GLQ3205 Géophysique appliquée 2. Méthodes EM: Introduction. Plan du cours

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1 GLQ3205 Géophysique appliquée 2 Méthodes EM: Introduction Gabriel Fabien-Ouellet gabriel.fabien-ouellet@polymtl.ca Été 2019 Plan du cours 1.Révision des méthodes électriques 2.Propagation des ondes EM 3.Génération et mesure des champs 4.Circuit équivalent 5.Exemple: conducteur enfoui 1

2 <latexit sha1_base64="euuppb5jiyxgrviirkwaspas2tu=">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</latexit> <latexit sha1_base64="f68czonzc6u7mt8ovikyxoebzz0=">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</latexit> Révision des méthodes électriques La loi d Ohm La loi d Ohm nous dit comment le courant se réparti dans le sol 2

3 <latexit sha1_base64="d9yopsee/nva1unh249yrwod3xa=">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</latexit> <latexit sha1_base64="ix6u1hvrxymjiw9qattnmo+blki=">aaadn3iclvlbbtnaej3uxeq4pfsrl4uicseroawofakuqsb4qkeibvedrwt306xie631oqwy8if8da/wcfwb/avnbwcvoqpyy/hsmxpozkw2lljdujd82lolrly9dn39rvvmrdt37ny27h2uprkjgiumnfyolqvkda5gtrtuhrvwysxo1we83/f5w4wyptb5o3deqhemt3m91yl0gcadzy8nc7ennkbftitoamvsry9u6qqyikgvpu5nlii7m8t6oyp0pjxctjrdslf1pmqsfwb9xsirs80amo3we4rohawlvffginjyifosvoi5pj6fvaabuw3mitkcv7sknrqvwaomcxso31psjhs0x957lqxoceqk10ip6be0bjyl2j8mof+xs0cv867z09d2jm/cegvahc2a/k23yv6rzvfiaeq73ingtwujvrukcal4kr5ycaerb4ccmi9pkleie1au5ixyu3lvfras89+y6vg/txpurd+bknmgzzytjovp4v4d98wfkvl/2zgr7zplm7xvdmuhxr1jyvwqxxpw+ikz/6/s4stlhaene7i6boly4gcr1w97/bfb3cgguzhrdj8e0mp47dcaxtoqrqjgi32iz/qlebc8ct4ew5/utvaj2atfvvd+b/2twzq=</latexit> Révision des méthodes électriques Potentiel spontané Les mécanismes en PP sont analogues aux mécanismes causant des différences de potentiel naturelles. La polarisation résulte de la séparation de charges. Potentiel électrocinétique Potentiel de minéralisation anomalie Sens du courant O 2 gazeux Potentiel électrochimique: réduction Surface cathode H 2 O Fe ++ Fe +++ OH - HFeO 2 - O 2 dissous H 2 O 2 OH - table d'eau oxydation H + Électrons Fe(OH) 2 Fe(OH) 3 FeS 2 + H + Fe ++ Fe(OH) 3 anode 3

4 Révision des méthodes électriques Polarisation spontanée Le principal attrait de la polarisation spontanée est que c est la seule méthode permettant de suivre l écoulement de l eau Dérive thermique 4

5 <latexit sha1_base64="qmf9fo+qqydzmxsle1x5crstkc4=">aaadlniclvlbbtnaej3uxeq4pfccxmukcalviniqifpsfakheayctjwaennuulnvn63xczxlf+breixf4a/glzgzdvarqoc1es+eoefszhjdijgl8/1vnq3vytvr1zdvdg/eun3nbm/r3n6zvzbskyhpcnsybqvotkynzrhehxzwb2my6ipw9cxnd5balibp3ruzqs/s4cqzsykcb2je257art6vdrw3ak8faloszif6adq8m6/wzhp1tlg1at7r+4odzz6w+jmydnxzfwrxon/qbnoujimnicpksvngdnfcazv4jmhiphxazlqds4im5du11iw2akudeqa9xf8jdkctmmhpnqwoi5ys4gehvpqymhw8i5hpu5kvxjnry7xr8etazvaow68uqkmf0l/p1sx/1xevjmlalr4meioe4e6i1qwsqxdl6kjxdg4fmi6pkbeii1gu56xeu0rvpnta8t+fysjvo5zb0y+2ygzisqavsv0z3gvgzfyiiv5mm0hyj5yz2dee4qpg7fhklfrxbbhfcvp/lx2c2fx4urih68umlg/2dwzdfzb86/dho/zgbtjdekrp4pecrvsgxjrbbz/om32hr94d74x3ynt9tt3otjr79nvyxj8bvxbadq==</latexit> <latexit sha1_base64="wxhhcnw02yawnwkfj8nhu7wfhro=">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</latexit> <latexit sha1_base64="i7s4rdqyrkhlokpgjvj6q5nqrbs=">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</latexit> Révision des méthodes électriques Mécanismes de conduction Pour comprendre l effet PP, il faut comprendre comment les mécanismes de conduction électrique. Potentiel d électrodes Conduction ionique Potentiel de membrane : Porosité : Saturation en eau 5

6 Révision des méthodes électriques <latexit sha1_base64="stcbkydr4rjcykp2mossfimqz9k=">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</latexit> Déviation du potentiel Les inhomogénéités du sol dévient les lignes de courant et les équipotentiels. 6

7 <latexit sha1_base64="ezdq14xsgnfw+065cg7jawwjp6a=">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</latexit> <latexit sha1_base64="axoe+gdfupreld7obx/2uqzjd7a=">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</latexit> Révision des méthodes électriques Méthodes électriques: injection de courant Pour mesurer la résistivité des sols, on injecte du courant à l aide d électrodes plantées à la surface. Électrodes loin de la surface C 1 Source de courant C 2 Surface Électrode à la surface milieu homogène Ligne de courant Équipotentielles 7

8 <latexit sha1_base64="fqowozez6r75q3ht0h2c+inglus=">aaadk3iclvldahnrej50q9b401txypvfiipi2a2khviithfecc2yttcesht60i7zp86ets0hj+dteksp0jdo36lfjcdskakew+7ofdpfd2zmt1ymswwd4lyx5c3fun1n5w7z3v0hd1dba4/2qqi2svdvkrbmii4qnsa57tvepvqgndrk4ltvx5mtju9ptamsiv9sz0o9zkljpbknkrkarq0xe3/th4xnpgydc1kmum/ke86d+9q5o1y76htfbvj+n0bycws1ya2dyq3xigz0raupqikjttlz2clfvgefukgblccgnanmycus1zsnjrg1sjqyiqatvi/hhto0h8+albavtknxgdb9eg5ogtwdm0/zjv6lmqm3ac9ek2s7wzd2whlqsyda/8zbzp4rj3uxnkz16sfbt6ug3j1ykrvmhsv3r3vlovacy/sicqnbcxmxz184lftos40kfigzjlkvxg5nl67khmiptcut+nooz4bz5hqv8t8bcsi6yzmddwmwvgjoipvuqx9ngpgpzp4/s40t59d2e/dwcdn8m429bicmouhu23av527kcj2lz/qseu+prx9ph/qo4ct9o+/0w3vibxgfvo2fqusnx3lmvy3v0xvxnr5s</latexit> Révision des méthodes électriques Modification du potentiel: méthode des images Comment le potentiel est affecté par les hétérogénéités? À l interface, un portion k du courant sera réfléchie. Lumière Image C Medium (1) Medium (2) C l 1 Le coefficient de réflection est entre -1 et 1. X P X P l r 1 r 2 miroir semi-transparent V =U (a) ( b ) P r 3 P l 8

