Ph.D Xiao-Fu Li

* Li

Dr Xiao-Fan Li

Exploring criminal responsibility of PTSD patients; findings from a survey in Chinese Mainland courts Explorer la responsabilité pénale des patients atteints de PTSD; résultats d'une enquête dans les tribunaux de la Chine continentale

Keywords: Criminal Responsibility, Legal Identification, Mainland China, Post-traumatic Stress Disorder Résumé

Background -The Wenchuan Earthquake in Sichuan Province is China's deadliest natural disaster in a generation; after such disturbance, a kind of mental illness named post-traumatic

aux États-Unis avec des cas particuliers. En utilisant des outils académiques et en analysant les décisions judiciaires, ainsi que les informations clés des sites officiels du gouvernement, nous constatons que même dix ans après la catastrophe de Wenchuan, les tribunaux chinois hésitent encore à accepter le TSPT comme défense mentale des jeunes délinquants, alors que certaines règles pertinentes existent. Il existe des lacunes juridiques dans les lois lorsque les tribunaux rencontrent des criminels mineurs atteints du TSPT, comme l'absence de procédures ou d'instructions pour le lien entre le diagnostic et le jugement. Nous croyons qu'il est temps que le gouvernement établisse des règlements détaillés pour les troubles mentaux spéciaux afin de suivre le développement de la technologie scientifique. Une analyse en trois parties pour l'examen médico-légal du TSPT pourrait être un bon moyen pour les tribunaux chinois dans certains cas particuliers.

Mots-clés : Chine continentale ; Identification légale ; Responsabilité pénale ; Trouble de stress post-traumatique

Background

The Wenchuan Earthquake ten years ago in Sichuan Province is China's deadliest natural disaster in a generation [START_REF]Earthquake relief work for Wenchuan[END_REF]; after such disturbance, a kind of mental illness named post-traumatic stress disorder (PTSD, also c Legal Identification alled delayed psychogenic reaction) raises concern in Mainland China [START_REF] Slovenko | The watering down of PTSD in criminal law[END_REF], but probably not rapidly sufficient [START_REF]American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders[END_REF].

Different from that in the USA, earthquake is both the reason and focus of PTSD research in China.

In 1980, PTSD was first officially recognized by the American Psychiatric Association's third edition on its Diagnostic and Statistical Manual of Mental Disorders (DSM-III) and included in the psychiatric nomenclature [START_REF]American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders[END_REF]. In the fifth edition (DSM-5), PTSD was updated to four groups. DSM-5 also estimated that the rates of patients with PTSD during a given year are between 0.5% and 1% [START_REF]Diagnostic and Statistical Manual of Mental Disorders[END_REF]. Relevant information regarding PTSD patients, such as population and age distribution, is not largely available in Chinese official websites or private organizations. A domestic scholar found that 420 (14.1%) college students who experienced the earthquake in Wenchuan in 2008 suffered from mild to severe PTSD [START_REF]The influence of social support and personality on adolescent's post-traumatic stress disorder after an earthquake[END_REF]. In Mainland China, PTSD's description in the third edition of Chinese Classification of Mental Disorder is the same as the American counterpart in the DSM-III. Although PTSD is under stress-related disorder category, the disease definition and symptom criteria are the same. The symptoms last for more than a month after the traumatic event [START_REF] Zhi-Wei Y | Forensic psychiatric expertise of post-traumatic stress disorder[END_REF].

Methods

In order to find out the relationship between the PTSD defense and criminal responsibility in Mainland China, the current authors decided to use certain academic tools and analysis judicial decisions. The authors identified key information from government official websites.

Data collection

China National Knowledge Infrastructure (CNKI, http://ezlibrary.sufe.edu.cn) is one of the most popular academic network platforms in Mainland China. The authors used Chinese phrase for PTSD as keywords in searching CNKI.

In Mainland China, each court has a mandatory requirement of uploading the judgment of a case on the official website from January 1, 2014. The Provision of Publishing Judgment Documents on the Internet, which was released by the Supreme Court in Mainland China, and its amendment (2016) [START_REF]Supreme People's Court of China. The Provision of Publishing Judgment Documents on the Internet[END_REF], mandated that judgments should be published online; for state secret, minor crime, mediation or confirmation of the effectiveness of people's mediation agreement, divorce or related minor child custody or guardianship, or commercial secret, the court shall take some technical approaches to protect the privacy or secret. China Judgment Online (http://wenshu.court.gov.cn) is the official website for downloading judgments in Mainland China. PTSD symptom is not confidential for adult criminals, but judgments should employ particular measures to protect minor PTSD patients and keep their identities confidential.

Technically, trauma means wound; psychologically, as defined in the Webster's Second New College Dictionary, trauma means "an emotional shock that creates substantial and lasting damage to the development of the individual." Metaphorically, trauma is a suffering that strains the psyche [START_REF] Xiao | The role of core beliefs challenge, subjective fear, and intrusive rumination in association between severity of traumatic exposure and posttraumatic stress disorder among adolescent survivors after the Yaan earthquake[END_REF]. Whether the criminal justice system should establish some special rules or treatments when perpetrators of criminal assaults or homicides exhibit a high risk of suffering from PTSD should be determined. Moreover, the mechanism to assess the criminal responsibility of the actor should be investigated. PTSD and its effects can undermine the mental stability of a criminal defendant. Certain Chinese scholar demonstrated that a person experiencing PTSD may present nervous illness or grown arousal coupled with tough focusing or completion of tasks. 7 All of these symptoms of PTSD in a criminal defendant can potentially sap the client's ability to resist law enforcement's coercive tactics or satisfy the competence to stand trial criteria; in addition, American criminal cases showed that when someone develops PTSD, he/she may hurt people around them, even loved ones or passerby [START_REF] Aprile | PTSD: when the crime punishes the perpetrator[END_REF].

Data analysis

When checking the relevant data of criminal cases of PTSD patients, the authors also pay attention to four general forensic psychiatric issues.

A. Do Chinese forensic psychiatric practitioners realize the relationship between the PTSD defense and criminal responsibility? B. What is the legal role of forensic psychiatric practitioners in Chinese courts? C. What is the Standard of criminal responsibility for PTSD patients in Mainland China? D. How does the legal insanity work as defense in a Chinese trial?

Results

PTSD is not only catalogued in Chinese hospital textbooks as a mental disorder, but a large number of judicial authentications also acknowledge and diagnose PTSD patients. In CNKI website, the annual number of articles (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) whose abstract contain "Chinese phrase for PTSD" increases considerably after the Wenchuan earthquake in 2008 (Table 1).

These papers or articles are mainly on medical research or clinical trials, and they analyzed the etiology, pathogenesis, clinical manifestation, diagnostic criterion, treatment, and prevention of PTSD. Moreover, approximately one-fifth of these articles are on the relationship between earthquake and trauma. Mongolia Province delivered the opinion that she was in a long-term state of physical and psychological suffering, which caused PTSD symptoms and prompted her to commit the criminal offense. Additionally, the court considered the killer with diminished criminal responsibility, and the woman obtained a 12-year imprisonment sentence [START_REF] Court | Unbearable domestic violence to kill her husband[END_REF]. Article 232 of Criminal Law of the People's Republic of China (CLPRC) states that whoever intentionally commits homicide shall be sentenced to a fixed-term imprisonment of not less than 10 years or more severe punishment, e.g., life imprisonment or death penalty. With the 12-year imprisonment, the court accepted Ma as a quasi-mental patient for suffering PTSD, but not as a complete mental patient.

