean sections.

Category 1 :- Category 5 :

 15 Full compliance with protocol -Category 2: Decision-delivery interval greater than that indicated by the protocol -Category 3: The color code used did not match that provided by the protocol -Category 4: Non-compliance with the protocol in both cases (inappropriate color code and decision-delivery interval greater than the maximum time imposed by the protocol) Missing data (decision time and/or color code not mentioned in medical record) Statistical analysis Quantitative variables are described as follows: N, mean -standard deviation, minimum -Q1 -median -Q3 -maximum. For qualitative variables, the effective (N) and the percentage (%) are presented for each modality. To compare the different populations (years 2015, 2016, _2017 and 2018), the following statistical tests were used: Fisher (F) test for qualitative parameters and Kruskal-Wallis (KW) test for quantitative parameters. In case of p < 0.05, 2 to 2 tests with a correction of the threshold of significance according to the method of Bonferroni (for Fisher) or Dwass, Steel, Critchow-Fligner (for Kruskal-Wallis) were carried out. The analyses were carried out with the SAS software, version 9.4.

  Patients flow chart.

Figure 2 .

 2 Figure 2. Change in the compliance with the protocol from 2015 to 2018.

Table 4 .

 4 Maternal and neonatal outcomes.

	Evolution of compliance with the protocol from 2015 to 2018
	90.00%
	80.00%
	70.00%
	60.00%
	50.00%
	40.00%
	30.00%
	20.00%
	10.00%
	0.00%
	2015	2016	2017	2018
	Full compliance with the protocol
	Adapted color code but decision-delivery interval not respected
	Inadequate color code but decision-delivery interval is respected
	Total non-compliance with protocol
	Missing data

Table 1 .

 1 Characteristics of the general population per year

		population	2015	2016	2017	2018	p
		n = 800
			n = 201	n = 198	n = 201	n = 200
	Age (years)	31.2 ± 5.9 30.8 ± 5.9 31.4 ±5.4 30.5 ±6.3 31.9 ±5.7 0.07
	BMI	25.5 ±5.9	24.8 ±5.5 25.9 ±6.9 25.3 ±5.4 25.8 ±5.8 0.24
	Primiparous	405	101	94	122	88	0.006
		50.6 %	50.2%	47.5%	60.7%	44%
	Scarred uterus	230	55	58	44	73	0.01
		28.8%	27.4%	29.3%	21.9%	36.5%
	Therapeutic termi-	4	1	2	0	1	0.43
	nation of preg-nancy or fetal	0.5%	0.5%	1%	0%	0.5%
	death in utero
	Cesarean section	658	168	172	149	169	0.005
	during labor	82.3%	83.6%	86.9%	74.1%	84.5%
	Induction of labor	317	67	87	89	74	0.06
		36.9%	33.3%	43.9%	44.3%	37.0%
	Gestational Age	38.3 ±3.5	38.5 ±3.6 38.6 ±3.1 38.0 ±3.8 38.1 ±3.6 0.25
	(WG)

Legend : BMI : body mass index. Results expressed on mean ±standard deviation and n (%), significant results in bold.

Table 2 .

 2 Mean decision-delivery interval per year and color code

		Global pop-	2015	2016	2017	2018	p
		ulation
		n = 586	n = 71	n = 139	n = 184	n = 192
	Green codes	n = 243	n = 7	n = 53	n = 79	n = 104	0.48
	DDI (minutes)	51.1 ±35.5	38.7 ±15.8	48.8±34.6	51.5±33.3	52.9±38.6
	Respect for DDI	194	6	43	62	83	0.31
	≤60 minutes	79.8%	85.7%	81.1%	78.5%	79.8%
	Orange Codes	n = 258	n = 40	n = 63	n = 83	n = 72	0.31
	DDI (minutes)	26.6 ±10.5	28.6±14	25.3±7.4	28±12	25±8.2
	Respect for DDI	200	30	50	61	59	0.60
	≤30 minutes	77.5%	75%	79.4%	73.5%	81.9%
	Red Codes	n = 85	n = 24	n = 23	n = 22	n = 16	0.05
	DDI (minutes)	12.6±3.5	13.6 ±5	13.3±2.4	11.8±3	11±2.2
	Respect for DDI	73	15	21	21	16	0.002
	≤15 minutes	85.9%	62.5%	91.3%	95.5%	100%
	Legend : DDI: decision-delivery interval (in minutes)

Results expressed by mean ± standard deviation and effectives n(%), significant results in bold.

Table 3 .

 3 Issues of red code cesarean sectionsLegend : DDI: decision-delivery interval. Respect of DDI for the red code cesarean is defined by a delay between decision of cesarean and birth less than 15 minutes.Results expressed on mean -standard deviation and n (%), significant results in bold.

		Global	2015	2016	2017	2018	p
		population
		n = 86	n = 24	n = 24	n = 22	n = 16
	Justified red code indication	69	18	20	15	16	0.06
		80.2%	75%	83.3%	68.2%	100%
	Mean DDI (in minutes)	12.6 ±3.5 13.6 ±5 13.3 ±2.4 11.8 ±3 11 ±2.2	0.05
	Respect of DDI	73	15	21	21	16	0.002
	≤15 minutes	85.9%	62.5%	91.3%	95.5%	100%
	Type of anesthesia:						0.72
	-Epidural anesthesia	28	10	6	8	4
		32.6%	41.7%	25%	36.4%	25%
	-Spinal anesthesia	1	0	1	0	0
		1.2%	0%	4.1%	0%	0%
	-General anesthesia	57	14	17	14	12
		66.2%	58.3%	70.9%	63.6%	75%
	Arterial pH <7	n = 77	n = 18	n = 22	n = 22	n = 15	0.71
		11	4	3	2	2
		14.3%	22.2%	13.6%	9.1%	12.5%
	Apgar score <7 at 5 minutes	16	4	5	5	2	0.89
		18.6%	16.7%	20.8%	22.7%	12.5%
	Neonatal death	4	1	1	2	0	0.77
		4.7%	4.2%	4.2%	9.1%	0%

Table 4 .

