Induction: Circuit équivalent

Átírás

1 <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">aaade3iclvjdtxnbfl3tkkivkproy8anisgk2suafwzcc4+ywccbptkdprbhvzizwyvnf4mv+kp8b/ijsdz3ohcughq23d4595wz996drcly6+l4e6cbphq89gr5pff02eraen/j+b6tw6p0snvfbq6z1ooir/ti5a7qh43razkv+ia73+h8wuwbm9fvj3fr6hgznlb5nfepaztprx9ptarmuxo7wktztpprpihlhfedxacr+bvxb3q26zhoqczflzwkqskhukculj4jsiimbtiy5samolzymhbug7yfs4oraj3h+xs7i49w2lonfbxckqv+bsqqxkntg2cq82mh5ftxzvrv3npx5nou8j95rxkoozogd+lump+q414ctemd9jcjp0yq7k55l1amwpwhd7pycgiacxycvegsrhkz51a0vnrn2aas/yfmrnmvplelk19lbesztkuu+iu4z4ezc4ak+junbwgfqzzbvhkuxwrnrytv6tsjmd4t5v8ri5y4upp0ca+tp2/d/wb/e5deg+tj22g49ddymv7sk3odv/c0pf3ao5hczk90sd+610eubazbv6jdjte8on9w8o4n9xc2gq==</latexit> <latexit sha1_base64="8bd+5rzx/cciei4ammgt4lou+n4=">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</latexit> <latexit sha1_base64="+mdfrp+eluouq9rgyqyghqlpjde=">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</latexit> Détection d anomalie conductrice Induction: Circuit équivalent Les parties en phase et en quadrature varient aussi avec le paramètre d induction. Paramètre d induction 1

2 Détection d anomalie conductrice Application du circuit équivalent Allez à et sélectionnez InductionRLcircuit_Harmonic.ipynb 2

3 Détection d anomalie conductrice Caractérisation d une anomalie conductrice Lorsqu on recherche un corps conducteur, par exemple en exploration minière, le modèle en boucle s applique directement. Il existe des abaques pour déterminer la profondeur, le pendage et le produit conductivité-épaisseur. 3

4 Détection d anomalie conductrice Caractérisation d une anomalie conductrice Abaque pour une couche mince verticale 4

5 Détection d anomalie conductrice Caractérisation d une anomalie conductrice Le pendage de la couche conductrice affecte aussi la forme de l anomalie. Les composantes en phase et en quadrature sont déplacées vers la direction de pendage. Il existe des abaques aussi permettant de déterminer le pendage et les profondeurs de telles anomalies 5

6 Détection d anomalie conductrice Circuit équivalent: Résumé On peut modéliser le sol comme un circuit équivalent Le champ secondaire au récepteur dépend de 3 termes Facteur géométrique Un facteur d amplitude dépendant des propriétés du sol Un facteur de phase dépendant des propriétés du sol La déphase et l amplitude sont mesurés comme les parties en phase et en quadrature Ce modèle permet la détection de conducteurs enfouis 6

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8 <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="vpwbvd7jiigdgbkedvf1llnv6i4=">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</latexit> <latexit sha1_base64="ybdza5n230jb18/7+gb2mosojoq=">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</latexit> <latexit sha1_base64="ihommqy9z0sxrdumsegbata60ys=">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</latexit> Paramètres du circuit à déterminer On a vu que pour un circuit simplifié, les mesures au récepteur sont: avec le nombre d induction et la phase: Pour trouver les propriétés du circuit électrique analogue, il faut supposer une géométrie de la sous-surface particulière. 8

9 Réponse d un sol homogène Le sol n est pas une boucle! Comment passer vers un modèle plus réaliste? Comment relier le nombre d induction et la résistivité d un milieu homogène? Quelles sont la profondeur d investigation et la résistivité apparente? 9