9 <latexit sha1_base64="ii2n64kg21j//walprogb6xapje=">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 b4pmrm7qpbppd+g3tqn6q/s0rawf6sv9oj/oayd2rfneundajeyurszn0y+iwdm4</latexit> <latexit sha1_base64="05qrrbmo32gu9ctqdthpfbanbnu=">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</latexit> Révision des méthodes électriques Résistivité apparente La mesure du potentiel permet d obtenir un estimé de la résistivité du sol, la résistivité apparente. I où K est le facteur géométrique, propre à chaque configuration d électrode V C 1 A P 1 M P 2 N C 2 B r 1 r 2 r 3 r 4 9

10 <latexit sha1_base64="pjqvaafycuuxu6nbbv2xo8kql3g=">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</latexit> Révision des méthodes électriques Profondeur d investigation La résistivité apparente est une mesure moyennée sur la profondeur. La profondeur des lignes de courant dépend de l écartement des électrodes. où L est l écartement entre les électrodes 10

11 <latexit sha1_base64="pjqvaafycuuxu6nbbv2xo8kql3g=">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</latexit> Révision des méthodes électriques Profondeur d investigation La résistivité apparente est une mesure moyennée sur la profondeur. La profondeur des lignes de courant dépend de l écartement des électrodes. où L est l écartement entre les électrodes 11

12 Révision des méthodes électriques Sondages électriques Pour retrouver la résistivité vraie des couches, il faut faire plusieurs mesures qui sont sensibles à différentes profondeurs du sol. I A M V N B 12

13 Révision des méthodes électriques Abaque: 2 couches, dispositif de Wenner Les abaques sont une série de courbes normalisées! 13

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sha1_base64="ddg+ruhq4qdqwybfg0ekggd6bn8=">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</latexit> <latexit sha1_base64="vlirlbnalxxsvnokkfho5jltsxk=">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</latexit> Révision des méthodes électriques Interprétation: Principe de similitude Les méthodes d interprétation se basent sur le principe de similitude. Principe de similitude: Les résistivités apparentes mesurées par deux dispositifs peuvent être les mêmes si certaines proportions sont respectées: Soient 3 facteurs de similitudes: Alors: 14

15 Révision des méthodes électriques Tomographie En général, on utilise la tomographie pour retrouver la distribution de résistivité dans le sol. 15

16 Révision des méthodes électriques Choix du dispositif et sensibilité Dipôle-dipôle Schlumberger 16

17 <latexit sha1_base64="a8ehzknmqvzrtx09qmckas6shza=">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</latexit> <latexit sha1_base64="kou+j/3mb6u3dw3hiiwkxmfl6pw=">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</latexit> Révision des méthodes électriques La PP dans le domaine du temps Différentes définitions équivalentes de la chargeabilité existent. Selon les potentiels: Signal haute fréquence Selon les résistivité: 17

18 <latexit sha1_base64="8xrgvjtsxlyzaydmha4vmubnpca=">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</latexit> <latexit 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sha1_base64="txzjipgleq2d2yvp6fy4gx6yczu=">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</latexit> Révision des méthodes électriques <latexit sha1_base64="ugdtip/b5eajerwlcrjnkh/19di=">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</latexit> <latexit sha1_base64="ixh4ifottyk5vbedvqwffveb2lc=">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</latexit> Résistivité moyenne Attention: La direction de mesure peut grandement affecter les valeurs obtenues de résistivité apparente. Résistivité transversale (résistances en série) Résistivité longitudinale (résistances en parallèle) 18

19 <latexit sha1_base64="3kt3lyyjpbdwga7j1qdws++5lci=">aaadfniclvjdtxnbfl1lvbb+upcrl42nxphydxssewzic4+qucchtbm7nzyj+5wd2qpp+cu84l/yh8i/8nzlyfbi1nls986555y593bskjpwrdg31krw6pgt1bwn7wfpx7xc72xshtqyqzueqjir6+m0stozhr464zj9xnu6ydnmh6vnnzl/tnc1nwvx4c4qpc6tewfmriuo0kszobjmnietfjhs09kfp5p+pnonepgs8geq+6blfu2vg633nkiplasoozw0feqqz5sqxxncmuvuarvtelinyehe0yw1ow3a0makqm/wo8fuxkmf9uxpra1wsoa3hjkkn9cu4nwi+brq8o04m/on76v4cm0x+kbekwfq6bto33r3zh/vcs+ozrqjprj0vanc3snv0shuuplwxlcodhuwjqfi14ivko/mhirgsu8820ty34xjko+v5zz046ssghyraevsfwh3jxbmllar/2djqdhnjmewbwrfuedsakvk/xmcjc+e+f/klk68vpe0cq/j32/dw+cw34ujxry/3r0m/i1coy16te/g94kgtet7neqf53rf1/q1oobt8ch4eetdaxnnk/plbts/al8htcq=</latexit> <latexit sha1_base64="3fwvsvxiq9rxvhyzvgim5w02+i4=">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</latexit> Révision des méthodes électriques <latexit sha1_base64="/9amqgwrrvrfw/nay4jhvw9f9io=">aaadfhiclvlbbtnaej3eueqakskri0vaqiaio0jtj5g4ccwsass1uwrvno1v22ut16fv1d/ptfwtfwa/gxgzbfghqrrroz59897bmcmmvz7vloq+ttrbnbtr99bvdx48fltxulv5zk82jvv6pexu7ega1drpsj1ymcv1qwv1uqs53k+p33n+f6ltnznykzut9krijspsnqneazp2u2o7mnnbofyz48lfdddt9qj+jcu8hsq+6jffu2az9zrgncndihoqsfnjdnfocdv4dimmicpge1obs4gyyws6ow60dvgajatomx6psdv0aik9e9aivjglx2uhdoklnay8i5hpcyxfidoj//jeisfxdopv6r0koi4wqp+nu2tevme9ojrtjvsqoadkeo5oezdgpskvh1e6cncoghe8q94ivqk8nhmomlp659kmkv8mtez5rzy3oe++yhliz5lwifwxcf8bz+ysfff/nhgefezybvumujwizo61vkl/t4dxptbvr+zhxlmrtwf3mp771l0p9gb9oorhh9/1hkn/i9fpgt2nv/dbpif9of0aoyilndmffwn/cf4eb4k3v6jtltc8pt9wsputlgu15w==</latexit> <latexit sha1_base64="3fwvsvxiq9rxvhyzvgim5w02+i4=">aaadbniclvjnaxrbeh27oyaux4kblyiolklwsmxiqi8lxjxgcjnassjmpdc7zl7o6dkklpklxvwv+q/05k/iq7ij0sbqd7nt/eq911w1ntzf3roo+tlrbzdu3lpzvt24c/fe/qdr6w932rqzmzlkdvhbvtrptzfxzujyv5i9xpqktauzmx6/kfzuwtg2r6v37qwx0zi5qvjznivooam7rz+sdanrpcu8hsq+gmkv7xq99wihoesndb1kgfrwjaskapnsi0aehtgus2kwua55g3mmqo3immqkri/5e8tdvkcr7swzvxxguwq+lsoqz6mpybom5brq8506c/on76v6sm1n/kbeqytqmcf6n90l81910ovddk+1h5w9nypid5l36xqqunl4psthh4ayxifmw8azki/nhkqm1d5ltonmvyptunlnntvhm6+yinki0yq1/orus+lcxlai+c+miojptm8q35sku8xfsduqzc8jcl5q5v8rhzzx/moz4d2mf79114odl6m4gsxvtobjsb+rq3imz9ik3yum8rbbmlccot7iez73vwepgifb0x/ufs9rnvdlcjyvaaxcsw4=</latexit> Sondage: Principe d équivalence Attention! Deux modèles tabulaires différents peuvent donner des courbes de sondage très similaires l une à l autre. Couche mince conductrice entre deux couches résistives Couche mince résistive entre deux couches conductrices Profondeur Seul le produit conductivité-épaisseur peut être déterminé Profondeur Seul le produit résistivitéépaisseur peut être déterminé 19