Discussion

Rules and jurisprudence in identifying the criminal responsibility of PTSD patients

Individuals are responsible for their behavior, including criminal behavior or civil behavior, unless the court determines otherwise. Rules of criminal responsibility for mental patients exist in both material and procedure laws. Crime and crime composition are different concepts in Mainland China. The Soviet Union criminal jurisprudence exerts a major influence on Mainland China, despite that other theories from certain Western countries, especially the dissemination of German and Japanese three-stage criminal construction systems, were recommended in the late 1990s. To date, the majority of legal occupations, such as judges, lawyers, scholars, and forensic psychiatric practitioners, are still affected by the system of four-element criminal construction traced to the early 1980s [START_REF]Chinese criminal Jurisprudence[END_REF].

Article 4 of CLPRC stresses on the equal application of law, and Article 5 formulates that the degree of punishment corresponds to the crime committed. Article 13 states that an act will be a crime if it endangers the society or public and is punishable by criminal law.

Moreover, CLPRC excludes minor offenses that cause no harm to the society. The essence of CLPRC is crime composition. CLPRC emphasizes the integrity of objective and subjective elements in composing crime. Objective elements include acts, outcomes, and causal relations;

subjective elements include intention and motive. Court/judge considers the crime composition in adjudicating a case. The integrity of objective and subjective elements means that the establishment of crime not only requires the person to commit an offense that threatens the social security objectively and possess intentional and negligent purpose subjectively, but also requires the unity of objective and subjective contents of crime. An act is only a crime if a person conducts an act purposefully, and his/her act endangers the social and personal interest objectively. If the person did not act purposefully, and no prerequisite knowledge exists about the object, he/she should not be responsible for the offense he/she committed [START_REF] Tursun | Feminist perspective to teenage rape in Chinese Criminal Law[END_REF]. In China, if a crime is committed consequent to a mental disorder as determined by law (i.e., psychotic disorder), the court may excuse an individual from criminal responsibility, suspend sentencing, and refer the offender to psychiatric treatment, whether inpatient or ambulatory, by executing the appropriate order. A direct relationship must exist between the crime and the mental illness, e.g., the medical test and/or the lack of capacity to avoid the crime (irresistible impulse).

Free will is assumed the foundation of Chinese criminal laws, responsibility doctrines, and practices. A defendant who fails to satisfy the criteria for legal insanity is said to have free will, and the defendant who succeeds with the defense is said to lack it [START_REF] Morse | Criminal responsibility and the disappearing person[END_REF]. PTSD patients obtain sentence mitigation, or exemption is also justified and reasonable because the illness causes the difficulty or impossibility for the actors to obey the law or stop what he/she is doing. Aggravation and mitigation are significant sentencing concepts in both Western countries and Mainland China. The court/judge imposes a lower sentence than normal/average sentence through a/some mitigating factor(s) and vice versa. When confronting PTSD patients, the important question for Chinese criminal justice system is the factor that is appropriately classified as mitigating factor, and a question more important than this is often referred as punishment theory [START_REF] Grey | Neuroscience, PTSD, and sentencing mitigation[END_REF].

A sanction should not merely be helpful or useful-it should treat the offending conduct as wrong. Punishment aims to display disapproval for the actor's wrongdoing and clearly blame his/her criminal actions. Consequently, the justice system punishes, the government/court penalizes to censure (retribution), and government/court does not castigate merely to assist a human being to improve (rehabilitation). CLPRC clauses contain retribution and consequentialism. Retribution distributes punishment according to the blameworthiness of the offender. Furthermore, consequentialism distributes punishment on the basis of the consequences that punishment is likely to yield, i.e., based on what is most likely to prevent future crimes [START_REF] Grey | Neuroscience, PTSD, and sentencing mitigation[END_REF]. When someone lost free will, retribution and consequentialism are not needed, and technical treatments should be established.

A Chinese judge does not need the National Medical Licensing Examination, but confronting a criminal case might be a work, including medical certification and law knowledge. When dealing with mental defense and following the rule of law, Chinese courts determine criminal responsibility through a two-tiered approach: scientific verification and subsequent legal decision, which means that judges review the criminal responsibility of mental disabilities on the basis of medical evaluation.

Legal role and function of forensic psychiatric practitioner for criminal responsibility

Mental defense requires evidence and diagnosis. Forensic psychiatric practitionerplays vital role in judgment of criminal responsibility and they are the bridge between science and law. Chinese forensic psychiatric practitioners follow no common criminal jurisprudence with regard to their role or function for criminal responsibility. They are used to reference the counterparts from law school or scholar, thereby raising questions on their practice. Chinese forensic psychiatric practitioners are confronted with three misunderstandings of the legal role.

First, some victims and their relatives who consider service from forensic psychiatric practitioners, especially lawyers holding the mental status diagnosis of a defendant, are aim to absolve the patients from liability. Second, some citizens prioritize expert opinion and even regard forensic psychiatric practitioner as judge. Third, when the public confused the accuracy or valuation of diagnosis, the forensic psychiatric practitioners should provide explanation immediately [START_REF] Xiao-Fu | Two issues on judgment of criminal responsibility of patient in mental disorder[END_REF].

When the forensic psychiatric diagnosis or report satisfies the judges, medicolegal expertise challenges three primary misconceptions in Mainland China. First, most Chinese courts mistakenly believe that the defendant's legal capacity is positively correlated with the level of severity of patient's condition. However, the relationship between legal capacity and the level of severity of patient's condition should be treated individually. Second, the majority provides mechanical interpretation on mental ability appraisal and considers it ridiculous that patients can do A but not B, when A and B are equal in degree. Third, both society and courts do not provide sufficient attention to the normal mental activity of patients [START_REF] Tian | Proposal on assessment guideline of ability of taking criminal responsibility[END_REF].

Criminal Procedure Law of the People's Republic of China (CPLPRC) established several articles on the identification of criminal responsibility for PTSD patients on which the legal role and function of forensic psychiatric practitioner are based. Article 48 of CPLPRC underlines that any material proving the facts of a case could be evidence. In the same article, forensic examiner's opinion is contained as a kind of evidence. Article 50 of CPLPRC regulates that forensic psychiatric practitioner, such as adjudicators or prosecutors, must comply with legal procedures to gather kinds of evidence, especially when this information or evidence can prove the suspect or a defendant as guilty or innocent, or they are mitigating and aggravating factors. Article 53 of CPLPRC also confirmed that all the evidence needed to decide a case is verified through legal procedures.

Therefore, forensic psychiatric practitioners are not judges, and they only have the authority of identification in Mainland China [START_REF] Turack | The new Chinese Criminal justice system[END_REF]. As a sub-speciality of psychiatry and related to criminology, forensic psychiatry encompasses the interface between law and psychiatry. A forensic psychiatrist provides services to governmental organizations, such as courts, police offices, or individuals, and the determination of forensic psychiatrist aims at competency to damages or stand trial. Forensic psychiatrists working with courts/judges evaluate the competency of test object to stand trial, defenses based on mental disorders (i.e., insanity defense), and sentencing recommendations. As a kind of expert, forensic psychiatric practitioner delivers opinion to the Chinese court/judges; such opinion is limited to whether a suspect/criminal has the ability to understand what he/she was doing at that moment of crime.