10 <latexit sha1_base64="lchvrjfode7n3msul5vmwlgqdk8=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="hnaimmi5vo8knupd2tqjupknhhy=">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</latexit> Réponse d un sol homogène Pour un demi-plan homogène, il est possible de trouver que: Le rapport du champ primaire est devenu assez complexe. Par exemple, pour HCP: Ces formules sont utilisées dans leur cas limite, qui sont beaucoup plus utiles. 10

11 <latexit sha1_base64="lchvrjfode7n3msul5vmwlgqdk8=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="hnaimmi5vo8knupd2tqjupknhhy=">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</latexit> Réponse d un sol homogène Pour un demi-plan homogène, il est possible de trouver que: Le rapport du champ primaire est devenu assez complexe. Par exemple, pour HCP: Ces formules sont utilisées dans leur cas limite, qui sont beaucoup plus utiles. 11

12 <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> Réponse d un sol homogène Attention! Les graphiques sont ici pour les rapports des champs totaux et primaires! Champ en phase Champ en quadrature 12

13 <latexit sha1_base64="9eshmw/r4zjpwkaspa2kt+iibwi=">aaaefniclvlnbtnaeb7x/jtwl8kry4oiqxcinkicxhcrkqqeg0tssnww1tu1s+r6r+t1smx5pxgghoib4sqvn4c3yhbqvi0vgq7lepab7/t2zrjxqvvlg+cht+bfuhnr9vqd3t179x887g88mldfbysciuixzj/mldqqlzorrjb7pze8i7xci492xh5vju2livy9psnliunprhilueuo6n8otuzszpgylpow43ypug7etlhvxtqwbwhuurtpo2z3z9qy1+z6wvmpuhuarssl/zbum7fd2tleqttjlmzqkgbhkcmum9m2w23uhwtdgba7goy6yaddmhyb3gsi4rakefbdbhjysbhr4fdhcwajckbebaenygyjrxkjlfrqwynliomjeos/ke4oojthvfossc3wfi2vqswdz6gpkgcwdqcxytfk7nc/etfk6wo7ww/cewwiwlgi+i/dgfn/da4xcwlsuw8keyojcd2jzqwmqbjk2ywuldquiln4epmgy0hkszkz0ltuu5stp/xpyjru7uxhrefxv2woydfnk6p6c3rvehfmfvbk/rmfic4notocb4ykj4q7x4qqloctcpikmndxdvde9sltw3s4+vpwxq3m4+eogi7ebq0mk+5grsmteaqb6pckjralu5ib8pres++nn/e/+v/8r/63u+qa12kew6xlf/8n9tnxkq==</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="1tzaaulucsz/honi6ye/h/cgfjg=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> Limite résistive Dans le cas d un mauvais conducteur: Les réponses deviennent: À remarquer que Les parties en phase sont nulles Les parties en quadratures sont proportionnelles à la conductivité. 13

14 <latexit sha1_base64="ztxaf8znvuqxvnhcnoufkzcnqfc=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="gu+bvyajlo8rwdxq14ae6+ji07e=">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</latexit> <latexit sha1_base64="hysahz2vxaojki31cuefhy5ydc4=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> Limite inductive Dans le cas d un excellent conducteur: Les réponses deviennent: À remarquer que Les parties en phase sont dominantes Les parties en quadratures sont proportionnelles à la résistivité. À la limite, la partie en quadratures devient nulle, il y a saturation. 14

15 Comparaison avec le circuit L analyse d un sol homogène confirme les résultats du circuit équivalent: Aux limites, la partie en phase devient constante Pour un nombre d induction faible, la partie en quadrature est proportionnelle à la conductivité Pour un nombre d induction élevé, la partie en quadrature est proportionnelle à la résistivité. Pour un conducteur parfait, la partie en quadrature est nulle 15

16 Réponse d un sol homogène Le sol n est pas une boucle! Comment passer vers un modèle plus réaliste? Comment relier le nombre d induction et la résistivité d un milieu homogène? Quelles sont la profondeur d investigation et la résistivité apparente? 16