 4 Changes in maternal and neonatal issues over the years Legend : WG: weeks of gestation, neonatal death: death of a newborn in the first 28 days of life (Source INED). mL: milliliters; PPH: postpartum hemorrhage. Results expressed on mean -standard deviation and n (%), significant results in bold.

		Global	2015	2016	2017	2018	p
		population	n = 201	n =198	n = 201	n =200
		n = 800
	Fetal outcomes
	Mean birth weight
	(grams)	3028±880	3076±	3070±809	2985±	2982±	0.56
			878		916	915
	Prematurity	185	43	42	53	47	0.51
	(<37WG)	23.1%	21.4%	21.2%	26.4%	23.5%
	Mean arterial pH	7,219 ±	7.202 ±	7.206 ±	7,231 ±	7,235 ±	0.01
		0.120	0.121	0.121	0.117	0.120
	Arterial pH <7	37	13	8	8	8	0.48
		5.0%	7.1%	4.5%	4.1%	4.2%
	Apgar at 5 minutes <7	63	19	15	21	8	0.08
		7.9%	9.5%	7.6%	10.4%	4.0%
	Hospitalization in neo-	238	60	58	66	54	0.64
	natal unit	29.8%	29.9%	28.4%	32.8%	28.0%
	Neonatal death	11	5	3	2	1	0.36
		1.4%	2.5%	1.5%	1.0%	0.5%
	Maternal outcomes
	Total blood loss during	434.4± 322 442.5±	485.9±	430±327 379.8±	0.01
	cesarean section (in		302	351		300
	mL)
	Surgery duration (in	41.2±14.1	42.2±	42.8±15	40.8±	38.9±1	0.02
	minutes)		13.8		14.7	2.8
	PPH	272	76	70	65	61	0.42
		34.0%	37.8%	35.4%	32.3%	30.5%
	Severe PPH	72
		9.0%

Acknowledgements

The authors would like to thank all participants in this study, Felicity Neilson for English editing.

Disclosure of interest

The authors report no conflict of interest. Funding : None.

Ethics

The local ethics committee approved the study (Reference: 20.119).

Ethics Approval

The local ethics committee approved the study (Reference: 20.119)


J.-P Montagner

G Burgos

Y Capdeville

E Beucler

A Mocquet

The mantle transition zone dynamics as revealed through seismic anisotropy

Keywords: Anisotropy, Surface waves, Tomography, Mantle Transition Zone 1 INTRODUCTION: TRANSITION ZONE STRUCTURE AND ANISOTROPY

The mantle transition zone (MTZ) of the Earth lies between 410 and ∼1000 km in depth and has a key role in mantle convection processes. In particular, the discontinuity at 660 km and its associated endothermic mineralogical transformation can slow or inhibit the passage of matter between the upper and lower mantle. The MTZ thus acts as a boundary layer within the mantle. The depth variations of radial and azimuthal seismic anisotropies enable the detection of boundary layers within the mantle. However, the 3D imaging is difficult due to the lack of sensitivity of surface waves of fundamental modes, and the poor global coverage of this depth range by body-wave data. We present a new 3D general anisotropy model (both radial and azimuthal anisotropies) of the mantle down to 1200 km in depth using surface-wave overtone datasets. We find that there is little seismic anisotropy in most of the MTZ, except below subduction zones around the Pacific Ocean and, more surprisingly, in a large area beneath eastern Eurasia where the Pacific subducting plate is stagnant. Seismic anisotropy is usually associated with intense deformation processes but also possibly to water transportation or to fine layering. This significant anisotropy in this part of MTZ might reveal a large water 'reservoir' associated with hydrous minerals or a strong stratification. It reflects a complex history beneath central Asia, 2

The role of the mantle transition zone (MTZ) in the global dynamics of the Earth has been debated for many decades, and is related to the long-standing debate on a whole mantle versus two-layer convection. Here, we consider the MTZ in a broad sense, as located around the 660-km discontinuity, and divided into the upper transition zone (410-660 km) UMTZ and the lower transition zone (660-1000 km) LMTZ. There is no doubt thanks to seismic tomography, that plates can descend through the MTZ into the lower mantle in most subduction zones, although their final fate can be diverse [START_REF] Van Der Hilst | Evidence for deep mantle circulation from global tomography[END_REF][START_REF] Fukao | A theory of earth's background free oscillations[END_REF]. The transfer budget between material subducting into the lower mantle and material remaining in the upper mantle is poorly known, which makes the nature of the MTZ controversial. There were also seismic observations showing a change in seismic properties around 920km depth since [START_REF] Kawakatsu | Seismic evidence for a 920km discontinuity in the mantle[END_REF]. A change in the shear velocity spectrum was recently found around 1000km depth [START_REF] Durand | Confirmation of a change in the global shear velocity pattern at around 1000 km depth[END_REF], which might correspond to the lower limit of LMTZ. Are the 410 km and 660 km discontinuities only due to phase changes and mineralogical transformation, or is the MTZ a chemical boundary between the upper and lower mantles that strongly limits the flow between them?