Standard of criminal responsibility for PTSD patients

Articles 144-147 of CPLPRC are vital in diagnosis of mental patients, but these clauses cause problems in practice. Article 144 of CPLPRC states that experts shall be assigned or invited to give his/her evaluations when judgment is needed. Section 1 of Article 145 of CPLPRC mandates that expert has a duty to write a conclusion of evaluation and affix his/her signature after evaluating a matter. Furthermore, in Section 2, accompanied by false verification, he/she shall assume legal responsibility. To consider PTSD as either a mitigating factor for defense or exemption factor in Mainland China is more difficult than in the American judicial system. Victims, their relatives, and friends doubt the validity of PTSD, similar to any other mental illness, despite that PTSD has now gained further recognition in science and in the USA [START_REF] Aprile | PTSD: when the crime punishes the perpetrator[END_REF]. Assessing the validity of a PTSD diagnosis in a particular context is controversial. The period between the first definition of PTSD until today is more than half a century. Chinese lawyer can also obtain abundant resources from Americans to make good defense for the defendants. In brief, both Chinese and American judges are concerned that an individual who presents a claim of PTSD defense in the court might fake symptoms to avoid penalty [START_REF] Grey | Neuroscience, PTSD, and sentencing mitigation[END_REF]. Article 146 of CPLPRC confirms when needed, by the criminal suspect or the victim, a supplementary expert verification, or another expert verification could be conducted and submitted to the court. Article 154 of CPLPRC sets a period of two months for each criminal investigation, but Article 147 of CPLPRC supplements that the verification time for the mental illness of a criminal suspect is out of the procedure period for handling the case. In practice, a PTSD criminal case requires a long-term medical verification. Additionally, details for the legal responsibility and scope of supplementary expert verification are lacking, thereby causing many questions in other cases because fake expert verification has no punishment.

Expert report also has no authority with the absence of rule stating the exact number of times for diagnosis. Section 3 of Article 187 of CPLPRC is also vital for diagnosis when someone (might be the party, the defender, or the agent) doubts the credibility of the expert opinion or verification, which is concerned for judgment. Chinese court also has the power to ask the expert to appear in court. If the expert does not testify in court, the expert opinion or verification cannot be used as a basis for mental defense [START_REF] Guang-Hua | PTSD and related problem s of forensic medicine[END_REF]. Therefore, diagnosis and regulations present some ambiguities. If PTSD is recognized as a useful defense in Chinese criminal cases, both plaintiff and defendant might use it in each case, which is different in the US. The problem with using PTSD as a cause of the issue is both the legal system and the current cultural state of the US [START_REF] Slovenko | The watering down of PTSD in criminal law[END_REF].

Unlike Americans [START_REF] Ptsd | Introduction of PTSD[END_REF], Chinese culture in Mainland China demonstrates no convincing acceptance of the link between PTSD and criminal behavior. Conversely, American experience merits attention because PTSD is a common issue in the society. Similar to American courts, certain traumatic experiences can trigger PTSD symptom, which gained sentence mitigation in the case of Ma Yu-xia. We strongly call for Chinese courts should learn from the American Bar Association and accept a three-part analysis for forensic consideration of PTSD because procedures or standard guidelines for the relationship between diagnosis and judgment do not exist. When confronted with a claim of PTSD, the following questions should be answered: [START_REF]Earthquake relief work for Wenchuan[END_REF] Was the underlying incident a trauma within the meaning of the scientific standard (i.e., was it an event that reasonably could be found to have produced the symptoms)?, (2) Did the trauma produce the present symptoms, or are they the result of other factors?, and (3) Are the symptoms real or feigned? Although the courts have not explicitly recognized these central issues in forensic evaluation of PTSD, this format would permit the courts to address systematically the validity of PTSD claims [START_REF] Brown | Another emerging "storm": Iraq and Afghanistan veterans with PTSD in the criminal justice system[END_REF]. Moreover, this formulation accords closely with recent scientific developments that are changing the conceptual and clinical understanding of PTSD.

The government and public fight for crimes using law, and one principle of criminal rules is treating criminals fairly. The same situation will result in the same outcome, and different situations will result in different outcomes. An alleged perpetrator's PTSD must be considered in evaluating his/her competence to stand trial, regardless of whether the mental condition existed before or after the crime occurred. In practice, the majority would retain the ordinary constituted man or the reasonable man test of provocation when penalizing mental patients with PTSD. Consequently, disagreement arises among the majority and might cause unfair treatments from the courts/judgments and the principle of rule of law. determinative of some issues. The test cannot be wholly objective or wholly subjective. The mental defendant may have been less angry with the victim at the moment of murder than at some time in the past (when he/she checked the impulse to hurt or kill) is irrelevant, if the trier of fact can conclude that given the total experience of the defendant with the victim, the act of violence can be understood in terms that lessen the defendant's blameworthiness [START_REF] Kanter | The law: what's disability studies got to do with it or an introduction to disability legal studies[END_REF].

The prerequisites for the use of expert testimony vary with each justice system. Generally, the expert's testimony is the basis for mental defense cases. violence risk scale, such as Violence risk screening-10, should also be taken into account [START_REF] Xiu-Yu | The enlightenment of the risk assessment of aggression behavior in foreign countries with mental illness[END_REF][START_REF] Abderhalden | Predicting inpatient violence in acute psychiatric wards using the Broset-Violence-Checklist: a multi-center prospective cohort study[END_REF].

New rules or rule changes are essential steps for PTSD criminals and the Chinese justice system. A brief introduction and comparison of the American history is helpful in understanding this evolution. The court or society will need several years to accept that criminal with PTSD should obtain light or mitigated punishment. Acceptance of PTSD as a mitigating reason for judgment is inconsistent at first, which is chiefly because courts/judges treat PTSD unfairly and frequently with judicial skepticism. Prior to 1980, Vietnam War veterans involved in criminal prosecutions attempted, without much success, to introduce their war experience as a causative factor of their criminal behavior. In 1978, PTSD symptoms were first used in the capital case of Charles Heads: domestic violence was accepted by the jury, but they rejected the plea of insanity at first. Three years later, the jury found Charles Heads not guilty of murder because of temporary insanity stemming from his war experiences. The defendant's second trial brought testimony from some veterans about stress resulting from Vietnam War. After the spread of DSM and confession of PTSD, the lawyer began to persuade the court that Charles Heads is a mental disorder patient, which could be a basis and important evidence for the application of insanity defense [START_REF] Slovenko | The watering down of PTSD in criminal law[END_REF]. The jury, convinced that Charles Heads was suffering from PTSD, concluded that the defendant is not guilty by reason of insanity. The jury was apparently convinced that Heads' reversion to combat-like behavior is caused by a combat flashback that made it impossible for him to distinguish right from wrong (Louisiana has the M'Naghten Test for criminal responsibility) [START_REF] Swanson | Preventing the unpredicted: managing violence risk in mental health care[END_REF].

Cases For instance, under the American Law Institute (ALI), the Control Test is also known as Irresistible Impulse Test in other areas: when the defendant is incapable of controlling his/her behavior as the result of the mental illness, even if he/she is aware that the nature of the act as illegal or guilty, the actors might be exculpated. The ALI test provides two chances for PTSD patient(s) to propose a plea of not guilty by reason of insanity [27].

Conclusion

After the considerably strong earthquake in Sichuan province in 2008, a large number of survivors suffer from PTSD. PTSD patients occur in all races, classes, religions, and nationalities, and some would unfortunately be criminals. This pattern reveals concern for the boundary between the reasonable use and abuse of PTSD in view of medicolegal expertise practice. Expert testimony or opinion cannot replace the judges' decision. Chinese courts should learn from the American Bar Association and accept the three-part analysis for forensic consideration of PTSD. Further details regarding the regulations for resolving the criminal responsibility of PTSD patients should be obtained.