17 <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> Réponse d un sol tabulaire Réponse pour un sol tabulaire pour le dispositif HCP, avec deux couches d épaisseur constante. Champ en phase Champ en quadrature 17

18 <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> Réponse d un sol tabulaire Réponse pour un sol tabulaire pour le dispositif HCP, avec deux couches de conductivité constante. Champ en phase Champ en quadrature 18

19 <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> <latexit sha1_base64="prmorsyuphuryjm8p2euef2yuby=">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</latexit> Réponse d un sol tabulaire Réponse pour un sol tabulaire pour le dispositif HCP, avec deux couches de conductivité constante. Champ en phase À remarquer: Champ en quadrature La conductivité et l épaisseur des couches affectent grandement l aspect des courbes Les asymptotes restent les mêmes que pour le sol homogène Il est difficile de déterminer l épaisseur des couches en variant le nombre d induction, de faire un «sondage». 19

20 <latexit sha1_base64="z/zfod7a7jzcihhnpkbm/qxkmys=">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</latexit> <latexit sha1_base64="yeqwxumayeithhikr5ajxtyzzwi=">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</latexit> <latexit sha1_base64="1yfll4pwjnp3/feuwedtdtfyazc=">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</latexit> <latexit sha1_base64="dhydloqnmkfgkorea0azzqjchce=">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</latexit> <latexit sha1_base64="umdrilwdhgoa5wn2eez33hqoqai=">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</latexit> <latexit sha1_base64="is5c6texorhrk4s99+ppordhlug=">aaadbxiclvjnb9naeh2jgzbw1vl1riusigtienmounumxivjk0hbqusv7wycvx/jxgeqqd+ba/vb+af0xf/gzbbflruc1ni8++a9tzotjassbwwqfo10vvu37ywt3+3du//g4aov1cd7tdnwirklzvbwb3humcwtzmimnjmhvw2ipm7mfnz8rvl7c1m3avm8tyevgefrreinarjzqu8mr+hrsj8yblr8m0hogj7c2ilxo6/warousnaih0ebyzhdhibpiuieqiinssbwm0o1b3ckhrutwyamiogxf2fchtq04f48g1unpcxjw1pp4zk1jxk1yznn13yrzol+yxuhnllbcb+x88qjwnwk+jfdjfnfddklxrtb2kpknipfplveubq6fancv9kvpunftoij8zxjrjwxc/zv02jvmtti89+ukajse8dtcegqlih80mnlwn9b9wvxyc5zkfxny0xez6pnig9mxwffxbhrks2vcqg+v+b/k/s88ftk0+m9dh+/dtedvdedmbieu5v94dddygu8wto8pn8whnilhyxywqxfcibz7ndv3dvwnv6kdjtos4zry3vxa8y0slm=</latexit> <latexit sha1_base64="s1mn/kogfma778jgu9wfu7qjxeq=">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</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Réponse d un sol tabulaire: Limite résistive Dans la limite résistive, des formules simples peuvent être dérivées, qui ont la forme: Par exemple: 20

21 <latexit sha1_base64="p/afew1jjbjwvblimrb11wwidba=">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</latexit> <latexit sha1_base64="yzzqotbnyspm5ipjyzoemah56ii=">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</latexit> <latexit sha1_base64="sjw9rmrsm0hsdrln8sunoud8j78=">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</latexit> Réponse d un sol tabulaire: Limite résistive On peut évaluer la profondeur d investigation en utilisant la formule pour une couche: 21

22 <latexit sha1_base64="as+ocdna9fwgesxrrdexfpenj5c=">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</latexit> <latexit sha1_base64="attmwrimq73pzj9y4zu5lonyk0c=">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</latexit> <latexit sha1_base64="fdzkxt2zic4hm8rudzfxiifvu3q=">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</latexit> <latexit sha1_base64="cuegyhvrubk+ypqvk/cmbdwrlde=">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</latexit> Réponse d un sol tabulaire: Limite résistive La sensibilité du dispositif est donnée par la dérivée des facteurs géométriques de la première couche. 22