An efficient way to investigate the mantle flow circulation is to map the seismic anisotropy for this depth range [START_REF] Montagner | How to reconcile body-wave and normal-mode reference earth models?[END_REF][START_REF] Karato | Seismic anisotropy in the deep mantle, boundary layers and the geometry of mantle convection[END_REF]. Seismic anisotropy is related to the dependence of seismic wave velocity on the direction of propagation. It can have multiple causes at microscopic and macroscopic scales. Most mantle minerals are strongly anisotropic [START_REF] Mainprice | Seismic anisotropy of the deep earth from a mineral and rock physics perspective[END_REF], and anisotropy is investigated with respect to the symmetry axes of minerals. Following the pioneering work of [START_REF] Nicolas | Mechanisms of flow in naturally and experimentally deformed peridotites[END_REF][START_REF] Nicolas | Interpretation of peridotite structures from ophiolitic and oceanic environments[END_REF], the fast axis of olivine, the main constituent of the uppermost mantle, tends to align in the flow direction [START_REF] Christensen | Pyroxene orientation within the upper mantle[END_REF], according to its lattice or crystal preferred orientation (later on referred to as LPO or CPO). This microscopic anisotropic property can remain at very large scales, provided that the deformation field is coherent at scales larger Anisotropy in Mantle Transition Zone 3 than the seismic wavelength, opening the possibility to map mantle convection through the orientation of seismic anisotropy. In the MTZ, olivine and pyroxenes transform into wadsleyite (410-520km depth range), ringwoodite (520-660km depth range) and garnet, and ultimately into Mg and Ca perovskite (Mg-perovskite now named Bridgmanite), ilmenite and ferropericlase (also named magnesiowüstite).

The mechanisms of alignment producing this intrinsic anisotropy in the MTZ are still being debated [START_REF] Tommasi | Strain-induced seismic anisotropy of wadsleyite polycrystals and flow patterns in the mantle transition zone[END_REF][START_REF] Kawazoe | Seismic anisotropy in the mantle transition zone induced by shear deformation of wadsleyite[END_REF]. Other processes can give rise to seismic anisotropy at these great depths (named extrinsic anisotropy), such as fluid inclusion oriented distribution (although this might be a secondary effect in the deep mantle), or fine layering of isotropic material with very different velocities, which also creates a specific case of anisotropy: radial anisotropy [START_REF] Backus | Long-wave anisotropy produced by horizontal layering[END_REF].

Radial anisotropy is characterized by five independent elastic parameters [START_REF] Love | A treatise on the mathematical theory of elasticity[END_REF] and no horizontal azimuthal velocity variations. The corresponding medium is a transversely isotropic medium with a vertical symmetry axis, which is usually known as the vertical transverse isotropy (VTI) medium.

An example of such a finely layered or laminated medium with partial melting is illustrated by the millefeuilles model of [START_REF] Kawakatsu | Seismic evidence for sharp lithosphere-asthenosphere boundaries of oceanic plates[END_REF] of the asthenosphere. Even though the interpretation of observed anisotropy is non-unique, for large-scale mapping of fast directions of velocities, we need both radial and azimuthal anisotropies, which provide unique information on convective flows in the mantle [START_REF] Tanimoto | Mapping convection in the mantle[END_REF][START_REF] Montagner | Low anisotropy channels below the pacific plate[END_REF] and which can be compared to geodynamic models (e.g. [START_REF] Gaboret | The unique dynamics of the pacific hemisphere mantle and its signature on seismic anisotropy[END_REF]; [START_REF] Becker | Comparison of azimuthal seismic anisotropy from surface waves and finite-strain from global mantle-circulation models[END_REF]; [START_REF] Simmons | Joint seismic, geodynamic and mineral physical constraints on three-dimensional mantle heterogeneity: Implications for the relative importance of thermal versus compositional heterogeneity[END_REF]; [START_REF] Long | Mantle dynamics and seismic anisotropy[END_REF] ...).

Seismic data enable us to observe these two main kinds of anisotropy: radial anisotropy, as above, which only requires a VTI medium to explain the Rayleigh-Love discrepancy [START_REF] Anderson | Elastic wave propagation in layered anisotropic media[END_REF], and azimuthal anisotropy of different body waves since the first observations on Pn [START_REF] Hess | Seismic anisotropy in exploration seismics[END_REF]) and SKS splitting [START_REF] Vinnik | Anisotropy in the lithosphere from observations of SKS and SKKS[END_REF][START_REF] Silver | Shear wave splitting and subcontinental mantle deformation[END_REF], and surface waves at the regional [START_REF] Montagner | The early structural evolution and anisotropy of the oceanic upper mantle[END_REF] and global [START_REF] Montagner | Global upper mantle tomography of seismic velocities and anisotropies[END_REF] scales. A VTI model is characterized by 5 parameters A, C, F, L, N [START_REF] Love | A treatise on the mathematical theory of elasticity[END_REF], but for the inversion technique, they are recombined as

V P H , V SV , φ = C/A = (V P V /V P H ) 2 , ξ = N/L = (V SH /V SV ) 2 , η = F/(A -2L).
The corresponding sensitivity kernels are modified accordingly. Among the five independent elastic parameters of a VTI medium, the most easily accessible parameters are the V SV velocity and the ξ parameter, which expresses the difference in the velocities between horizontally and vertically polarized S-waves (ξ = ( V SH V SV ) 2 ). A correct account of the crustal structure is mandatory to avoid a bias between the shallow structure and the deep structure, especially the radial anisotropy. This non-linear effect was first made evident by [START_REF] Montagner | Vectorial tomography -II. Application to the Indian ocean[END_REF] and later on carefully investigated by [START_REF] Marone | Non-linear crustal corrections in high-resolution regional waveform seismic tomography[END_REF]; [START_REF] Ferreira | On the robustness of global radially anisotropic surface wave tomography[END_REF]; [START_REF] Chang | Joint inversion for global isotropic and radially anisotropic mantle structure including crustal thickness perturbations[END_REF]; [START_REF] Chang | Improving global radial anisotropy tomography: the importance of simultaneously inverting for crustal and mantle structure[END_REF]. We make use of the crustal model of [START_REF] Burgos | Oceanic lithosphere-asthenosphere boundary from surface wave dispersion data[END_REF] derived from the joint inversion of short period group and phase velocities (periods of 15-40s). This kind of simple ξ anisotropy was introduced for the 1D spherically symmetric preliminary reference earth model (PREM) in the uppermost 220 km of the mantle [START_REF] Dziewonski | Preliminary reference earth model[END_REF]. Azimuthal anisotropy cannot be explained by a VTI model and requires instead a more complex model of anisotropy. When derived from surface waves, additional eight parameters are necessary [START_REF] Montagner | A simple method for inverting the azimuthal anisotropy of surface waves[END_REF], with the best-resolved azimuthal parameters being the modulus G and its associated angle Ψ G related to the azimuthal variation of V SV .