20 <latexit sha1_base64="3fwvsvxiq9rxvhyzvgim5w02+i4=">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</latexit> Révision des méthodes électriques <latexit sha1_base64="3fwvsvxiq9rxvhyzvgim5w02+i4=">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</latexit> Sondage: Principe de suppression Attention! Deux modèles tabulaires différents peuvent donner des courbes de sondage très similaires l une à l autre. Modèle deux couches Modèle 3 couches, résistivité intermédiaire Profondeur Profondeur 20

21 Révision des méthodes électriques Conception de levés électriques Lors de la conception d un levé électrique, il faut aborder les questions suivantes: 1. Problématique: Que veut-on mesurer? 2. Propriétés géophysiques: Est-ce que les propriétés électriques sont sensibles au phénomène étudié? 3. Méthode de mesure: Est-ce que la méthode peut mesurer efficacement et assez précisément les propriétés désirées? 4. Mesures sur le terrain: Quelles sont les précautions à prendre pour obtenir des mesures de qualité? 5. Traitement des données: Veut-on des mesures quantitatives ou une simple détection est suffisante? 6. Interprétation: Peut-on obtenir une information géologique des mesures géophysiques? 7. Synthèse: Intégrer les informations géophysiques pour répondre à la problématique formulée au départ. 21

22 Méthodes électromagnétiques 22

23 Méthodes électromagnétiques Mesures électriques vs EM Tomographie Électrique Méthodes EM 23

24 Méthodes électromagnétiques Mesures électriques vs EM Tomographie Électrique Avantages Haute résolution Inversion assez bien contrainte Bon pour les anomalies résistives Assez robuste aux bruits culturels Inconvénients Mise en oeuvre ardue Échelle régionale impossible Nécessite l accès au site Profondeur dépend de la longueur du dispositif Méthodes EM Avantages Rapide et simple de mise en oeuvre Échelle régionale possible Accès au sites n est pas nécessaire Une bonne profondeur par rapport à la grandeur des dispositifs Inconvénients Interprétation souvent qualitative Inversion doit absolument être contrainte Très sensible au bruit culturel 24

25 Méthodes électromagnétiques Applications courantes de l EM Les méthodes EM sont utilisées dans presque tous les champs d application de la géophysique! Ces différents applications utilisent différentes méthodes EM évidemment! Exploration minérale Estimation de ressources minières Exploration pétrolière Suivi de réservoir pétrolier Études hydrogéologiques Caractérisation de sites d enfouissement Détection de dolines Détection du pergélisol Détection d infrastructures souterraines Archéologie Contamination des sols 25

26 Méthodes électromagnétiques Types de méthodes Méthodes à champ uniforme (non vues dans ce cours) VLF (very low frequency): Utilise le champ magnétique créé par des antennes radios lointaines de très basses fréquences. TURAM: Utilise un long câble (centaines à plusieurs kilomètres). Mesure du champ magnétique à l aide de deux boucles séparées d une dizaine de mètres. MT (magnetotelluric): Utilise les champs électromagnétiques terrestres pour aller cherche les résistivité en profondeur de la Terre (300 m à plusieurs km). AMT (Audio magnetotelluric): Même principe que la MT, utilise les sphérics produits par les éclaires. CSEM (controlled source electromagnetic) ou CSAMT (controlled source AMT): On utilise un très long dipôle (~2km) pour produire un champ électrique entre 0.1 Hz et 100 khz. 26

27 Méthodes électromagnétiques Types de méthodes Méthodes à champs dipolaire (vues dans ce cours) FEM (Frequency EM): Regroupe les méthodes utilisants un boucle émettrice et une boucle réceptrice qui utilise une ou plusieurs fréquences à la fois. Conductivitmètre ou LIN (Low Induction EM): Méthode en fréquence FEM qui est conçue pour fonctionner dans le régime à faible nombre d induction. TEM ou TDEM (Time Domain EM): Regroupe les méthodes utilisants une boucle émettrice et une boucle réceptrice dont le courant est une impulsion dans le temps. Méthodes aéroportées: Les méthodes FEM et TDEM peuvent être déployées sur des avions ou des hélicoptères. 27

28 Méthodes électromagnétiques Types de méthodes Méthodes à champs dipolaire (vues dans ce cours) FEM (Frequency EM): Regroupe les méthodes utilisants un boucle émettrice et une boucle réceptrice qui utilise un ou plusieurs fréquences à la fois. Nous verrons séparément les deux grandes Conductivitmètre familles ou LIN de (Low méthodes Induction la semaine EM): Méthode prochaine: en fréquence FEM qui est conçue pour fonctionner dans le régime à faible nombre d induction TEM ou TDEM (Time Domain EM): Regroupe les méthodes utilisants un boucle émettrice et une boucle réceptrice dont le courant est une impulsion dans le temps Méthodes aéroportées: Les méthodes FEM et TDEM peuvent être déployées sur des avions ou des hélicoptères Cours 1: FEM Cours 2: TDEM 28

29 Différentes méthodes selon la fréquence Profondeur (m) Fréquence (Hz) 29 (Pellerin et Wannamaker, 2005)

30 Méthodes électromagnétiques Bonne références Voir le site de UBC sur le EM: 30

31 Méthodes électromagnétiques Comprendre les bases de l EM 1. Comment se propagent les ondes électromagnétiques? 2. Qu est-ce qu on mesure et comment le mesure-t-on? 3. Comment peut-on détecter une anomalie dans la sous surface? 31

32 Propagation des ondes électromagnétiques 32

33 <latexit sha1_base64="gpjx3anh9ea0tdt2ajlc/xsnl3a=">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</latexit> <latexit sha1_base64="dvltlhbalwtfk+eve23y6xkqntu=">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</latexit> <latexit sha1_base64="wnb5gfepkvpotjctroeb9vt3f98=">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</latexit> <latexit sha1_base64="pwzjkjkeuoijbdbhiya0unoxy2g=">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</latexit> <latexit sha1_base64="szhmjwgf8lgarglleglutgv86m0=">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</latexit> <latexit sha1_base64="de121o9pkx505bxhdgo1bkj+qh0=">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</latexit> <latexit sha1_base64="qdpexm3sjp1ri/jf1fybktq4vvu=">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</latexit> Propagation des ondes électromagnétiques Équations de Maxwell Les équations de Maxwell sont à la base des méthodes EM! Équations de Maxwell Loi d ampère: Équations constitutives Loi de Faraday: Loi de Gauss: Loi de Gauss: (magnétique) 33