23 <latexit sha1_base64="sjw9rmrsm0hsdrln8sunoud8j78=">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</latexit> <latexit sha1_base64="cuegyhvrubk+ypqvk/cmbdwrlde=">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</latexit> Réponse d un sol tabulaire: Limite résistive À remarquer: Pour le même espacement de boucle, la configuration HCP a une meilleure profondeur de pénétration La configuration VCP est plus sensible aux variations en surface Faire un profil avec VCP et HCP permet de déterminer si le sol est homogène ou non. 23

24 <latexit sha1_base64="z/zfod7a7jzcihhnpkbm/qxkmys=">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</latexit> <latexit sha1_base64="lo9+ll5lbntj4x/jrb/srro/zay=">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</latexit> <latexit sha1_base64="1zuvz72tnp0k+mm53flj6smxiz4=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">aaade3iclvjdtxnbfl3tkkivkproy8anisgk2suafwzcc4+ywccbptkdprbhvzizwyvnf4mv+kp8b/ijsdz3ohcughq23d4595wz996drcly6+l4e6cbphq89gr5pff02eraen/j+b6tw6p0snvfbq6z1ooir/ti5a7qh43razkv+ia73+h8wuwbm9fvj3fr6hgznlb5nfepaztprx9ptarmuxo7wktztpprpihlhfedxacr+bvxb3q26zhoqczflzwkqskhukculj4jsiimbtiy5samolzymhbug7yfs4oraj3h+xs7i49w2lonfbxckqv+bsqqxkntg2cq82mh5ftxzvrv3npx5nou8j95rxkoozogd+lump+q414ctemd9jcjp0yq7k55l1amwpwhd7pycgiacxycvegsrhkz51a0vnrn2aas/yfmrnmvplelk19lbesztkuu+iu4z4ezc4ak+junbwgfqzzbvhkuxwrnrytv6tsjmd4t5v8ri5y4upp0ca+tp2/d/wb/e5deg+tj22g49ddymv7sk3odv/c0pf3ao5hczk90sd+610eubazbv6jdjte8on9w8o4n9xc2gq==</latexit> Conductivité apparente (limite résistive) La réponse d un sol permet de définir une conductivité apparente dans la limite résistive: En prenant la partie en quadrature: 24

25 <latexit sha1_base64="mznigwr2fdobuvj24wttw784twq=">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</latexit> Conductivimètres Attention! Les appareils donnant des conductivités supposent la limite de faible nombre d induction. GEM-2 25 EM-31 EM-34

26 <latexit sha1_base64="1zuvz72tnp0k+mm53flj6smxiz4=">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</latexit> <latexit sha1_base64="q2rwpnzndnndq747swb9rexqr/8=">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</latexit> <latexit sha1_base64="4iwrzku9czl/ku/0x9v/6i6sq7a=">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</latexit> Conductivité apparente (limite résistive) La conductivité apparente est donnée par: Cette formule n est valide que dans la limite résistive! 26

27 <latexit sha1_base64="t9dukuoasm8wyo//tgsbhbuv0rg=">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</latexit> <latexit sha1_base64="pt3jqmufxmdmx90ysgvqchbgczk=">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</latexit> <latexit sha1_base64="ick//sc0cguwc4aeii432zv8m30=">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</latexit> <latexit sha1_base64="vt3nb+rfgesblm3nxvk3fmkauvy=">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</latexit> <latexit sha1_base64="f9ybdahzujc6o+gnd7wbkd5tv+w=">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</latexit> Conductivité apparente (limite résistive) On peut utiliser la sensibilité pour calculer la résistivité apparente: Attention! L intégration commence à la hauteur du dispositif! 27