For several decades, there has been good observational evidence for radial and azimuthal seismic anisotropies in the top 300 km of the upper mantle and in the bottom D"-layer. In the transition zone, 1D radial anisotropy was introduced to explain eigenfrequency data [START_REF] Montagner | How to reconcile body-wave and normal-mode reference earth models?[END_REF], and it was extensively investigated later [START_REF] Beghein | The signal of mantle anisotropy in the coupling of normal modes[END_REF]. Since then, several global tomographic models [START_REF] Kustowski | Anisotropic shear wave velocity of the earth's mantle: a global model[END_REF] and have shown that there might be some secondary maximum (although small) of radial anisotropy in the MTZ. Some hints of azimuthal anisotropy in the MTZ [START_REF] Vinnik | Shear wave splitting in the mantle from ps phases[END_REF][START_REF] Wookey | Mid-mantle deformation inferred from seismic anisotropy[END_REF] have been provided by different kinds of body-wave data (e.g., P-to-S receiver functions, shearwave splitting), which have demonstrated lateral variations in anisotropy in the transition zone. On a global scale, the first long-wavelength azimuthal anisotropic 3D structure in the MTZ [START_REF] Trampert | Global azimuthal anisotropy inthe transition zone[END_REF] has been obtained by the inversion of Love wave overtone data, which have a limited, although significant, radial resolution in this depth range. Its lateral resolution, more than 5000 km, was too poor to gain insights into the coupling and transfer of matter between the upper and lower mantles. More recent tomographic models displayed azimuthal anisotropy distributions down to the transition zone [START_REF] Yuan | Seismic anisotropy changes across upper mantle phase transitions[END_REF][START_REF] Debayle | An automatically updated s-wave model of the upper mantle and the depth extent of azimuthal anisotropy[END_REF][START_REF] Schaeffer | Azimuthal seismic anisotropy in the earth's upper mantle and the thickness of tectonic plates[END_REF], but the agreement between them is rather poor [START_REF] Huang | Constraints on seismic anisotropy in the mantle transition zone from long-period ss precursors[END_REF]. The discrepancies might be due to the fact that rms amplitude of the lateral variations in MTZ was found to be very small (about 1%, within the error bars), and to be much smaller than in the uppermost and lowermost mantle (the D"-layer).

ANISOTROPY TOMOGRAPHY FROM OVERTONE DATA

In this study, we combine two datasets of surface wave (Rayleigh and Love waves) overtones (higher modes), [START_REF] Beucler | Computation of large anisotropic seismic heterogeneities[END_REF][START_REF] Visser | Global anisotropic phase velocity maps for higher mode love and rayleigh waves[END_REF] using different methods and different data.

The merged dataset improves the global coverage of the Earth, and enables us to derive a global 3D map of the radial and azimuthal seismic anisotropies in the MTZ down to the mid-mantle (∼ 1200 km). The merged dataset improves the global coverage of the Earth. It enables us to derive a global 3D map of the radial and azimuthal seismic anisotropies in the MTZ down to the mid-mantle (∼1200 km). This model has a lateral resolution of 1000 km down to a depth of 1200 km. It also includes phase

Anisotropy in Mantle Transition Zone 5 velocities of the higher modes of Rayleigh waves up to order 6, and higher modes of Love waves up to order 5. In the period range of 35 s to 250 s, the number of measurements of the merged dataset varies from 70000 for the fundamental Rayleigh mode (and 50000 for the fundamental Love mode) down to 30000 for the 6 th Rayleigh higher mode (and 8500 for the 5 th Love higher mode). The measurement techniques are different for each of the datasets, but both include data uncertainties. [START_REF] Beucler | Computation of large anisotropic seismic heterogeneities[END_REF] uses the roller-coaster algorithm [START_REF] Beucler | Measuring surface wave higher mode phase velocities using a rollercoaster type algorithm[END_REF]) that clusters close events and extracts the individual phase velocities for each overtone by non-linear inversion. [START_REF] Visser | Global anisotropic phase velocity maps for higher mode love and rayleigh waves[END_REF] uses a model-space search approach [START_REF] Yoshizawa | Nonlinear waveform inversion for surface waves with a neighbourhood algorithm: Application to multi-mode dispersion measurements[END_REF]. Several tests have been performed

to check the compatibility of each of the datasets, by doing separate inversions (regionalizations of phase velocities at different periods), and joint inversions of the datasets [START_REF] Burgos | Tomographie du Manteau Supérieur par Inversion des Ondes de Surface[END_REF] . The path and the azimuthal coverages for the fundamental modes of Rayleigh and Love waves are presented in Figures 1 and 2 of [START_REF] Burgos | Oceanic lithosphere-asthenosphere boundary from surface wave dispersion data[END_REF]. Path and azimuthal coverages for overtones have similar distributions but with a smaller density.