34 <latexit sha1_base64="gpjx3anh9ea0tdt2ajlc/xsnl3a=">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</latexit> <latexit sha1_base64="8qygmmpaeyfr+ajfpdsriiaqljk=">aaaefxiclvjlaxrbek7z8rhja6nhl42liajltc56erbmyrhecg4sycyhz9itm/q86olzdcp8dn+nn/hqwzp/qh+cn6sqhc1lenvyneqvvu/rqppoa6mbf0xfg0f45eq160s3lm/eun3n7ndl3kztttzts6wyld1kzaomltxmawfuvm2vlfkjntp9f5tfxcjb6kp86w5qns/kxqlznumh0m6wseqzgikspwvvifo7uki7as+en8qzftmljyljrcy6pjbwawnoya31/d+063ego2gc8rjng9ghi/brvvojppdallsqqqsfkcjbywxaqoppnsqqqy3yhdreleaa8wp6weztiyyfdinopv7v4w7boyxuybnhdyangpxzvap4hjokerzjok1wvmvnqv/l3ben1xaa79r7fyg6eiforboj5mv11iudhj5xdxp7qhmh7jlv0vjuqhjxrcuhdjvifo9i3mkcsfjozoi1dfdos5wc/8fmqmmfew4lp32vjslvevof11+ie4c4mrdyex2zospkk/mz5jui4gpj5nhwlerpbahfmpp/lsm8st/2ujvrrdxcl4jxnvvat4r2dbms3uxocfhgld7h+psnprtsri7jaby/iuatib/ns/aahsjjrouptgak6zddcr7br2aqhohh8fp4ofxysb0exnmftqzw62/nzubc</latexit> <latexit sha1_base64="wgotwzww56muczjzg1a0do31/ag=">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</latexit> <latexit sha1_base64="dvltlhbalwtfk+eve23y6xkqntu=">aaadqhiclvlbbhmxej10uzrws+grf4sicvui2uufhkckqeg8bok0rd2o8rposeq9ypygqtx+df/dk7zxb/axzexdkfqi8gqz4zpnhm9mxdtw+jcmxwybyywlly5vxhlevxb9xs3r1q0dx7do6bmqbe12c+m1nzwebxos3m2clmvh9ai4ek75xvo7b+rqdthu9lkuh5vzgsudqvujj3klcytfhkypvcibsuhe9okpejcvnfrd3kgxjlqnmwd9/xmj/f5one5sxuj8kmvgdhhn6q3bnurwaduoakeedruejc1i8pjsqqypnigtoupmywq4r6ghiwpbzglksesp8pcqd3srrxbpnp7vck+x+dpucrihmhp5dmm6txc+zwdc/+tdssfvdozfinqviaz4i+jfdkfmf9vrlwfw8jh7mnhtwwh1p6jly1ohyswzrgi6nihrfib5h7fi5emcbws8906zlzz/ykxcaa8it4vvscokkxc8rzlrr9c9q5yya6yi/rmli+sz4jpit0dfe8bj0xov+scecf8z8/+vyzyxp/mm8r5mv9+688how0mwtrjx6xg6jtdye+7axbipfo9gci9hbnos4an8he/wodlozskiexnc3rhezw34zsxfdwsax8q=</latexit> Propagation des ondes électromagnétiques Propagation des ondes EM Les méthodes EM se basent sur la propagation d une onde électromagnétique. On peut en effet trouver une équation d onde à partir des équations de Maxwell: À partir des lois d Ampère et de Faraday: On prend le rotationel de chaque équation: 34

35 <latexit sha1_base64="4k+kklvi674iqetkrz7b6hbxpqi=">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</latexit> <latexit sha1_base64="bbcjunijzsleb0dlgo1o0p/edgc=">aaad2niclvjnb9naej3ubur4suhizuwevjci7fzguiksqujyjnjwqtnq7w7cquu1tbtoqsxfucgu/dqu/ap4c5yygdwqubcwlupzn++9nzlsvhntqxx/7q1f61euxtu43r9x89bto4pnu7u+rf2upnlpsrefsa+mtmoaddbqv3jkfplre9njc8rvlzxzursvw1mlzovcwd3xuqwihq3svmplzuthwdwrqdelqoq0qeu6dzjv0kq6okvplyirwikqymtt2t9qd8erznw9emlvzm2lvmyl+ggwjecxl3e5slpgcn3aktd7jygfyyghhxokugahygxagsfnabkioujsbg1idipnequt9ffbi0shqyj6gr8l3b10qmu9expw53ikwdehusbd1jticxjtaylzntst+ifvhj2ptjp8zp1xgwian4j+txfo/fcd9rjgds+4b409vyxqd3nnuvnuqhkx0lvahwoxio8x7zdowxk+z8eaz73tbcxnvzctunrnhbegr12vfpftnlbb9vt0bxan5hirov9sxgj5zpkm8s1q8zzxcvrcpbqyaoflzv6/cogntitph+9h8uutuxzsjkdjpepexcpjplurg3afhsaw+j2fcbyehzhibz/gwy/qrudp9c56h334qv3rdzp78nokpn4hdg7y0g==</latexit> <latexit sha1_base64="wna2/mkijcihkrn68mp0p44ktv8=">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</latexit> <latexit sha1_base64="nd48vsjpxlqwpklwarekbpkbdxw=">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</latexit> Propagation des ondes électromagnétiques Propagation des ondes EM Les méthodes EM se basent sur la propagation d une onde électromagnétique. On peut en effet trouver une équation d onde à partir des équations de Maxwell: Sachant que on obtient: Ceci a la forme d une équation d onde: 35