28 <latexit sha1_base64="ng59s/nw6nyzvsdv4m7+6sjjlai=">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 mzbpd9+gbanlmfdqkaq1rwuf6rj/pi/fck7y5d3hcxwo5zw36zxkffgdip8zb</latexit> <latexit sha1_base64="ypm8xkhk6yn6adbn/7z++xy47pe=">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</latexit> <latexit sha1_base64="fhebbadd2hc9xyeope0wmctastw=">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</latexit> Conductivité apparente (limite résistive) Pour faciliter les calculs, on utilise habituellement la courbe cumulative: Ce qui donne: 28

29 <latexit sha1_base64="m4y65p5hohkfkqpxzy9+bsm9xlu=">aaaecniclvllbhnbegxneqtzcudizyrf5ajh7fpbicskshdibreqtijllwt3mzaj7ev7mesw/4cv4ya4cuax+ao4ciuj1e0jchihyfb29lrx1xt3tpjhpqxc90tjytl3/slf5uvny1euxrvewrmxu2z1eel+lmvzsrcgpy5nqvuvqwk9lxc6smjy74ahtzi/o9ffabl0vxwu60esjfmzmlfqarq2qr804yqybuqxwu149152vpwnttvl4wlgipny/ebqxdwz50dpde+fihkllno53mzyartdv5y6g3g2ajnd29lky4t8oqcmiqopiu0pvyhjcqjes08euzqdg9auwihisf7tjjrq1mbpmakgh/gfy7dv0rr79ixfhegugl8cskv3omnakxdzauryttgz+ifvqxhybud4h9yravrra6b/0x0z/1xhvvq0oofsg0fpusdcxwrdapkkv64wuqrgkapj+ad5anekyum5k9gu0jvpnpd8v2eyyvvicmv6zqtmgbyrasvsfwr3kxbmtlarf7obiowzkjpyn4tiredsweqv+vcegj8i8/+vbzw4w3i4yqeijauvtc8s97mdco/4jviyg8fj/oywd9g7fwppbju9rud2vrcb7c1h9jyv0y26tr3u8oa2ayu2qy8kptn3+ke/nxfoe+ed83foxwpyzu06szxpvwdtpnqi</latexit> <latexit sha1_base64="ph+p3xt20y476ywkkafn3qoselq=">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</latexit> <latexit sha1_base64="ym9dvxywsqyxenpj7ds1o+mxdfe=">aaadyxiclvllbhnbegxnesth5caxlwulizpzjqjbseirwiesqgsbk0ixzc1oxs4q+2jn1isxfola13cfb+ep4c+o7kxqielaroztqa6q6e6dpmps66loa2suuht5ytx5hcvr12/cvnveur1ty6bwpqflrkx3e2vnlham51kxmd2qnippmrothg5wfmdiapuwxvt3xjlbrszfokq1cocg7bt9m45znvths/bxd3ut7b/ysmkzfvs5wzi/ezgp252og8kklwaxdzrk11a51nqkpu1tszoayslqqq5xroosnj2kkaik2icmwgpeqeqnzwgr2gysa4yceoj/mxz7hi2wz08rao1tmvxqkeo6d00jxo2ytwsl34gzo3/ynoon13amd+k9cqcodod+txfg/fcd9+jore+khxq9vyjwd9q7ndivrjw815wdqwwm433ka8ralgdzdkvjpxeerzl8n2eyynvtuq1991uwqn7lthkpv4d7fdgzj6iiv9laepyzyrnsm0bxjdg7wqns/jwa4xnh/r+ygxnn5x6u8rlom+nl0evpfeunwju+cx3zjebx+oywdzj+/czedlzxunhujv+vdtaf+ts8t8t0jx6gljvap03aoh4q+eif6dn9cv4e74kj4osuotfymjv0ywo+/acrfcgr</latexit> Conductivité apparente (limite résistive) Exemple avec 3 couches et dispositif HCP: hauteur du dispositif: 1 m distance entre le boucles: 4 m couche 1: d=1.5 m, sigma = 1 ms/m couche 2: sigma = 10 ms/m 29