Declaration

Table 1

 1 Numbers of articles which containing the phrase "PTSD" from 2005 to 2015 in

	China National Knowledge Infrastructure
	Year	2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
	Number 78	82	66	129 203 211 255 231 219 232 224
	On October 5, 2016, the authors used the Chinese phrase for PTSD as keywords in
	searching the China Judgment Online and obtained 816 results. The subject matters were
	obtained from 89 criminal cases, 618 civil cases, and 14 administrative cases. A total of 332
	results deal with medical identification, and 281 are involved in compensation on personal
	injury. The situation is confusing when some victims were diagnosed with PTSD in criminal
	cases or civil cases, but no defendants were identified or recorded as PTSD patients in the past
	two years and nine months. The previous studies showed mentally disorder offender are
	diverted from the prison system to forensic hospital, general hospitals, or back into the
	community (Every-Palmer et al) [10]. However, the authors cannot pick up the information of
	prisoners with PTSD from the website of Bureau of Prison Administration in China
	(http://www.moj.gov.cn/jyglj/node_213.htm).
	Given that no legal demand to upload judgment paper in the Mainland China before 2014
	is available, searching for the criminal cases of actors with PTSD is relatively difficult. Only a
	case with PTSD can be reviewed on the government official website: a 42-year-old woman
	named Ma Yu-xia testified to an unhappy married life and frequent violent incidents by her
	husband, Mr. Yuan. She was beaten, choked, or humiliated in various ways. They divorced in
	2003, then remarried, and lived together after their family members persuaded them. One day,

before Yuan went to bed, they had a terrible quarrel. Afterward, Ma could not sleep and used an ax to attack and smashed Yuan on October 2, 2007. The Court of Chifeng City, Inner

Table 2

 2 China's criminal responsibility system

	Age	Responsibility	Act
	Under 14	No		No criminal charges
	14 and 15	Possible		8 criminal charges: causing serious injury or death of the
				person, or committing rape, robbery, drug-trafficking,
				arson, explosion or poisoning
	16, 17 and 18 Lesser	than	472 criminal charges, according to Criminal Law of the
		adult		People's Republic of China and 9 Amendments (including 8
				criminal charges for age 14 and 15)
	18 and above	Full		472 criminal charges, according to Criminal Law of the
	(normal)

People's Republic of China and 9 Amendments (including 8 criminal charges for age

14 and 15)

  The objective ordinary constituted man or reasonable man test leads courts into inquiries, which are morally blameworthy to some extent. According to medical research, several factors are attributed can determine which emotional or mental diseases are extraordinary, and different countries may have different standard or definition. China has the largest population in the world and consists of 56 ethnic groups. One court commonly identifies a particular condition, for instance, domestic violence, which is sufficient to mitigate responsibility, whereas another court considers the same situation not an extraordinary example to become a major factor in obtaining a below-average sentence. In addition, PTSD criminal still commits crimes even if the traumatic event is over. Whether in Chinese society or not, the basic question in a criminal case of mental patient(s) is whether the actor is as culpable as a citizen who hurts or kills solely for self-aggrandizement or out of sheer malevolence with many mental disabilities worldwide. To address this question and obtain a fair result for the actor, judges must place themselves empathetically in the defendant's relatively distinct actual situation. The whole situation should be assessed generally, not only one article of the criminal laws or procedure rules should bind the judge. An inquiry into what most people would do (i.e., what "ordinarily constituted" or "reasonable" people would do) in such circumstances cannot be completely

  The expert testimony should be cognate and should comprehend the trier of fact. Chinese courts have been increasingly called to determine the appropriate qualifications for experts offering testimony concerning PTSD cases. Resembling Insanity Defense Reform Act of 1984 of United States[23], Chinese legislation should change rules for the expert testimony in PTSD case concerning admissibility procedure of expert testimony. The government should establish particular mental disorder qualifiers for reducing capacity, but the defendant or lawyer should present powerful medical or forensic evidence to prove the connection between crime commission and PTSD effects, as in the American case United States v. Johnson (49 F.3d 766 (D.C. Cir. 1995)). Therefore, the new rule should prohibit expert(s) from expressing his/her own opinion on whether the suspect or defendant is a patient with PTSD. Nonetheless, the expert should interpret how serious the special traumatic event is and whether PTSD symptoms will diminish the capacity of normal citizens. Changing rules aim to create scientific explanations for courts/judges to make decisions and eliminate confusion created by conflicting expert testimonies on trier of fact.Under Clause 1 of Article 18 of CLPRC, the PTSD patients may not bear responsibility, but his/her family members or guardian should be ordered to keep him/her under strict surveillance and support health care. Thus, aggressive behavior risk assessment of PTSD criminals is necessary. The stressor feature of PTSD may assist in its validation, both in law

and society. Three assessment methods for PTSD patients, namely, include clinical approach, actuarial approach/statistical approach, and structured clinical judgment, are available worldwide. Assessment instruments, such as Historical, Clinical, Risk management-20 and

  promote legal changes. California was the first and Minnesota was the second state in 2008 to produce particular statutory rules for convicted veterans with PTSD. Subsequently, many other states and the US federal government joined them. Embracing PTSD as a mitigating element needs legal tests in the US, where various legal tests for insanity are available. The M'Naghten Test (also called M'Naghten Rule) is the main mental test, which takes its name from the known English case (Queen v. M'Naghten, 8 Eng. Rep. 718 [1843]). Approximately half of the 50 states in the US utilize the M'Naghten Test to assess the sanity of a defendant, despite that other insanity test formulations do exist [27].

Thanks for Prof. Li Xin-feng's

Funding

The authors declared receipt of the following financial support from Youth Project of National Natural Science Foundation of China (Grant No. 81200400), National Social Science Foundation of China (Grant No. 14ZDC016), Outstanding Youth Project of Fujian Province (Grant No. JA14130 & 2016J06018) and Young Top-notch Innovative Talents Project &Joint project of scientific and technological innovation of Fujian Province (Grant No. 2016Y9025).

Availability of data and materials

The data that support the findings of this study are available from China National Knowledge Infrastructure and China Judgment Online, and so are publicly available.

Ethics approval and consent to participate

The study received the ethics approval from the Chinese government. All the participants in the survey red and signed the informed consent forms.

According to laws of Chinese Mainland,when it comes to the academic research, after the final decision from court, authors can use the information of cases from the criminals when he or she is a adult without his or her agreement, like Ma Yu-xia case. We just use the materials of the case for the official website (http://old.chinacourt.org) for paper. And we are not the only one who discussed the case without her consent. So we do not consider it needs consent from Ma Yu-xia or her relatives for publication.

Competing interests

On behalf of all authors, the corresponding author states that there is no conflict of interest disorder and criminal responsibility in a Post-Iraq/Afghanistan. World Developments in Mental Health Law 2010;29:59-60.


Théo De Clercq
email: theo.declercq@valgo.com

Abderrahim Jardani
email: abderrahim.jardani@univ-rouen.fr

Pierre Fischer
email: pierre.fischer@univ-rouen.fr

Laurent Thanberger
email: laurent.thannberger@valgo.com

Minh Tan
email: minh-tan.vu@univ-rouen.fr

David Vu

Jean-Marie Pitaval

Philippe Côme

Begassat

Tan Minh Vu

David Pitaval
email: d.pitaval@groupeginger.com

Jean-Marie Côme

Philippe Begassat
email: philippe.begassat@ademe.com.