We did not find large discrepancies between the two datasets, and the data of the higher mode phase velocities were jointly regionalized by taking into account their respective error bars (Figures A1 andA2). The 3D anisotropic tomographic method is an improved version of a classical twostep inversion procedure [START_REF] Montagner | Regional three-dimensional structures using long-period surface waves[END_REF]) based on gradient least-squares optimization [START_REF] Tarantola | Generalized nonlinear inverse problems solved using least squares criterion[END_REF]. The first step consists in regionalizing the measured phase (or group) velocities at different periods along the different paths in order to get the global geographical distribution of velocities. The second step is devoted to the inversion at depth of these velocity distributions in order to retrieve the 3D-distributions of seismic velocities and anisotropic parameters. The complete technique is detailed in the Appendix. The output tomographic model consists of the V S velocity and some robust anisotropic parameters, ξ = ( V SH V SV ) 2 , the S-radial anisotropy, G, with Ψ G expressing the horizontal

azimuthal dependence of V SV velocity (V SV = V SV 0 + G cos(2(Ψ -Ψ G )))
, and to a lesser extent, E,

with Ψ E expressing the azimuthal dependence of

V SH velocity (V SH = V SH 0 + E cos(4(Ψ -Ψ E ))).
Sensitivity kernels computed in PREM show why higher modes make it possible to obtain good depth resolution down to 1200 km, well below the upper (410-660 km) and lower (660-1000 km) MTZ, which are the main focus of the present study. Figure A3 (see Appendix) shows examples of the sensitivity kernels of Rayleigh and Love waves, respectively, with respect to SV-wave and SH-wave velocities for different higher modes. The maximum sensitivity at a given period increases with the order n of the higher mode. For example, at 51 s, the 4 th Rayleigh higher mode (Figure A3a) has a maximum sensitivity in V SV at 800 km in depth. The sensitivity of Rayleigh waves to V SH is small, whereas the higher modes of Love waves can also be very sensitive to V SV . This property was used by [START_REF] Trampert | Global azimuthal anisotropy inthe transition zone[END_REF] to retrieve SV-wave anisotropy in the MTZ by using only the Love wave data. Parameter G (and similarly, parameter E) associated with the 2 -ψ (and 4 -ψ) azimuthal dependence of SV-waves (resp. SH-waves) has the same kernel as V SV (resp. V SH ), and therefore it can also be recovered down to the mid-mantle at 1200 km in depth (even though only the results down to 800 km in depth are presented here). V SV , V SH , G and E are the most robust parameters that can be retrieved by inversion at depth of the higher mode phase velocity distributions. In the second step of the tomographic technique, the inversion at depth of all of the azimuthal dependence functions of the Rayleigh and Love wave local phase velocities is performed at every point, to retrieve these most robust elastic parameters. The local crustal structure was previously derived by [START_REF] Burgos | Oceanic lithosphere-asthenosphere boundary from surface wave dispersion data[END_REF].

PREM [START_REF] Dziewonski | Preliminary reference earth model[END_REF]) is used below the crust as the starting reference model. But (2019) by using long-period SS precursors. It confirms the weakness of anisotropy in most oceanic areas except around subduction zones. Consequently, we now focus on the only areas where azimuthal anisotropy is significant, above the error bars, i.e. subduction zones and Central Asia.

THE UNIQUE ANISOTROPY BENEATH CENTRAL ASIA

The azimuthal anisotropy in the MTZ as displayed in Figure 1 is well correlated with subducting plate slabs and is relatively small in other regions, with the noticeable exception of central Asia.