30 <latexit sha1_base64="kbrvgyariazroqyhbcws7cbb2ig=">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</latexit> <latexit sha1_base64="ixwidm9benukcyhfg8kb7tl08a0=">aaad3niclvjnb9naej3ufjtylckry4oiqqgr7agbqqpucq69obze2kpjfgxne6z6s+t1abvy5ya4cuiv6zx+af4b/avetleoucfgrcszb957ozpeqeytyvr+18acd+78hyull5yux7l67xpz+czwvdqm1t24sauze4wvtpncd21iu71tgh1muaq3o91nnn+ealmlrf7a7pd6kiwtpbkncwgbdzup+luyycjh+h44m525wlw94p6rlded07k7clla3vmockhn2gz5bv+wohselmirw5vfcmod+jsigmkqksnnovnekyvu4elrqd6vway0a2yqjzlxnkclaguwnbgh0f38t7drotthnj0rucc4jcxpqknodjqfeayxn6ykx4szo3/ynokn17apd+s8mqcw3gl9m+6e+a867sxsmj5idwl6kgxh7mlnustuuhj1qislhxiyxypkdejylcdzvqkppheebsj5b8jklpex49b03vwza3kn08qk/hzum+dmnkii/mydqdhnlgewbwtfnudswemv+ucegj8k8/+vlzw4p/vwlc9fm0pfml447oabco/4jvrln4bh8rta3ohg9xt7ntjqtao/hbx82fp76m7zit2i27scwh7tgq3tjnvrwqed0hc68t54h7yp3qdj6kldaw7sl8v7/aow7m8+</latexit> <latexit sha1_base64="tf/5xvtwnqih0krtp+jvzl86cde=">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</latexit> <latexit sha1_base64="tjdophsqjjj+mneejdqopksjdgw=">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</latexit> <latexit sha1_base64="zhlromsx0ho7pmca3l5rhbn+u9q=">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</latexit> Conductivité apparente (limite résistive) Il est possible d effectuer un sondage avec les conductivitmètres: Il faut varier l espacement entre le receveur et l émetteur Pour un milieu à deux couches, il faut 3 espacements pour trouver les conductivités et l épaisseur de la couche 1 En pratique, les sondages sont peu utilisés, car il est difficile d avoir de grands écartements avec les appareils disponibles. Pour un milieu à deux couches, avec des conductivités et et une épaisseur d: On a 3 équations, 3 inconnus! EM-34 30

31 <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> <latexit sha1_base64="u3dhie+lvnzcmdv82xa4oygvey4=">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</latexit> <latexit sha1_base64="hfnxr2fmuwy2ohiqfed6e8mnita=">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</latexit> <latexit sha1_base64="6u++m5yg+fzy7+s/n9sedclflls=">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</latexit> <latexit sha1_base64="bi+uuj2qpol4xlvdzfiw4aupl1s=">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</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Pseudo-sondage EM-34 Milieu à deux couches: = 10 ms/m = 640 khz-m2 = 100 ms/m = variable 31

32 <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> <latexit sha1_base64="u3dhie+lvnzcmdv82xa4oygvey4=">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</latexit> <latexit sha1_base64="hfnxr2fmuwy2ohiqfed6e8mnita=">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</latexit> <latexit sha1_base64="6u++m5yg+fzy7+s/n9sedclflls=">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</latexit> <latexit sha1_base64="bi+uuj2qpol4xlvdzfiw4aupl1s=">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</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Pseudo-sondage EM-34 Milieu à deux couches: = 10 ms/m = 640 khz-m2 = 100 ms/m = variable À remarquer: Les conductivités apparentes sont plus faibles que les conductivités vraies La conductivité maximale est plus grande pour VCP L épaisseur de la couche 1 déplace la courbe de sondage 32