36 <latexit sha1_base64="gd0a+1mblsxj/ay02n1fb0czco4=">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</latexit> <latexit sha1_base64="51oh/zq50jwirlfn8xb7si61iiu=">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</latexit> <latexit sha1_base64="afxy0n8g9jxx5n2ngkm/xpo4squ=">aaadshiclvjnbxmxej10+sjhk4ujf4siqycidnobc1iehdgwibsrumnk3trb1pau1t5afeup8wu4ll8a/4kzwuwbcgfebxb85r3nmyml2mgf0vsss5vcunzl6va17vubn2/d7u3c2fdv25rqxfamaiaf9mpop8zbb6mmdaoklyw6ke5euv5gqrqvk/c2nnzqauxc6bkuzubo1nu1mztzghk0fe+efrnxcytfblurv1ytphgsclv7bsq3gr4nh4q8tsxqxvo8f+ms108hks9xmchi0ie49qqdzipi4rgqkkefcwocbiwnspd4heigkdsitwgfwior5rycnxrr2yjliumieok/c9wdrtthnjw9q0s8xedboflaa9ruygswptme51t2jvrp3iv2pnpo8vtel4toghei/k13zvxxhfusya7puaenpdwmuhdldgl5kls52ogqoeongmxhmg8wlll5pmfbgs+902wl578yk1dal5hbwrdypupka0/lcv0o3veie3ojfdf/nmwefoz8bvkwqpjiodl6rll9nadhs2b+v7kpj643ni7ew+z3w3cx2b8osnsqvun7o1g8kdtwd+7dlvo9hrg8hj0yywwf4docwzdkmeyswsj/ulc6uxmxflnj++/opsfo</latexit> <latexit sha1_base64="kj4r9cn/f43qdazghxwciah3udk=">aaaduhiclvllbtraekyneytw2scri8ukidpkzgwehlqshhjbbilnimvxwxbgyyh+awwvrkv8cvf4j/4a/olqzgqfigsmteue6qqa7vaktwhbloq+dtack1evxv+/sxhz1u07d4eb93bbunezmwz1ubv9nglnyssz7wxxmp3gmarmc7oxhr+q/n7sunbw1dvupdhzmllunrdz0he6ha5ndwkwsfg83apnjq3zw+eogke6wstb7imr/nqpnwfbmoeintl0kgfqownciehl5waxijte5lgrc4ys5g1osuftt5yhiyf6zp8fdwcerbgxz1bvgu8p+hnuhnhetu2eyyynhzrv1vnqp3mv1fnqo+e79v4l0q7vif5nd878v5300ihhu+3bsqdgeeku8y69tkuqdy901dghisbxefoocabk8zmhqmm1d5ltovlvyhru9pnn9vjuq6yifnbplvp/rfcvcweuwzf8s7ki4pprgekbuvfrcxfsturzcwkcl5x5/8ortzy98eivl1vbaf8grzz3tz+i7oqmzhsx0+psts3vcpz7jb0c7g6n42gcv4lgk4m/zet4gid4zfqeyijt7gdkcpb4hm/4ejwl3gwlwj5r1wzecx+/rmd9amwdwwi=</latexit> <latexit sha1_base64="/dyz293u77edmg7a1r+wzqf0ig0=">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</latexit> Propagation des ondes électromagnétiques Propagation des ondes EM Les méthodes EM se basent sur la propagation d une onde électromagnétique. On peut en effet trouver une équation d onde à partir des équations de Maxwell: Posons une solution de la forme : où est la fréquence angulaire. 36

37 <latexit sha1_base64="aljzsupwvlh2guyyclj/a30ev9m=">aaadfhiclvllbtnafd2jeztwsmhjzkraqiaiuwtggxsjdcsikbrsgyrbnrsrfskep62i/glb+cf+ah4cce5ligovaszyfofcc87ceznjnwetc8ppvx5w6fkvq2vxbtdv3lx1e7h+z9zwxzpaavrlvbodxk3ns9joxezyu103ni6s3g4lh68kv7w0tztv5vt3utt5er+u2sjly0dobzjclemkj827dtmzl01o9oajcbzqmhedyacj+lvzrfceyxf7qjciqwgleo5xjhgtnx1ecfetm2nfrgguad7ifanqo7isgthrq/4eclfj0zj78wxvnfkung9dpcfdairygszymtf8p86c/sl7pz5s2wm/ifcqidq8j/o33rnzx3xsi8mcl7shjd3vikh3qxfpdcpsutnxlandtuzifeybxqkqz+zsvnnq7zlbwpnflcmo7fpp7fdvv1ksodjpfvp/sfcvcweuwzh8z3nfxgehz4hvqswx4ulyapx25wqexyrz/5ujnnh67hnwhka/37qlwwxjhixj6e04mkz8jvzdpdzhi/o9xwsvsykpk1jiaz7iu/9b8cb4ejz9qe33voyuflnbs++ombs7</latexit> <latexit sha1_base64="juxzrxjce5jwr//yjfe0os++yce=">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</latexit> <latexit sha1_base64="51oh/zq50jwirlfn8xb7si61iiu=">aaadshiclvlbbhmxej10uzrws+grf4siqycidvmcl0irainhipe2ujenvfsnmnre1dobqkl8ef/da/kc+atmbhcfkgr4tdnxmxoozyyuaqn9snozzlzy6fkvq9vxutdv3lx1u7dzz99xbvoqcvmzqpku0iujnrohhyya1i2stjdqodh5qfmdpwq8rtzbcfqrqzulp+e6laghwe/lbu5kyetrudwrwurel6wuuw1fxlm1kokxyfxttancbno0fcjy2harv2vxxkszxj8dplzexsclqr/i2qt2oo8gh2oooiqwlchweda2imhjcwgzpfajnouvyg1gmvmk1tbfbysshqyj6an+lnb3gfghe/l0rc7xfinvg0obd1btia/bme4tng/zmda/ea/yk2o7xw8rvsyiad4h+jfdofnfddrlgdk84x409lqzqt2v0axlqvdlyqorga41yhqfy77bugtl+zwfazz3trovnp/ktejpx0zuc99ilq6rdzwty/u7df8htswlvkt/2zqr8pnzgerbooij4+touur1cwkel5n5/8o+nrjeelp4d7pfb93fyh84ynjb9ibtj0bxrm7dpbgpu+j3febwgvzgjbv8gs9wbl+sytjjzon8qd3qrm1d+gul778d12lh0q==</latexit> <latexit sha1_base64="n0/jkw6ezt2bzoj0i2y6+3ft9xq=">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</latexit> <latexit sha1_base64="c2afbss9nhvwiop2iwknwo+ety0=">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</latexit> <latexit sha1_base64="fypgqfsat+2m1zu/gjhi/wedlsk=">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</latexit> <latexit sha1_base64="qzmarxh2hamgygtb4mdcqfpfhs8=">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</latexit> Propagation des ondes électromagnétiques Approximations possibles Différentes figures de cas sont possible selon les fréquences utilisées Méthodes DC Méthodes EM Méthodes Radar Régime permanent Régime diffusif Régime propagation 37

38 <latexit sha1_base64="aljzsupwvlh2guyyclj/a30ev9m=">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</latexit> <latexit sha1_base64="juxzrxjce5jwr//yjfe0os++yce=">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</latexit> <latexit sha1_base64="51oh/zq50jwirlfn8xb7si61iiu=">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</latexit> <latexit sha1_base64="n0/jkw6ezt2bzoj0i2y6+3ft9xq=">aaadmxiclvlbbtnaej3uqeu4pfdylxurukfqzpefviafiaskp1ylbau6vgt3e1b12pz3haiifavfwyt8bx/q/gvnhy0qvahyy/hsmxpozkw2qwttxrx/6yxfn27ewl653b1z9979b73vh/u2aptcjfkqqjrdtfpv6fknnhafoqwbju1wqips9jxph8xuy3vvvnvntrobos31rofsatrubaynpcwk+w5tbagtuqunrorutcktjjpk8vsktcnmrxfihyipe/14epms14mkbh0ka6da7tyjle6oopxamqsojie4iekwzxelffmnbexzya0izxlfc+pc24klwjbat/e7xe4oocx23toyoscpbd4gskfpoknaaxd70wtnw3b26j+85+zpazvdnwtebqij90d/prtk/qvo9+joqlvcg0zpnso+uzy4tdwvx7m40pwdqw3mxyfin4hzvl7owbdgcu9+tplz58z0qn/ngdvsraiybpkbp2w4/hluc+ceounf/j8bm+j9jnyg982g+mi4d7rcpfo5ay/pmpn/yj5oxfx5urihye+37nqwvzli4kgyg/ehw3ajv2inhtm6/j7tklzph0ao4bn9pi/0nvqlxkbb0zsf1kvo0dyix1a09x0wyl7x</latexit> <latexit sha1_base64="c2afbss9nhvwiop2iwknwo+ety0=">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</latexit> <latexit sha1_base64="c2afbss9nhvwiop2iwknwo+ety0=">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</latexit> <latexit sha1_base64="fypgqfsat+2m1zu/gjhi/wedlsk=">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</latexit> <latexit sha1_base64="qzmarxh2hamgygtb4mdcqfpfhs8=">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</latexit> Propagation des ondes électromagnétiques Approximation quasi-statique Différentes figures de cas sont possible selon les fréquences utilisées Méthodes DC Méthodes EM Méthodes Radar Les méthodes électromagnétiques ne sont applicables que dans l approximation quasi-statique: Régime permanent Régime diffusif Régime propagation 38