The use of electrical resistivity tomograms as a parameterization for the hydraulic characterization of a contaminated aquifer

Keywords: electrical resistivity tomogram, hydraulic tomography, hydrogeophysics, inversion, 2 inverse problem, stochastic inversion

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

Introduction:

The strong industrialization of the last century has led to an increase of contaminated sites that currently represent a real threat to the health of the population and the quality of the ecosystem (air, water, soil, flora and fauna). To address these environmental issues, several remediation technologies have been developed in order to remove contaminants or to reduce their spread in water resources; among them, we cite: natural attenuation, in situ thermal desorption, in situ chemical oxidation or reduction, , hydraulic containment, and pump and treat [START_REF] Yeung | Remediation Technologies for Contaminated Sites[END_REF][START_REF] Zhang | Groundwater remediation from the past to the future: A bibliometric analysis[END_REF][START_REF] Ossai | Remediation of soil and water contaminated with petroleum hydrocarbon: A review[END_REF]). However, their applicability and effectiveness still strongly depend on the dynamic of the aquifer, in other terms, to the hydraulic conductivity of soils. The groundwater flow and the migration of contaminant plumes are conditioned by the spatial heterogeneity of the hydraulic conductivity which can be sharply ranged even on a small scale and within the same geological formations. In addition, the brownfields hydraulic conductivity field may be affected by the presence of concrete foundations buried in the shallow aquifers.

In general, the characterization of the hydraulic conductivity is performed by means of traditional pumping tests in which the analytical formulations of the groundwater flow equations, either in the transient or steady states, are used to interpret the piezometric responses to water extraction, in order to derive an average value of the hydraulic transmissivity [START_REF] Theis | The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground-water storage[END_REF]Hantush 1961a, b). The permeabilities can be progressively estimated with a permeameter test carried out on soils sampled during drilling operations. However, both approaches neglect the heterogeneity of the hydraulic properties in the aquifer, which leads to an inaccurate and incomplete understanding of contaminants transport during the remediation process.

The hydraulic tomography tool appears as an interesting and relevant option to deals with the heterogeneous aquifers through a conjoint interpretation of a piezometric dataset associated with multiple pumping tests conducted successively at various wells [START_REF] Yeh | An iterative stochastic inverse method: conditional effective transmissivity and hydraulic head fields[END_REF][START_REF] Kitanidis | Introduction to Geostatistics: Applications in Hydrogeology[END_REF][START_REF] Borgne | Equivalent mean flow models for fractured aquifers: Insights from a pumping tests scaling interpretation : equivalent mean flow models[END_REF]Li et al. 2008). The tomogram of the hydraulic conductivity field, provided from a hydraulic tomography technique, is the result of an optimization algorithm also called "inverse algorithm" in which this field was chosen thanks to its ability to match the observed drawdown data.

Inversion algorithms can be deterministic or stochastic. They both rely on an iterative process in which the groundwater flow equations (forward problem) are solved numerically at each iteration, in order to evaluate the mismatch between the observed and predicted hydraulic drawdown [START_REF] Huang | Stochastic inverse mapping of hydraulic conductivity and sorption partitioning coefficient fields conditioning on nonreactive and reactive tracer test data: INVERSE MAPPING CONDITIONING ON TRACER DATA[END_REF]). However, these inverse algorithms do not guarantee to get a unique solution for the following reasons: i) the limited number of the hydraulic data to capture overall unknown parameters [START_REF] Zhou | Aquifer imaging with pressure waves-Evaluation of low-impact characterization through sandbox experiments: AQUIFER IMAGING WITH PRESSURE WAVES[END_REF] ; ii) The strong sensitivity of the solution to the data noise [START_REF] Ramos | A stable computation of log-derivatives from noisy drawdown data: computation of moisy log-derivatives[END_REF]) ;

iii) The numerical uncertainty of mathematical models that cannot describe all the physical mechanisms involved in the experiment, to which it adds the numerical imperfections related to the numerical tool (e.g., finite difference and finite element) used to solve the groundwater equation [START_REF] Berg | Comparison of Hydraulic Tomography with Traditional Methods at a Highly Heterogeneous Site[END_REF][START_REF] Hochstetler | Hydraulic Tomography: Continuity and Discontinuity of High-K and Low-K Zones: D. L. Hochstetler[END_REF].

Over the last few decades, several efforts have been made to deal with the ill-posedness and the uncertainties of the inverse problem via the incorporation of complementary information on the unknown parameters in order to generate a realistic model [START_REF] Zhou | Inverse methods in hydrogeology: Evolution and recent trends[END_REF]. This additional information is referred as soft data or a priori model and can be deduced from various ways such as: geological characterization (e.g, lithostratigraphic logs, grain size analyses on the soil cores) [START_REF] Jardani | Geostatistical inverse modeling of the transmissivity field of a heterogeneous alluvial aquifer under tidal influence[END_REF][START_REF] Zhao | Validation of hydraulic tomography in an unconfined aquifer: A controlled sandbox study: hydraulic tomography in an unconfined aquifer[END_REF], hydrogeological investigation (e.g, permeameter test on the soil cores, tracer and slug experiments) [START_REF] Sanchez-León | Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization: E. Sanchez[END_REF]) and geophysical prospections (e.g. Electrical Resistivity Tomography ERT, Electromagnetic Very Low Frequency VLF, Georadar and Seismic methods) [START_REF] Hyndman | Coupled seismic and tracer test inversion for aquifer property characterization[END_REF][START_REF] Jardani | Geostatistical inverse modeling of the transmissivity field of a heterogeneous alluvial aquifer under tidal influence[END_REF]). Among these attempts: Soueid [START_REF] Ahmed | Image-guided inversion in steady-state hydraulic tomography[END_REF] used the geometry of the geological structures identified by geophysical tomography as a priori information in the inversion of pumping test data to image hydraulic parameters. [START_REF] Bohling | A field assessment of the value of steady shape hydraulic tomography for characterization of aquifer heterogeneities: A FIELD ASSESSMENT OF HYDRAULIC TOMOGRAPHY[END_REF] applied cross-well georadar tomography to delineate the shape of the main hydro-facies in which hydraulic conductivity values were then determined by analyzing pumping test data. GPR velocity tomograms were used to support tracer test data for the prediction of hydraulic properties [START_REF] Dafflon | Three-dimensional stochastic estimation of porosity distribution: Benefits of using ground-penetrating radar velocity tomograms in simulated-annealing-based or Bayesian sequential simulation approaches: 3-D STOCHASTIC ESTIMATION OF POROSITY[END_REF]. [START_REF] Jardani | Stochastic joint inversion of hydrogeophysical data for salt tracer test monitoring and hydraulic conductivity imaging[END_REF] In this paper, we apply the zonation inversion methodology to image the spatial variability of the hydraulic conductivity field. This approach consists of two steps: first, we delineate in 3D the main geological structures of a contaminated aquifer by using ERT. In the second step, we predict the hydraulic conductivity of these structures by inverting the pumping tests data recorded in 13 wells with a Markov chain Monte Carlo-based algorithm.