33 <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> <latexit sha1_base64="u3dhie+lvnzcmdv82xa4oygvey4=">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</latexit> <latexit sha1_base64="hfnxr2fmuwy2ohiqfed6e8mnita=">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</latexit> <latexit sha1_base64="6u++m5yg+fzy7+s/n9sedclflls=">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</latexit> <latexit sha1_base64="bi+uuj2qpol4xlvdzfiw4aupl1s=">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</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Pseudo-sondage EM-34 Milieu à deux couches: = variable = 640 khz-m2 = 100 ms/m = 20 m 33

34 <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> <latexit sha1_base64="u3dhie+lvnzcmdv82xa4oygvey4=">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</latexit> <latexit sha1_base64="hfnxr2fmuwy2ohiqfed6e8mnita=">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</latexit> <latexit sha1_base64="6u++m5yg+fzy7+s/n9sedclflls=">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</latexit> <latexit sha1_base64="bi+uuj2qpol4xlvdzfiw4aupl1s=">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</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Pseudo-sondage EM-34 Milieu à deux couches: = variable = 640 khz-m2 = 100 ms/m = 20 m À remarquer: Plus la conductivité 1 est faible, plus les courbes sont rapprochées Ceci montre la difficulté de déterminer l épaisseur d une couche résistive avec les méthodes FEM 34

35 <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> <latexit sha1_base64="u3dhie+lvnzcmdv82xa4oygvey4=">aaadcniclvlbtttaej3ehukgxn/gxrahoaqkbfspfyzufx5bihajimsbtvjhm7zrtcjij3ilp8yfwdsfwjnrgrioarsr27nn5pydgu9cptryilhtnl0pu9mfz2zbc/offhaxllcotvfxieolrvpu/tgyktw56lltu9uvkxvlcaqo4osf7d8aq8roij+wl6uazneo10odrbzq/8tourad7pwutynoimt/b4toajnbe8vy4zod0bkvlfbngsnkycjokskdfuwhbvqcg9aewavli1/rfbxarrglebebvcb7hnoxq3ocwdmio8etkz4ktj+2wckqv8hm23zx16lm6j+0j6ljuv3igzutdkilc6b/4z1f/iupa7e0po9sg0znpsbcxejuaukkz+6/qmpcoqtg9hn8fexeme999ovjphbubst+o4lklm+ji63p3mwza/kp3cok/xzqe+acouzg/m8ggrdouo5g3rimx4kzopes1xmhgb9l5p8z27jx6svuyq7dt1p33jjc6yrbj9z/2u523uto0dpt0jb0vlgxdmmpejjt13rdv5sp3pq34bnxbtycz5vele/li70usu8=</latexit> <latexit sha1_base64="hfnxr2fmuwy2ohiqfed6e8mnita=">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</latexit> <latexit sha1_base64="6u++m5yg+fzy7+s/n9sedclflls=">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</latexit> <latexit sha1_base64="bi+uuj2qpol4xlvdzfiw4aupl1s=">aaadbniclvllahrbfd0z7soojyqkbkrshitgyugoqlwouhezwukccztutk3spf9uv08mq37brfm1/ihu8gk591qrabc1mp6+de45p+69u2lt5k2lornep7hx89btptudu/fup1hewx241dadzcwkq4va7qrja4q8mhoxu8lsnnykzvqy7ftwjes358a2ev29d8enmzbjfpxp8ixxatmp67npk8nofokkrwexd4bwa7ne7b3eb+yhroyojqwqomyferr8dhejqknsiguxyyjxvmejbtr2zbkyeqkh/n3nbtejfffi2ao64ykfx0tlibfu1orzxnjaqplonqx9k/dcpaw2y35t71usdtgg+jfdjfnfddklwwyvtyecptwkshezd+l0klj5ekurr4egmmr7zfvgmsov5xyqptxezbaj5r8pu1dzz57b4buvsijypnmqtf6k7gviwpyzivnppoqiz0zpen+uis+ki2orvzqfexb8rsz/vw554smvz8b7gp9+664hw+ujobrf714nx2n/i5fwbm+xrr8njpewm5iwggn8wvec9s+dx8ht4nkpar/nny/wywrwlgbnbrex</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Pseudo-sondage EM-34 Milieu à deux couches: = 10 ms/m = 640 khz-m2 = variable = 20 m 35