39 <latexit sha1_base64="tnlp0vtwvbeimiynquwg8zkel/e=">aaadihiclvjnb9naej3u0jyajyujhfzesihk0bqx0kolcc45fom0ldoq2e4mroov2eu0jcqfx8mv/g3/op0xvbm2qfchwlqoz9+893zmsngz2tpp/b21fny5u7yyeq99/8hdtued9cd7ddfuirkmrvpub3fum9tmzuiss81bwzkoi1ozh5+85fz+zfs1lfl37rw0oyya5nzik8gbgneedcznakcnxlqzd3n7vgrmgimnnlt2athudhvpy1i3g9ahxfjrt1hvvaijoqacemooi0m5ocqprvtjoasqnjxarjqhvigykje0oda0dvggjajocx6n2b16nmeepwtrjzglxvtbqegfnav4fwi+tum+ewdg/+y9f0+u7rzf2htlqb19bhqb7or5rzruxdgexkspfj2vgnb3ixdpzcpcubrwlyndcyzjy+qrxikor+asrfnl7zzbspixwmsu94nnnntpq8ybnmq0mqk/h/scodnnqij/s5eg7dorm9g3hujmchaspurzawkmz4t5/8outlxce9q4h+gft+5mslfzc3uvfke7/b6/kav0lj7ts/htuz8gtetdvpczvtbx+ha0ax1sbds/qustr3lcv63gzq/gl7jp</latexit> <latexit sha1_base64="gutjwlgxg6pogzyls3cgmeu9hos=">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</latexit> <latexit sha1_base64="uqkfkklxdwug2kpebh3k8mzxbkc=">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</latexit> <latexit sha1_base64="gjx6d3xbcu7dkyqhnog+pe+y8z4=">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</latexit> Propagation des ondes électromagnétiques Régime diffusif: FEM La solution de l équation de diffusion: On pose la solution: Ce qui nous permet de trouver: La solution est alors: 39

40 <latexit sha1_base64="gutjwlgxg6pogzyls3cgmeu9hos=">aaadnniclvlbbtnaej3uxeq4nivhxlzesawpwe4lvcbfqqryulek0kzqqrr2nmfv32sv00uu/+jx8aq/0d+av+dm4kbchyc1hm+eoefszgtdplal8/3lxpp34+at2+t3mnfv3x+w0dp8efbmvrgzfptfwteidwlim5q+sy42g7wwogljcxgev+h84dwupc3s9+4sn6nez1i7tzf2gmatnd74vl1wvbgvziff9vml4cteti+xsvvdldezrzzavqvem7uct9p+x5elrgdbhbspxvvzzum5dwlcguvuuukgunkiy9ju4jmighzkgy1oaaxazcvvaelnacuwdbga6df+z9gd1wikpxuwoo5wsoy3gflru2gy8arefjqsfcxojp7jeygexnszvmhtlqb19bho33qr5r/qubdhu3olpvj0lavc3uw1syvt4crvla4chhjghe+qlxbholznwymmln55tlryx4xjko+jmlvrt7rkfmijtcur+lo4l4azc46k+d8bcci+uzmdfumotgvnx1kqnd8nwphcmp+vbope5zwnixsy/h7rrgcho53a7wtv/ha3w9/idxpmt2glfi+psz3apz4qukbp9jm+emrb9fa8tz+oa41a84h+wd7goz52wvc=</latexit> <latexit sha1_base64="1naeefafyhpda7hui+kqs4awyrk=">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</latexit> Propagation des ondes électromagnétiques FEM: Atténuation et profondeur de peau L onde EM est atténuée: La profondeur de peau, est donnée par: L amplitude du champ magnétique décroit de façon exponentielle dans le sol. La profondeur de peau est souvent utilisée pour décrire la profondeur d investigation des méthodes EM. 40

41 Propagation des ondes électromagnétiques FEM: Atténuation et profondeur de peau Quelques profondeurs de peau typiques 41

42 <latexit sha1_base64="gutjwlgxg6pogzyls3cgmeu9hos=">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</latexit> <latexit sha1_base64="idcjh5rtosnvvqao73znlxijgww=">aaadoxiclvllbtnafl2pgzbwsmhjxsjcqiwiuwlbpliknralilsv4qgatybb6vjbebyolh8jx8mwvoa/gl/gzgwkchucxnj859xzztx7m1mt88bg8zfbvndp8pxtnavda9dv3lw12r190fstkwomk12zo0w0suelmtncanvugywktkvd7oszyx9ulgnyqnxtt2u1kms6zfe5fbbq8ehxqkfeina/tjdkww6at8z26coi2e31xvovai3ctgirydef6pvjurspy17hxsdxqur+tavdwunkaukvswqpieulwcsabdv45prqtdwwbxxadkkc84p6gklbgqxaeebp8lvgbu7renvn2bba4hsn10az0n1okvamyndaypmwnr36j++opv1tp/hm3qsaaukn0l/pzpj/qno9wfrru+4hr081i6476v1anoqrpdzxlyvddczfs+qnysnkszmhrgm4dzdbwfmvzhso20vpbembr7ie8o6nvxd9jdw74i65quxup1sw4nxwfibzzab4z7hzblhk9xmcdt8w8/+veu7szz1d3mpk91t3mtjygyfxohn5kjpm/i3cobt0jx7a7wln6dlnayykptbh+ksfgyh4euydvz+owwovuuo/rgd+hvrqxio=</latexit> Propagation des ondes électromagnétiques FEM: Longueur d onde L onde se propage selon: Onde non-atténuée La longueur d onde est égale à la profondeur de peau: Onde atténuée L onde diffusive est atténuée rapidement et guère plus d une longueur d onde ne contient d énergie. 42

43 <latexit sha1_base64="gutjwlgxg6pogzyls3cgmeu9hos=">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</latexit> <latexit sha1_base64="jnhqqcgohk08ffpdkm64serfgt8=">aaadnhiclvjda9rafl3bqk3r11yfbqkugviwjkwwl8kcpggivhc3hwypk+xkdc2xm5pvevi3/dw+6n/wh+i/8nxrktui6orszpx7z5l7705c55l1qfblsofduhhpc+vy8mrva9dvjlzvzm3vmetpkiqvzegsrm6zus9c5nj9ubutijjx+/hxu47vr7wxwvw+die1xhrqvwzpligh6mgurp0nfprdsfqpu8b2rxftlbqvtdtrveiv6tqoackbrqrvduejctajzpnnqdidmfvrr9oepkcillrrqg0vpkkkb5ytiovnkeikqaa3obacacokrqmjibqnsjqyfnhj/k6wo+zzenv2tkjoceqo10dp0z1okuqzyd7nl3gjzsz+ybsvt67tbn+49yraonod9m+608x/1xevjllalr4y9fqlw90lvusju+hk/tndotju4bgvetfaishp5+ylxkrvpfsl8a+syszvkz63ow99lswydzktquov4d6c58w1kul/bcem+6rybvvgulwxnh2tvkl/tod5twt+v3kme7szzxd3mpz91p0h851jgezcv4/g02l/i7font2l+/b7tfn6tns0qwuf6cn9os/ehe+z98j7+sn1y9brbtevy5t/b1hcwr0=</latexit> Propagation des ondes électromagnétiques FEM: Vitesse de phase L onde se propage selon: La vitesse de propagation est: T1 T2 La vitesse de l onde dépend de la fréquence et de la conductivité du sol. 43