Description of the experimental study site

In this manuscript, a hydrodynamic characterization is performed on an experimental site located in a former refinery within a shallow alluvial aquifer contaminated by hydrocarbons. The industrial activities on the site have begun in 1929 and have been stopped in April 2013. The set up of this experimental site aims to understand the degree of heterogeneity in the soil of the former refinery and the nature of the contaminants in order to experiment various remediation protocols. For that reason, 13 piezometers were implanted on a small area (60 m x 60 m) to record the hydraulic fluctuations, and to identify the degree and type of contamination in the aquifer (Fig. 1). The site is mostly covered by an anthropogenic layer of gravel and in some places, of asphalt and concrete. This layer covers an alluvial formation composed mainly of fine sand (< 0.2 mm) and medium sand (< 1 mm) from 1 to 5 meters' depth, and medium (< 1 mm) to gravel sands (< 2 mm) between 5 and 8 meters depth. Preliminary geological investigations conducted on the site revealed highly heterogeneous materials constituting the aquifer. The laboratory analysis performed on three core samples indicate a quite constant porosity (from 28.9% to 24.6% between -7.2 and -10.5m), a hydraulic conductivity varying between [2.31x10 -5 to 6.87x10 -4 m/s] and a low quantity of clay. This alluvial terrace relies on an altered chalk formation (below -8.5 meters), and both aquifers are hydraulically connected to the Seine River; which is under tidal influence [START_REF] Jardani | Geostatistical inverse modeling of the transmissivity field of a heterogeneous alluvial aquifer under tidal influence[END_REF].

Consequently, the water table in the alluvial aquifer oscillates with time-varying amplitude.

The vertical geochemical profiles conducted on 12 wells with spacing measurement of 0.25 meters show that the water temperature is around 12 to 13°C with a vertical gradient of 0.13°C/m from 6 to 9 meters. The pH of the water is quite homogeneous between 6 and 7.5. The Redox potential fluctuates between -60 and -180 mV, which are high values. The absence of oxygen in groundwater is confirming the anaerobic conditions of the medium, which is also an index of intense process of hydrocarbon biodegradation (Sinke et al. 1998;[START_REF] Abbas | Geophysical and geochemical characterisation of a site impacted by hydrocarbon contamination undergoing biodegradation[END_REF]. The electrical conductivity of the water is quite homogeneous in the wells with values between 70 and 90 mS/m. All of these water measurements were realized in wells without floating LNAPL (Light Non-Aqueous Phase Liquid) layer and broadly indicate that the area is polluted with hydrocarbons and ongoing biodegradation processes that are boosted by the tide fluctuations [START_REF] Mercer | A review of immiscible fluids in the subsurface: Properties, models, characterization and remediation[END_REF][START_REF] Sims | Effects of a fluctuating water table: column study on redox dynamics and fate of some organic pollutants[END_REF][START_REF] Lee | Attenuation of Petroleum Hydrocarbons in Smear Zones: A Case Study[END_REF][START_REF] Yadav | An Overview of Biodegradation of LNAPLs in Coastal (Semi)-arid Environment[END_REF].

The chromatographic analysis of LNAPL indicates a partial degradation of gasoline-diesel mixture.

Moreover, the contaminant is approximately composed of 50% of light compounds (fewer than 10 carbon atoms) and the TPH (Total Petroleum Hydrocarbon) analyses confirm that the aliphatic fraction represents 80% of the total mass. Their dynamic viscosity is around 5 mm 2 /s while their density is varying between 820 and 830 kg/m 3 .

Geoelectrical investigations:

For the geophysical characterization, we performed 12 electrical resistivity profiles to get an idea on the main heterogeneity in the shallow aquifer. Theses 2D profiles have been made with a Syscal Pro resistivity meter and electrodes placed according to the Wenner schema with two meters as interelectrodes distance. The stack values were fixed between 4 and 8 with a Vab maximum of 800mV and an injection time of 500 ms. The distance between the profiles is about 10 meters with 5 profiles oriented north-south and 7 profiles into east-west direction (Fig. 1). The north-south profile were 46 to 64 meters long and the east-west profiles were 66 to 70 meters long for a total of 1811 quadrupoles inverted. The processing of the apparent electrical resistivity has been done in 3D using ERT-Lab64 software, developed by Multi-Phase Technologies and Geostudi Astier. This software relies on a Quasi-Newton inversion algorithm with a smoothness constraint and a forward problem solved by finite elements technique with a 0.5 m mesh for a total of 1 909 476 elements [START_REF] Labrecque | The effects of noise on Occam's inversion of resistivity tomography data[END_REF]. For the boundary conditions, we used an insulating condition at the air-ground interface and zero potential on the rest of the boundariesThe noisy data have been processed with a robust weighting algorithm based on data variance iterative reweighting [START_REF] Labrecque | The effects of noise on Occam's inversion of resistivity tomography data[END_REF][START_REF] Mercer | A review of immiscible fluids in the subsurface: Properties, models, characterization and remediation[END_REF]. Most of these noises are due to the bad contacts between soil and electrodes in some places covered by a 20 cm concrete layer. To improve the contact, we placed the electrodes in 30 cm hammer drilled holes.

The results of the 3D inversion of the 12 ERT profiles are obtained after 7 iterations, with a final RMSE of 0.67 Ω.m. We only present the distribution of the resistivity in the saturated and capillary zones of the alluvial layer (from 5 to 10 meters depth), which will be used in a second step as a guide to predict the hydraulic conductivity field. As shown on the figure 2 and3, this spatial distribution of the resistivity is ranging from 5 to 180 Ω.m. On the 3D model, we can distinguish three anomalies with high relative resistivity (> 35 Ω.m) and two anomalies with quite low resistivity (< 15 Ω.m). The 2D profile presented in figure 3, highlight these heterogeneities by crossing most of the heterogeneities If we compare the 3D model and one OIP (Optical Image Profiler) profiles, they are in the same range of value (Fig. 3). This is because the 3D model integrates larger volumes of soil while the OIP profiles are very local, with pores scale resistivity measurements. Indeed, those investigations methods are quite different. Both graphs show an increasing trend with depth from 6 to 8m and then a higher value above 8 m in link to the altered chalk. Thus, we can say that the 3D model confirms and completes the very local information from OIP profiles and water electrical conductivity of the wells. We suspect that this slight heterogeneity in electrical resistivity may be associated with the three-dimensional distribution of the flint blocks that have centimeter sizes that affects the hydrodynamic features of the aquifer. In the OIP profiles, the presence of flints is also at the origin of the increase in local resistivity (Fig. 4).

Hydrogeological investigations

We dedicate this section to the hydraulic tomography of the alluvial aquifer which is considered here as a semi-confined aquifer under tide influence. This characterization is based on a joint inversion of the hydraulic responses recorded in 13 wells during two quasi-static pumping tests conducted on the wells P16 (12 m 3 /h) and P13 (11.25 m 3 /h).

These hydraulic responses are also impacted with tide fluctuations, and therefore require a separation of the natural and anthropogenic responses to keep only the pumping responses for the tridimensional reconstruction of the spatial heterogeneity of the hydraulic conductivity field. The approach used for such processing is developed in the next section.

Data Processing

In this study, we will have to remove the tidal component because it has a significant impact on the hydraulic head variations in comparison to the pumping effect. In fact, daily tides have an amplitude of about 20 cm while the drawdown response is under the centimeter scale. To facilitate the removal of this impact, we decided to start the pumping test during the less curved part of the tide, at its midperiod of 6h10, for a pumping duration of 3 hours. Such a configuration makes it easier to process hydraulic data compared to a pumping at high-or low-tide momentum. The data processing relies on the reconstruction of the natural tide signature by fitting the data recorded before the pumping and after the recovery by predicting the coefficients of the general Fourier function with 5 terms, which has following form: In order to extract a steady-state drawdown value for the inversion dataset, we calculate the drawdown mean values in the last 5 minutes before cutting off the power of the pump. The inversion will be made with these mean values.