Fast V SV and negative ξ radial anisotropy is also observed in Canadian and Andean cordillera, but their lateral extension is much smaller than in Central Asia. The significant azimuthal anisotropy is limited to eastern Asia at 500 km in depth, but it extends through the whole of central Asia at 800 km in depth (Figure 3). Unfortunately, this region is not well covered by SS precursors as investigated region can be interpreted in terms of the mineralogy and/or the large-scale remnant plate structures and mantle convective flow. The mineralogical interpretation of the seismic anisotropy in the upper and lower MTZ is still subject of large uncertainties (e.g. the review of [START_REF] Mainprice | Seismic anisotropy of the deep earth from a mineral and rock physics perspective[END_REF]. In the UMTZ (410-660 km in depth), the 410-km discontinuity, attributed to the transformation from olivine to wadsleyite (orthorhombic), might result in a decrease in the anisotropy. A weaker discontinuity at 520 km in depth, e.g., [START_REF] Shearer | Transition zone velocity gradients and the 520km discontinuity[END_REF], has been attributed to the transformation from wadsleyite to ringwoodite. Wadsleyite (anhydrous or hydrous) can be strongly anisotropic whereas ringwoodite has a low anisotropy. This anisotropy might also be due to petrological layering caused by garnet-rich and ringwoodite-rich layers of transformed subducted oceanic crustal material [START_REF] Karato | Seismic anisotropy in the deep mantle, boundary layers and the geometry of mantle convection[END_REF]). However, notwithstanding some subduction zones where a tilted layering might be present, the resulting VTI medium would not cause any splitting for vertically propagating S-waves, nor produce the azimuthal anisotropy that is observed by [START_REF] Trampert | Global azimuthal anisotropy inthe transition zone[END_REF]; [START_REF] Yuan | Seismic anisotropy changes across upper mantle phase transitions[END_REF]; [START_REF] Debayle | An automatically updated s-wave model of the upper mantle and the depth extent of azimuthal anisotropy[END_REF]; [START_REF] Schaeffer | Azimuthal seismic anisotropy in the earth's upper mantle and the thickness of tectonic plates[END_REF] and in the present study. From 660-km to 900-1000-km deep (the LMTZ), the observed anisotropy might be due to the Bridgmanite lattice preferred orientation (and possibly to ferropericlase) that is caused by the deformation in the convective boundary layer at the top of the lower mantle [START_REF] Karato | Seismic anisotropy in the deep mantle, boundary layers and the geometry of mantle convection[END_REF]. Its lower limit might be related to a weak seismic discontinuity at 920 km, as identified by [START_REF] Kawakatsu | Seismic evidence for a 920km discontinuity in the mantle[END_REF] in several subduction zones. The mineralogy of the MTZ (not only subducted plates but as well other regions) is relatively complex, and different minerals were identified [START_REF] Vacher | Computation of seismic profiles from mineral physics: the importance of the non-olivine components for explaining the 660 km depth discontinuity[END_REF][START_REF] Anderson | New theory of the Earth[END_REF]) which can give rise to seismic anisotropy. The mineral stishovite SiO2 that is probably present in subducting oceanic plates is strongly anisotropic, and it might contribute to the observed anisotropy. Akimotoite, which is the ilmenite form of MgSiO3, might dominate in cold parts of the transition zone, i.e. in areas near subduction zones [START_REF] Shiraishi | Crystallographic preferred orientation of akimotoite and seismic anisotropy of tonga slab[END_REF][START_REF] Cottaar | Large-scale mantle discontinuity topography beneath europe: Signature of akimotoite in subducting slabs[END_REF]. Akimotoite has higher velocities than garnet at similar depths in hotter regions of the transition zone, and can produce a local high velocity that can be misinterpreted as a pile-up of subducted materials. So significant azimuthal anisotropy might be observed where the akimotoite content is high. A typical structure of perovskite may be cubic, but, in the LMTZ, when the crystal lattice is subject to strong distortion, silicate perovskites are in the orthorhombic crystal system. Bridgmanite is anisotropic [START_REF] Meade | Laboratory and seismological observations of lower mantle anisotropy[END_REF][START_REF] Mainprice | Predicted glide systems and crystal preferred orientations of polycrystalline silicate Mg-Perovskite at high pressure: Implications for the seismic Anisotropy in Mantle Transition Zone 15 anisotropy in the lower mantle[END_REF]) and a good candidate for explaining anisotropy in LMTZ since the CPO pattern and dominant slip system were carefully investigated [START_REF] Tsujino | Mantle dynamics inferred from the crystallographic preferred orientation of bridgmanite[END_REF]) but still controversial [START_REF] Kraych | On dislocation glide in mgsio3 bridgmanite at high-pressure and high-temperature[END_REF]. Ferropericlase is nearly isotropic in the LMTZ but its anisotropy strongly increases with pressure and might be as large as 40%

in the lower mantle.

A role for water can also be considered here. It was suggested that the MTZ might be a water reservoir [START_REF] Van Der Meijde | Seismic evidence for water deep in Anisotropy in Mantle Transition Zone 17 earth's upper mantle[END_REF][START_REF] Bercovici | Whole-mantle convection and the transition-zone water filter[END_REF]) that collects the water from the subducting plates through hydrous minerals. The effect of water on CPO and slip systems was extensively investigated since hydrous wadsleyite might store a large amount of water transported by subducting slabs. But there is still some debates on the dominant slip systems able to generate seismic anisotropy [START_REF] Tommasi | Strain-induced seismic anisotropy of wadsleyite polycrystals and flow patterns in the mantle transition zone[END_REF][START_REF] Kawazoe | Seismic anisotropy in the mantle transition zone induced by shear deformation of wadsleyite[END_REF]. A significant water content near subducted slabs (Chang & Ferreira 2019) can change the rheology of minerals (i.e., their viscosity and melting [START_REF] Ohuchi | Crystallographic preferred orientation of wadsleyite and ringwoodite: Effects of phase transformation and water on seismic anisotropy in the mantle transition zone[END_REF][START_REF] Ritterbex | Modeling dislocation glide in mg2sio4 ringwoodite: Towards rheology under transition zone conditions[END_REF][START_REF] Ritterbex | Deformation across the mantle transition zone: A theoretical[END_REF]). However, [START_REF] Ohuchi | Crystallographic preferred orientation of wadsleyite and ringwoodite: Effects of phase transformation and water on seismic anisotropy in the mantle transition zone[END_REF] argued that, due to changes in slip systems, anisotropy becomes weak if the UMTZ is hydrous and strong anisotropy near subducted slabs means a dry UMTZ [START_REF] Ferreira | Ubiquitous lower-mantle anisotropy beneath subduction zones[END_REF]. So, water transportation alone cannot explain this strong anisotropy and other mechanisms must be found [START_REF] Ritterbex | Modeling dislocation glide in mg2sio4 ringwoodite: Towards rheology under transition zone conditions[END_REF][START_REF] Ritterbex | Deformation across the mantle transition zone: A theoretical[END_REF].

Nevertheless, we observe significant anisotropy in and around subducting plates, because they are specific places where the physical conditions of strong deformation are fulfilled for the development of [START_REF] Fukao | Subducting slabs stagnant in the mantle transition zone[END_REF].

In order to investigate the convective flow below Asia, we also made some comparisons with geo- (

) 2010
). The directions of the anisotropy (Figure 3) and flow (Figure 4) are poorly correlated at both of these depths, with large angle differences between them. The important observation here is that the large change in anisotropy direction between the UMTZ and LMTZ is also associated with the dramatic change in the flow orientation. Further geodynamic modeling is necessary, as this depends on the chosen tomographic model and the viscosity profile. Some alternative modeling has been tried (e.g., [START_REF] Becker | Radial seismic anisotropy as a constraint for upper mantle rheology[END_REF]), but as long as the orientation mechanisms of the minerals in the MTZ are not so well understood, there is little rationale to go further in the interpretation. In the absence of consensus for the dominant mechanisms of alignment of bridgmanite-ferropericlase, it is difficult to reach strong conclusions, and a better understanding of the mineralogical processes in play in the seismic anisotropy of the MTZ will be necessary to reconcile the flow pattern directions and the observed anisotropy directions.