44 Propagation des ondes électromagnétiques FEM: Vitesse de phase Quelques vitesses typiques 44

45 Propagation des ondes électromagnétiques Propagation en fréquence Les applications de UBC sont une belle façon de comprendre la physique de la propagation en fréquence! Voir le notebook FDEM_Planewave_Wholespace. 45

46 <latexit sha1_base64="bz22qiq+bzndrcokmpbledsyz6a=">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</latexit> <latexit sha1_base64="gutjwlgxg6pogzyls3cgmeu9hos=">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</latexit> <latexit sha1_base64="uqkfkklxdwug2kpebh3k8mzxbkc=">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</latexit> <latexit sha1_base64="xsl8nqmlz2igwkdty+buhycvwxq=">aaadq3iclvlbbtnaej3uqeu4pfdiy4oicsel2fwl8okihjd6warpk+o0st1nwnu3dtdpg+xp4wt4hqf+ap6cs1mxfsoerox47jk5z2cmg5epmtb3v3zwvctxr62uxe/euhnr9p3e+t1du1q6keoksau9h0dgpiqxy6tskvdllamstuvefpzcxfcwuhtv5g/sspstljrnaqasyika9p5vt5fimri8npoino+1rcozjpi6ngqeru0dlirmkmgbrsjdegb8fhefdjeebnpm2uv7q5+xuaycfvspxtvfeucxhxrebsvuuuascrlakuvk8bxqqd6v4czug9naiuosgupcwyfliimce4zfoxyhlztj7zwnqxockulvuap6ce2bpa3sthmcr9jzsx/yrtnt1bben269mrcw3oh9m rhdlm3rkpsj0vdljuktal4qn4ioxf7qyccjboxyeuazowhk+z8eaw7272uyc/8azjnx7pm2t6htbzq7mhkevcf053gvwlnobitx/nmhg+cz4docbq3hkvhm0xkx8oqhhlzjz/5v9nnhcelq4h8hvt+4y2n0ybv4welxzh43ag7lg9+kbpylffo1om3zojao+0if6tf+8gffae+ufz6krnvzzj35znvwbl1hinq==</latexit> Propagation des ondes électromagnétiques TEM: Propagation d une impulsion La solution de l équation de diffusion: La solution pour une fréquence: La solution pour une impulsion: 46

47 <latexit sha1_base64="p1btne8c6yovdq2ei0mpa4deaoc=">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</latexit> <latexit sha1_base64="gebagv8k6emk0udfssvk0zn/bhu=">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</latexit> <latexit sha1_base64="p1btne8c6yovdq2ei0mpa4deaoc=">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</latexit> Propagation des ondes électromagnétiques TEM: Distance de diffusion Pour un temps donné, l onde EM a un maximum en z: La distance de diffusion est donné par: La distance de diffusion agit comme la profondeur de peau dans le temps. 47

48 <latexit sha1_base64="uzm5xwwz/ortxj/fgufdzyxdvta=">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</latexit> <latexit sha1_base64="nyy+x3yhmcbpbcz25otumztvxio=">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</latexit> <latexit sha1_base64="uzm5xwwz/ortxj/fgufdzyxdvta=">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</latexit> Propagation des ondes électromagnétiques TEM: Le temps du maximum Pour une profondeur donnée, l onde EM a un maximum à un temps t: Le temps du maximum est donné par: Le temps du maximum croit avec la profondeur. 48

49 <latexit sha1_base64="eyv7ycb22zsyih6kdjweatezrkg=">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</latexit> <latexit sha1_base64="kxeqw/2/nctauckjzgljdap2nvm=">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</latexit> <latexit sha1_base64="p1btne8c6yovdq2ei0mpa4deaoc=">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</latexit> <latexit sha1_base64="eyv7ycb22zsyih6kdjweatezrkg=">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</latexit> Propagation des ondes électromagnétiques TEM: Vitesse de diffusion Le maximum de l impulsion se déplace ainsi à une vitesse donnée par: Le temps maximal est donné par: L impulsion se propage dont de plus en plus lentement au cours du temps. 49

50 Propagation des ondes électromagnétiques Propagation d une impulsion Les applications de UBC sont une belle façon de comprendre la physique de la propagation en fréquence! Voir le notebook FDEM_Planewave_Wholespace. 50

51 Principes des mesures EM 51

52 Principes des mesures EM Comprendre les bases de l EM 1. Comment se propagent les ondes électromagnétiques? 2. Qu est-ce qu on mesure et comment le mesure-t-on? 3. Comment peut-on détecter une anomalie dans la sous surface? 52

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54 <latexit sha1_base64="u+vj2hxdtzea7cc/t3ftpqn10b8=">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</latexit> <latexit 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sha1_base64="urysrg+jvvmrju1bqd9elfuje9a=">aaadlhiclvlbbtnaej3uxeq4psdxwotfhftxenltjfpqpegvunlbrzc2upngtrspq/qm9toqlp8cx8mr/ad/ah/bmekwfsoerov49sw5z2cmg5eprmwqfo0seveuxru+fkn789bto3d7k/f2qqi2irolrvqygziqvkpznblapuqgncrk4lttx6fbnn+fk1ppin9jf6waznfjrmc6isygaw91z7rwn/njmyms5sxrttkyl9o3r+vtgbt+yde25mitnfb6wscq5v8oqhf0ya3dyqxzhmz0taulvfnginkyifokqmjzscefvakbuapminksv9rsf9oalavgbpquvyfyhto0x549k1enocxfa6d06te0bxggmz/ms74wz0b/5n2ij9e2wdd2xhlqs2+b/k13zvxxhfdiauab0ongt6ug3f3ixgqzclfux+jkwqeexvex8gzxisrzofuiqar3nm0k+w/czjt3iepw9n1vmqn5j9pkpp4c7g1wzs5ref9ne0hyzyznsg8mxxvb2bgsktxpcta+f+b/k/s4sb3wdhepw99v3evgb20qbopw1uz/ohq3cpke0inahd9tgtio7diifxykt/szvngpvc1v23t+rl3qom19+mv5l38aqjq/ia==</latexit> <latexit sha1_base64="aorkkmuia8jegpgupf+aomo1q34=">aaadcxiclvllbtnafd2jc7th0rzwfrurevkbkrireiwjswhzsqspvcjku5ni1s/z49aq9spywpfxb7dmb3ruzyr6uawmfefoueecufd64iplgxse3ztdb+nw7tvlk7279+4/wf1bf7jxlg2dmffszmw9h0enydlcjgxqm7nf1sbk48ym4+m3kh/ptn2kzfhoziszyaojip2mswqjjbdotufbn59+woshg0cxfz0ixdchwzvleucz3umqjrk0ygfqwdloekhhc4aqaspieyyi1yxszrucokdts5yhiyj6zpcrdwcolbgxz0bvcu/j+kup9pgempk8mrgc5mu+vwdbb/jeqkfunud/7lxyohyfif5nd878v530yjhfa+0hzu+vitjd4lxanypu7l/oytkhiibxifm140sv53p2vdno7zlbspm/lcmo7bphbfhtvvkq+attyrx+gu4l4skcssl5zhnfxgeqz4hvtmwj4ulyajxmzwqenynz/5v9nnh64enxhozxb931yo/fiawg4e7l/ndobuqyhmmtw/r7hsheygcj/rzf8bxfur+8dc/3nn9tux2neyrly3t+bs0wsfs=</latexit> Principes des mesures EM Boucle émettrice La champ produit par une boucle à un point quelconque de l espace est plus complexe à dériver, et est donné par: Lorsque r > 5a, la boucle agit comme un dipôle avec un moment dipolaire donné par: surface 54