F(t) = ∑ (

Inversion process

We devoted this section to the introduction of the inverse theory used to interpret the hydraulic data related to the pumping tests for inferring the hydraulic conductivity field in 3D. The wells are fully screened in the alluvial aquifer, thus it does not provide three-dimensional information on hydraulic head variations, especially on the Z-axis which remains an integrative data on the entire thickness of the aquifer. To fill the gap in vertical data, we used the ERT as a source of information to delineate the main heterogeneity of the field, which could correspond to variations in the hydraulic parameters. The values for the selections of the 8 electro-facies are calculated on the basis of 7 quantiles so that each electro-facies have the same size (Table 1). In other words, we assume that the number and shape of electro-facies recovered in ERT remain the same in hydro-facies, so that there is a correlation between the contrast (gradient) of electrical reactivity and hydraulic conductivity. This hypothesis is based on the fact that the electrical conductivity of the water in the study site is almost homogeneous. This strategy permits to guide the inversion, to avoid the non-unicity of the solution and to reduce the number of parameters to estimate. The limited number of unknown parameters pushed us to opt for a stochastic inversion by using a MCMC algorithm. The inverse problem is formulated in a Bayesian framework in which the posteriori probability function ( ) π | md is defined as a combination of the drawdown data of the pumping test and a priori information on the hydraulic conductivity model to be predicted during the inverse process [START_REF] Tarantola | Inverse Problem Theory and Methods for Model Parameter Estimation[END_REF].

( ) ( ) ( ) . (-10 . ℎ

0 π P | P m h m m obs ∞ , With ( ) ( ) T 1 1/ 2 1 1 P( | exp ( ) ( ) [(2π) det ] 2 h m) m h m h obs obs h obs N h f f -   = - - -     Γ Γ , ( ) ( ) T 1 0 prior prior 1/2 1 1 P ( exp [(2π) det ] 2 m M -   = - - -     m m) m m m m Γ Γ , ( 2
= , in 3D ℎ = 0 , at Γ ! (3)
Where h denotes the hydraulic head (in meter), Q is the hydraulic flux (m 3 /s) and m is the vector that contains the logarithms of the hydraulic conductivity K (in m/s).

We solve the diffusion equation on a pyramidal finite element mesh with COMSOL Multiphysics.

The meshing is defined as extremely fine with an automatic refinement around the boreholes.

Dirichlet boundary conditions were imposed on the boundaries, which were placed at 500 m from the investigated zone. The investigation zone is 60 by 60 meters with the hydraulic conductivity of the buffer fixed to 10 -2.1 m/s.

The stochastic inversion was led with a large constraint on the hydraulic conductivity in which the interval of sampling was fixed between 10 -8 and 1. To seek the best model that can reconstruct the hydraulic data and satisfy the constraints imposed by the prior information, we applied a stochastic approach which is based on a MCMC algorithm. This algorithm consists in a generation of an important number of random models using a proposal function. It then tests their efficiency in terms of data-matching and toward the prior models by computing the posterior probability function. The models tested with high probabilities are selected, otherwise they are rejected. The implementation of such approach does not imply any derivative computation of the forward problem, as it is the case in deterministic algorithms, which facilitates the implementation of such algorithm. However, their efficiency depends on the choice of the proposal density function that controls the random walk from one last selected model to the generation of another new one. In this paper, we used Adaptive Metropolis (AM) algorithm in which the covariance of Gaussian proposal function is iteratively adapted from the previous models in order to improve the strategy of the sampling as following [START_REF] Haario | An adaptive Metropolis algorithm[END_REF] :

" # = $ % "&'(( , ( ) , … , ( # ) + $ % +, (4)
Where Sd = (2.4) 2 /d, is a scaling coefficient with d the size of the unknown parameter to estimate, ɛ is a small positive number and I is the identity matrix. The model proposed with the proposal function will be accepted or rejected according to this following probability:

-. # ) , / 0 = 12 31, 4 ( 5 4( 678 9

(5)

Where : (; is the unscaled density, / is the tested candidate when the i-1 previous candidate has already been tested. In the end, these acceptance criteria guarantee the selection of models that present high quality in the fitting of the piezometric data. In our case, 10 000 iterations were carried out and the inverse result is the mean of the last 25 selected models.

Results

The result is presented as a 3D model in terms of logarithm values of hydraulic conductivity (K in m/s in Fig. 6). The inversion has been made on the mean drawdown value determined during the last 5 minutes of pumping. The means, minimum and maximum value of these last 5 minutes of pumping are shown on the figure 7.

The Root Mean Square Error (RMSE) of the inversion between all the measured and simulated drawdown is 5.23 mm. The coefficient of determination is almost perfect, as the weight of the pumping well drawdown is much more important compared to the small drawdown in the observation wells, and the slope of the linear regression is near one (a=0.9995). These values have a weaker fit if we focused on the observation wells drawdowns, but it can be related to the greater uncertainty about the actual value of the smallest drawdown. Indeed, if we only focused on the observation wells drawdown, the R² is about 0.73 with a slope near 0.9 (a=0.908). The RSME becomes a bit bigger: 5.37 mm. The small drawdowns are related to the low hydraulic connectivity, the large distance between observation and pumped wells, and the possibility that the pumped water is mainly coming from the underlying aquifer in the altered chalk.

Electro-facies -Log(K)

Electro-facie 1 4.450

Electro-facie 2 4.710

Electro-facie 3 4.762

The 3D model reveals a smooth spatial heterogeneity with a variation of only 2 orders of magnitude. The inverted values of hydraulic conductivity range (between 10 -3 and 10 -5 m/s as detailed in the table 2) are realist and in agreement with the laboratory results range (between 4.76.10 -4 to 2.31.10 -5 m/s). There is an order of magnitude of difference between the lab result and our model. This can be linked to the size of the lab sample which tends to decrease the measured value (Geotechnical Frontiers et al. 2017).Overall, the aquifer can be considered as a permeable formation linked to the presence of the gravels and flint blocks that have been revealed by their resistive signature in the electrical resistivity survey. As it is confirmed by the results of the comparisons between the high electro-facies (5 to 8) that have relative higher hydraulic conductivities (see table 2). In order to discuss further 3D hydraulic model obtained by stochastic inversion from the 3D electrical resistivity model, it was decided to perform trials of stepwise pumping in different wells in the study area. These pumping have been realized with an Electric Variable speed drive and a small pump. This device allows for stepwise pumping by varying the frequency (i.e. the flow rate) of the pump from 0.6 to 6.1 m 3 /h. Every pumping lasted about 30 minutes and 2 to 4 flow rates were tested depending on the observed drawdown in the pumped well.

Electro

The drawdown data have been treated as presented in data processing section in order to subtract the tide signal and then implemented in a software to treat stepwise pumping: OUAIP, created by the French institution "Bureau des Ressources Géologiques et Minières (BRGM)". We use the Theis function to simulate the pumping and the software provides an estimation of the transmissivity T (m 2 /s) and Storativity required to fit the stepwise pumping drawdowns. There is an adjustment coefficient "E" to validate the fitting (the closest to 1, the better), also called the Nash coefficient. This Nash coefficient has values above 0.9 in our cases. To be able to compare the result, we have made the integration of the different hydraulic conductivity K of the 3D model on the thickness of the aquifer to get a transmissivity value at the localization of the different wells.