So far, past ridge processes were investigated by seismic anisotropy in ophiolites [START_REF] Nicolas | Interpretation of peridotite structures from ophiolitic and oceanic environments[END_REF][START_REF] Nicolas | Composition, structure and dynamics of the lithosphere/asthenosphere system[END_REF][START_REF] Peselnick | Seismic anisotropy in an ophiolite peridotite: Application to oceanic upper mantle[END_REF]. The recent investigation of seismic anisotropy beneath and around subduction zones [START_REF] Nowacki | Mid-mantle anisotropy in subduction zones and deep water transport[END_REF][START_REF] Ferreira | Ubiquitous lower-mantle anisotropy beneath subduction zones[END_REF][START_REF] Sturgeon | On the origin of radial anisotropy near subducted slabs in the midmantle[END_REF]) provide new insights into our understanding of convective processes and the coupling between the upper and the lower mantles. What is observed at the global scale, e.g. the interaction between the remnant slabs beneath the continent for central Asia is almost unique in the world, and leaves an imprint through seismic anisotropy. The cluttering of the plate slabs in the MTZ might explain why some of the plates descend, why some others do not, and why some are stagnant in the lower transition zone. In addition to anisotropic minerals, several conditions must be fulfilled to observe the seismic anisotropy in the MTZ, the large-scale deformation field, and/or the probability of the presence of water carried by the subducting plates. These conditions are only present in subduction period of 51 s. All A n (ω, θ, φ) are related to some of the 21 anisotropic parameters p j that describe the medium [START_REF] Montagner | A simple method for inverting the azimuthal anisotropy of surface waves[END_REF][START_REF] Chen | Theoretical and numerical investigation of global and regional seismic wave propagation in weakly anisotropic earth models[END_REF]. These are inverted at every point (θ, φ) in the second step of the tomographic technique for retrieving an estimate of the whole parameter space at a given depth.

δV (ω, θ, φ, Ψ) = 1 V 0 np=21 j=1 ra 0 K j (ω, r, θ, φ, Ψ)δm j (r, θ, φ)dr
However, all of the parameters cannot be reliably retrieved. Figure A3 shows examples of the higher mode sensitivity kernels of the Rayleigh (Figure A3a) and Love waves (Figure A3b) with respect to the SV-wave and SH-wave velocities. The sensitivity of the Rayleigh waves to V SH is small, whereas the Love wave higher modes can be sensitive to V SV . The maximum sensitivity at a given period increases with the order n of the higher mode. For example, the 4th Rayleigh higher mode (Figure A3a) at 51 s has a maximum sensitivity in V SV at 800 km in depth. These kernels show that higher modes make it possible to obtain good depth resolution down to 1200 km, well below the upper (410-660 km) and lower (660-900 km) transition zones, even though we only show the results down to 800 km, which represents the main focus of the present study. Parameter G (and similarly parameter E) which expresses the 2 -ψ (and 4 -ψ) azimuthal dependence of the SV-wave (and the SH-wave) has the same kernel as V SV (and V SH ), and therefore it can also be recovered down to 1200 km in depth.

V SV , V SH , G, Ψ G , and E, Ψ E are the most robust parameters that can be retrieved by the inversion at depth of the higher mode phase velocity distributions. Variations in ρ, V P V and V P H are scaled on these parameters, down to 410 km in depth [START_REF] Montagner | Global upper mantle tomography of seismic velocities and anisotropies[END_REF], although they are free Anisotropy in Mantle Transition Zone 21 below this depth. The local crustal structure has also been inverted due to the shortest periods of the Rayleigh and Love wave dispersions in the datasets [START_REF] Burgos | Tomographie du Manteau Supérieur par Inversion des Ondes de Surface[END_REF].

Resolution tests

We performed numerous synthetic tests to check the robustness of the inverted parameters ξ, G, Ψ G , E, Ψ E , by exploring different vertical correlation lengths, different weigthing between the fundamental modes and the overtones. Some of these examples are presented in Figure A4. We search for the depth resolution of the tomographic method by perturbing the depth profiles of V SV and ξ at different depths using delta functions convolved with a Gaussian filter (Figure A4, green lines). We show examples at 300 km and 700 km in depth. The important result is that in both cases, the perturbations are retrieved at the correct depths. There is some spectral leakage towards other parameters V P H , η, Φ, because we invert for five parameters, whereas we only have two independent pieces of information in this case.

In addition, we can expect that in the real Earth, there should always be all kinds of anomalies for the five parameters that will occur simultaneously.

Figure 1 .

 1 Figure 1. Tomographic images of the S-wave velocity V SV , azimuthal anisotropy G (left) and radial anisotropy δξ = ξ -ξ ref (right) in different mantle layers: The upper mantle, at 100 km in depth (top). The transition zone, at 500 km (middle) and 800 km (bottom) in depth. δξ is plotted with respect to an average reference model, ξ ref = 2.7% at 100km, -1.5% at 500km, 0.4% at 800km. The error bars are calculated as in Burgos et al.(2014) and presented in[START_REF] Burgos | Tomographie du Manteau Supérieur par Inversion des Ondes de Surface[END_REF]. Error bars on ξ and G are everywhere smaller than 1% and even smaller than 0.5% in well covered regions of the northern hemisphere. The color scale varies with depth and its range is defined at the top left of each figure.

Figure 2 .

 2 Figure 2. Power spectra of the relative variations of S V -wave velocity (Left) and of the azimuthal anisotropy G (Right) at different depths: Asthenosphere, 200 km; Transition zone: 500 km, 600 km and 700 km, as indicated. 200km: green diamonds; 500km: light blue diamonds; 600km: dark blue diamonds; 700km: yellow circles.

byFigure 3 .