55 Principes des mesures EM Boucle émettrice 55

56 Principes des mesures EM Boucle émettrice Un dipôle magnétique agit comme un petit aimant Son champ est indépendant de la géométrie de la boucle 56

57 Principes des mesures EM Boucle émettrice Les émetteurs en EM: Boucles dans lesquels on fait passer un courant Produit un champ magnétique qui peut être assimiler à un dipôle magnétique Le champ magnétique se propage dans l espace selon les lois vues précédemment de propagation des champs électromagnétiques Boucle émettrice Tx Boucle réceptrice Rx 57

58 <latexit sha1_base64="gpjx3anh9ea0tdt2ajlc/xsnl3a=">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</latexit> <latexit sha1_base64="dvltlhbalwtfk+eve23y6xkqntu=">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</latexit> <latexit sha1_base64="wnb5gfepkvpotjctroeb9vt3f98=">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</latexit> <latexit sha1_base64="pwzjkjkeuoijbdbhiya0unoxy2g=">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</latexit> <latexit sha1_base64="szhmjwgf8lgarglleglutgv86m0=">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</latexit> <latexit sha1_base64="de121o9pkx505bxhdgo1bkj+qh0=">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</latexit> <latexit sha1_base64="qdpexm3sjp1ri/jf1fybktq4vvu=">aaadhhiclvjdsxtbfl1xw01t28b6uujl0laopytditgxs6aipu8wghvmkn11kg7ufzuzqshex+nr/t/+a/0xpfd2llyi2lk2e+fcc87ceznxmwpjg+c8sea9eli41hzuerz85omz9srzhvpuval6szew1v4cgzxqxpwttqnakysvzxgqduojt5zfnajk6cl/zqelgmbroncjnuqw0eh7xadm4tmxub/pd4wez5evwnb8on0juoes/2yquqbdbm0xk423nkbdkiihmjjsljnfnfjebs8+hrrqcwxim2avii15rxnqqvudpccigb7hd4zdvknz7nntidrbksneckqfxkntgfch5tn8ydfizoht3jpx5nqm+mbokwnq6tvqu3rxzpvqubdli/ogpwj0varc3sxopzapcox+ta4shepghb8ixyforhk1z180rnrn2uasvxamo7xphlems1dldushtcut+no4z4azc4kk+d8bcsi+izmdfwmojgvnrynvqj8tyhwizp9xdndi/nrtwj0m/711n4od990w6izfg06v525kk17sk3odvw3q0wfapj4qokft+kln3ql3zlvz1n9tfxpos0p/le/jl2lvuh4=</latexit> Propagation des ondes électromagnétiques Boucle réceptrice: Loi de Faraday Les équations de Maxwell sont à la base des méthodes EM! Équations de Maxwell Loi d ampère: Équations constitutives Loi de Faraday: Loi de Gauss: Loi de Gauss: (magnétique) 58

59 <latexit sha1_base64="dvltlhbalwtfk+eve23y6xkqntu=">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</latexit> <latexit sha1_base64="sfrqg5rd7cqg9e01bvrhzxsykqm=">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</latexit> <latexit sha1_base64="94gb9msgzg/b1paptqwedod6av8=">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</latexit> Propagation des ondes électromagnétiques Boucle réceptrice: Loi de Faraday Nous partons plutôt de la forme intégrale de la loi de Faraday: Forme différentielle Forme intégrale Les deux formulations sont reliées par le théorème de Stokes: 59

60 <latexit sha1_base64="fb7/axm8ey52aji51evzyzu/sgk=">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</latexit> <latexit sha1_base64="94gb9msgzg/b1paptqwedod6av8=">aaadyniclvjnb9naej3uqev4suhizuwehjcibc5wqrralthwkcppk9uhwq83zdx1h9brqgt51p/gn+aftfzhbzazdaglqsbaiwffvpd2zrxjau3lw/blbyw4cvxa6tr1/o2bt27fgazf3amk2ik9uyut3f4ik21nrifeekv3sqdllli9mxy+ovzuqrvkfpk7vyz1njmhuzkbjt1cs8h7udc5nzxpdivimkuatxyrtpai5a1txyz4ehnnw8rzj1utl9j5i+0p/2xb/kl8rfgldjyyhqoql7gcrf0whg5tfeu9xxbdcguoqceddtl4jc1iqpdzhwhckbgbqooyw8hwxkmlfdtwynlikige4v8b7vy7nmc9evasvnikxz9dpychqcmq5zcm0wtna3ym9e/edxtsbut8j51xhqihd4j+txfg/fcd9ejhds+5b4m9lyxqd6pzqxkqvlk415vhhxixilpmo4wvk8/mlfhtce80w8n5y2yssnvvcws46armefni08q4/hzdg8sjucck6jtngsgfoz9bvgkqpjfojhvxqx9ogpafm/9focqt23nph+9h9putuxzspb1f4sh6gw7h4+5grsf9eacp0o8zjoe1bmeek/gmx+ebfa/ebc5ybs0pdaxxae7bhruc/qdsktxk</latexit> <latexit sha1_base64="nkqwwjoa7zgxphkqc3gjls1b2mk=">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</latexit> <latexit sha1_base64="bbn6pf4pji8fippxqiyksfd8d/4=">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</latexit> Principes des mesures EM Boucle réceptrice: Loi de Faraday Loi de Faraday: Une force électromotrice causée par la variation d un champs magnétique dans une boucle. C est le principe d induction. Force électromotrice (volt) Flux magnétique 60

61 <latexit sha1_base64="bbn6pf4pji8fippxqiyksfd8d/4=">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</latexit> Principes des mesures EM Boucle réceptrice: Flux magnétique Le flux magnétique correspond à la composante champ magnétiques qui est normale à la surface recoupé par le champ. Le flux dépend: De la grandeur de la surface De l orientation de la surface par rapport au champ magnétique De la force du champ 61

62 <latexit sha1_base64="bbn6pf4pji8fippxqiyksfd8d/4=">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</latexit> Principes des mesures EM Boucle réceptrice: Flux magnétique Le flux dépend fortement de l orientation de la boucle réceptrice par rapport au champ magnétique 62

63 <latexit sha1_base64="nkqwwjoa7zgxphkqc3gjls1b2mk=">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</latexit> Principes des mesures EM Boucle réceptrice: Loi de Lenz La loi de Lenz stipule que la f.e.m induite par un champ magnétique dans un boucle produira un courant dont le champ créé s opposera au champ primaire. Champ primaire Champ secondaire 63