Discussion and conclusion

The use of electrical resistivity data to characterize the spatial heterogeneities appeared as particularly suitable for determining the properties of the medium studied in our application case and allowed for an easier and more complete identification of its hydraulic properties. We tried to use this link to inverse hydraulic data on the basis of electrical resistivity heterogeneities. This does not mean that there is a direct relationship defined in this article between electrical resistivity and hydraulic conductivity [START_REF] Mazac | Determination of Hydraulic Conductivities by Surface Geoelectrical Methods[END_REF][START_REF] Borner | Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements[END_REF] and particularly the presence of the flint blocs in the discontinuous ways in the aquifer that have a resistive signature in 3D ERT model. The use of quasi-static pumping data permitted to transform these electrical conductivities into hydraulic conductivity while maintaining the knowledge of the heterogeneities. Incorporating geophysics information also allowed to reduce the number of hydraulic parameters to be inverted. Instead of working with a regular grid of unknown parameters in the model, we only worked with 8 uniform zones. Naturally, the more zones we would define for the inversion in the model, the longer the inversion would become without necessarily improving the result. Our 3D models integrating geophysical information made it possible to approach more faithfully the vertical heterogeneities not displayable in 2 dimensions. Indeed, the classic pumping tests data we used are integrative along the depths of the aquifers in which one pumps. An alternative solution would be to use flowmeters in order to characterize the recharge zones according to lithology [START_REF] Kabala | Measuring distributions of hydraulic conductivity and specific storativity by the double flowmeter test[END_REF][START_REF] Paillet | Hydraulic tomography in fractured bedrock aquifers using high-resolution borehole flowmeter measurements[END_REF]Li et al. 2008). In addition, pneumatic packers can be used to isolate a pumping over a fixed thickness of the aquifer to characterize a more specified lithology of the aquifer [START_REF] Levy | A pressure-packer system for conducting rising head tests in water table wells[END_REF][START_REF] Bohling | A field assessment of the value of steady shape hydraulic tomography for characterization of aquifer heterogeneities: A FIELD ASSESSMENT OF HYDRAULIC TOMOGRAPHY[END_REF][START_REF] Cardiff | Hydraulic conductivity imaging from 3-D transient hydraulic tomography at several pumping/observation densities: Hydraulic Tomography Imaging Resolution[END_REF][START_REF] Paradis | A field proof-of-concept of tomographic slug tests in an anisotropic littoral aquifer[END_REF]. But this would increase the number of pumping, and therefore the amount of water pumped to be treated in the event of a contaminated aquifer. However, a supplementary amount of data to be inverted would also allow for a better characterization of the aquifer.

Another problematic encountered in our field with hydraulic data was that the natural tide signals did not simplify the acquisition of the drawdowns in response to the pumping tests. Besides, the tidal coefficient influenced the drawdowns. In fact, the underlying altered chalk aquifer is the most direct link between the Seine river and the study area and the variations of exchanges between these two aquifer units in high tide coefficients or low tide coefficients affect the recharge rate and therefore the water table level in the aquifer while pumping. Performing a cross oscillatory pumping appears as an interesting possible alternative as it makes it possible to extract the oscillatory variations data with a Fourier Transform [START_REF] Bakhos | Data processing for oscillatory pumping tests[END_REF][START_REF] Fischer | Harmonic pumping tomography applied to image the hydraulic properties and interpret the connectivity of a karstic and fractured aquifer (Lez aquifer, France)[END_REF] according to their known pumping-rate frequency of oscillation.

Overall, we observed in this aquifer a high permeable structure with the hydraulic conductivity ranging from the [10 -2.8 , 10 -4.6 ] and these slight variations seem dependent on the presence or absence of the flint blocs that heightened the transmissivity. The presence of the flints is electrically identified by the resistive values in the electrical resistivity model. The reconstruction is sufficient to determine the relative low and high hydraulic conductivity zones to better understand the aquifer behavior.

  combined the ERT, self-potential and salt concentration data acquired during a salt tracer test to map the hydraulic conductivity field. Pollock and Cirpka (2010) coupled hydrogeophysical inversion to synthetic salt tracer experiments. Doetsch et al. (2010) proposed cross-gradient joint inversion of crosshole -seismic, ERT and radar to retrieve the main geological units of a fluvial aquifer and their petrophysical parameters, as porosity. Gernez et al. (2019) linked the anisotropic patterns of the inverted electrical resistivity to the spatial distribution of the hydraulic conductivity in an alluvial aquifer.

Figure 1 :

 1 Figure 1 : Map of spatial position of ERT profiles with 2m electrodes spacing, of the wells used in the hydraulic characterization and the boreholes drilled for OIP (Optical Image Profiler) characterization

Figure 2 :

 2 Figure 2 : Resistivity (Ω.m) model from 3D inversion of 12 ERT profiles presented in Fig. 1

Figure 3 :

 3 Figure 3 : Cross-section extracted from the 3D inversion resistivity model at Y=54m.

  the number of terms of the general function set here as N=5.This equation is formulated as a sum of cosines and sines functions with 5 coefficients that will be determined by fitting the hydraulic data. To illustrate the effectiveness of the technique, we applied it on a theoretical case in which the groundwater flow equation was solved in a COMSOL Multiphysics model with a 20 cm oscillatory tidal signal with a period of 12h20 imposed on the boundary condition and a pumping test defined as a punctual source term for a duration of 3 hours. The model has a homogenous hydraulic conductivity of 10 -4 m/s and the same size as the study zone. The curve fitting technique allows to distinguish the 21 mm drawdown of the hydraulic level successfully as it is shown in the figure5.a and b.

Figure 5 :

 5 Figure 5 : graphs showing the reconstruction of the tide signal without pumping to extract the pumping drawdowns. With 4a. the numerical example and 4.b.the real hydraulic level variation.

  denotes the prior probability, function used as a complementary information to constrain the parameter m in the prediction process of the model. m Γ is the covariance matrix representing the degrees of confidence to the prior values prior m . to compute the effectiveness of the proposed model m to fit the hydraulic data h obs . h Γ is a diagonal covariance matrix to include uncertainties on the observed data. This inversion operator is based on a numerical resolution of the diffusion equation with Darcy groundwater flow in porous media.

Figure 6 :

 6 Figure 6 : Hydraulic conductivity (m/s) model after the stochastic inversion to reproduce the pumping drawdown

Figure 7 :

 7 Figure 7 : graph of measured (d_field) versus simulated (d_model) drawdowns with the error bar representing the max and min drawdown observed during the last 5 minutes of pumping.

Table 2 :

 2 hydraulic conductivities of the 8 electro-facies 18

Table 3 :

 3 comparison of classic versus 3D model values of -log TransmissivityIf the P11 transmissivity from the pumping is one order of magnitude smaller compared to the value found in the model, the three other values are convergent and validate the 3D stochastic inversion of the hydraulic model.

  ;[START_REF] Attwa | Resistivity Characterization of Aquifer in Coastal Semi arid Areas: An Approach for Hydrogeological Evaluation[END_REF][START_REF] Maurya | Subsurface imaging of water electrical conductivity, hydraulic permeability and lithology at contaminated sites by induced polarization[END_REF][START_REF] Weller | Permeability estimation from induced polarization: an evaluation of geophysical length scales using an effective hydraulic radius concept[END_REF]. conductivity and porosity. As we worked with the electrical variations in the saturated zone, the variations observed in the electrical model only reflect the variations in lithology

	temperature, fluid
	Wells	-log T	-log T
	tested	model	classic
	P6	2.57	2.93
	P11	4.03	3.01
	P14	3.75	3.70
	B4	2.53	2.41
	The advantages of the geophysics are well known. The 3D data of electrical resistivity provide a good
	and quick characterization of the heterogeneities of lithology in the aquifer. Indeed, the ERT is a
	useful non-invasive method for characterising the sub-surface soils in terms of their electrical
	properties. Electrical resistivity typically correlates with variations in lithology, water saturation,

Acknowledgments

We gratefully thank the Normandy Region and ADEME for their financial support of this work and the reviewers for their pertinent suggestions.