 3 Figure 3. Tomographic images of S-wave velocity V SV , azimuthal anisotropy G, in the central Asia transition zone at depths of 500 km (left) and 800 km (right).

  the preferred orientation of minerals or of fine layering. In addition, central Asia is the continent below which many oceanic plates subduct or have subducted. In particular, the Tethys plate and the Izanagi plate (now extinct in the Pacific Ocean; see Lithgow-Bertelloni & Richards (1998); Scotese & Golonka (1997)) subducted beneath Eurasia for more than 100 Ma (see Torsvik et al. (2010) for kinematic plate reconstruction). As the Tethys and Izanagi and nowadays Pacific plates subduct in orthogonal directions under the Asian continent, some strong interaction and even collision might occur between these plates beneath central Asia. The Tethys plate moved northward before descending into the lower mantle (van der Hilst et al. 1997), whereas the Izanagi plate became stagnant in the MTZ

Figure 4 .

 4 Figure 4. Flow models computed according to Simmons et al. (2009), for the depths of 500-550 km (a) and 800-850 km (b) (Courtesy of Alessandro Forte).

Figure A1 .

 A1 Figure A1. Phase velocity distributions of the different Rayleigh wave higher modes at the same period (T = 51 s). (a) n=0; (b) n=1; (c) n=2; (d) n=4. The black bars correspond to the maximum of 2 -Ψ azimuthal terms (azimuthal anisotropy), and their lengths are proportional to their amplitudes.

Figure A2 .

 A2 Figure A2. Phase velocity distributions of the different Love wave higher modes at the same period (T = 51 s).

  (a) n=0; (b) n=1; (c) n=2; (d) n=4.

Appendix

Tomographic method.

The 3D anisotropic tomographic method is a classical two-step inversion procedure. From a practical point of view, the same algorithm [START_REF] Tarantola | Generalized nonlinear inverse problems solved using least squares criterion[END_REF] is used for both steps. The forward problem can be generally written as:

(1

where d is the vector associated with the whole dataset, m is the model parameter space, and g is the functional relating d and m. The sensitivity kernels K are derived by first-order perturbation theory from equation ( 1). To generate an improved parameter estimate m k starting from an initial parameter model m 0 , we use an iterative algorithm, as expressed in [START_REF] Tarantola | Generalized nonlinear inverse problems solved using least squares criterion[END_REF]:

with

where K is the partial derivative matrix, In the first step, the higher mode phase velocities of the Rayleigh and Love waves are separately regionalized at different periods, to retrieve the different azimuthal terms of the local phase velocity.

The azimuthal dependence due to the presence of a general slight anisotropic elastic medium is a homogeneous trigonometric polynomial up to degree 4ψ, where ψ denotes the azimuth of the horizontal wave vector, measured clockwise from the north. For a given point located at θ, φ and for a given angular frequency ω or period T (= 2π ω ), V (ω, θ, φ, ψ), the local phase velocity is defined as a perturbation of an isotropic or VTI (Vertical symmetry axis, Transversely Isotropic) reference velocity (denoted as V 0 (ω, θ, φ)), such that V = V 0 + δV . The velocity perturbation δV (ω, θ, φ, ψ) can be expanded as a Fourier series in ψ [START_REF] Smith | The azimuthal dependence of Love and Rayleigh wave propagation in a slightly anisotropic medium[END_REF]:

The five local functions A n (ω, θ, φ) depend on ω, θ, φ.


Timothée Schmoderer

Control systems with paraboloid nonholonomic constraints

Control systems with paraboloid nonholonomic constraints

INSA Rouen Normandie, Rouen, France ABSTRACT In this talk, we present a characterisation and a classication of control systems (both control-ane and fully nonlinear) whose eld of admissible velocities forms a paraboloid submanifold in each tangent space. We thus continue previous works on ane and linear Pfaan equations whose admissible velocities form either an ane or a linear subspace in each tangent space; see [START_REF] Zhitomirskii | Typical Singularities of Dierential 1-Forms and Pfaan Equations[END_REF][START_REF] Zhitomirskii | Singularities and Normal Forms of Smooth Distributions[END_REF][START_REF] Jakubczyk | Feedback Equivalence of Planar Systems and Stabilizability[END_REF][START_REF] Zhitomirskii | Simple Germs of Corank One Ane Distributions[END_REF]. Precisely, we consider a smooth n-dimensional manifold X equipped with local coordinates x and we call a nonholonomic constraint paraboloid if it is given by an equation of the form

S Q (x, ẋ) = ż -ẏt Q(x) ẏ -b(x) ẏ -c(x) = 0,
where x = (z, y), with y = (y 1 , . . . , y n-1 ), Q is a smooth symmetric matrix of full rank, b is a smooth covector, and c is a smooth function. The case n = 2 corresponds to S Q describing a parabola ż = a(x) ẏ2 + b(x) ẏ + c(x) in each ber T x X and is treated (and generalised to elliptic and hyperbolic cases) in [START_REF] Schmoderer | Conic Nonholonomic Constraints on Surfaces and Control Systems[END_REF] and is extended to all dimensions by the speaker in his thesis [START_REF] Schmoderer | Study of Control Systems under Quadratic Nonholonomic Constraints[END_REF]. We will introduce a novel class of control-ane systems whose trajectories satisfy the paraboloid nonholonmic constraint given by S Q and we give a characterisation of that class among all control-ane systems. Next, we will classify paraboloid control systems under feedback transformations. In particular, we will insist on the dierences between the cases n = 2 and n ≥ 3. Moreover, we will show how our classication of control systems provides a corresponding classication of paraboloid equations S Q = 0. This is a joint work with Witold Respondek from INSA Rouen Normandie.