36 <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> <latexit sha1_base64="u3dhie+lvnzcmdv82xa4oygvey4=">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</latexit> <latexit sha1_base64="hfnxr2fmuwy2ohiqfed6e8mnita=">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</latexit> <latexit sha1_base64="6u++m5yg+fzy7+s/n9sedclflls=">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</latexit> <latexit sha1_base64="bi+uuj2qpol4xlvdzfiw4aupl1s=">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</latexit> <latexit sha1_base64="obzti4pndhe6tcx28kk3yqch4pw=">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</latexit> Pseudo-sondage EM-34 Milieu à deux couches: = 10 ms/m = 640 khz-m2 = variable = 20 m À remarquer: La conductivité de la deuxième couche n est jamais atteinte Une conductivité maximale est atteinte à 500 ms/m, la conductivité apparente redescend par après. 36

37 1.Révision FEM Conductivitmètre (limite résistive) Profondeur d investigation: Dans la limite résistive, elle ne dépend que de l espacement et de l orientation des boucles Profondeur d investigation EM-34 Séparation Profondeur (m) HCP VCP Profondeur d investigation EM-31 HCP: ~6m VCP: ~3m 37 Geonics EM34 Geonics EM31

38 Résumé La grande majorité des appareils en surface fonctionne dans le régime résistif (faible nombre d induction): Dans ce cas, la conductivité est donnée par la composante en quadrature, La profondeur d investigation est reliée à l espacement des dipôles, et non à la fréquence, quelques appareils permettent de varier l espacement entre les dipôles et donc de faire un sondage (ce qui est rare), Dans le cas typique, une carte de résistivité apparente est produite, sans la relier à une profondeur La composante en phase dans ce cas indique la présence de corps conducteurs (métaux enfouis). 38

39 Résumé Pour arriver à inverser les données FEM et avoir un modèle en profondeur, il faut: Plusieurs fréquences (Hz au khz), Idéalement, plusieurs orientations de dipôles, S assurer que certaines fréquences dépassent la limite résistive. Ceci est surtout possible avec les systèmes aéroportés, mais reste ardu. 39

40 Étude de cas 40

41 Étude de cas Problématique Après la réunification de Berlin, un boom de construction se produit. Deux problèmes majeurs surviennent: Les connaissances des fondations et des restes des édifices construits avant la guerre sont très partielles Les obus non explosés sont un danger majeur lors des travaux. 41 (Butler, 2005) p

42 Étude de cas Problématique La construction d un tunnel souterrain de diversion de la rivière Spree avait commencé l époque. La guerre avait arrêté les travaux en cours d exécution. 42 (Butler, 2005) p

43 Étude de cas Propriétés géophysiques et choix des méthodes Étant donné la complexité des sites urbains, une vaste gamme de propriétés géophysiques ont été sélectionnées: La résistivité électrique est un indicateur important en présence de vide, ou de matériaux conducteurs, et donc devrait permettre de détecter les fondations enfouies. 43

44 Étude de cas Acquisition des données Les données EM sont acquises avec l EM-31 ce qui a permis de couvrir une surface gigantesque ( m2) en très peu de temps. Les mesures du champs magnétique total ont permis aussi une très vaste couverture spatiale. 44 (Butler, 2005) p

45 Étude de cas Résultats: EM (Butler, 2005) p

46 Étude de cas Résultats: EM (Butler, 2005) p

47 Étude de cas Interprétation Les données EM et MAG ne permettent pas de déterminer la profondeur des structures. Des tomographies sismique et électrique entre forages ont confirmé la présence du tunnel. 47 (Butler, 2005) p

48 Étude de cas Synthèse Les forages et excavations ont confirmé la présence du souterrain, ainsi que plusieurs positions d ordonnances nonexplosées. 48 (Butler, 2005) p