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GLQ3205 Géophysique appliquée 2
Méthodes EM: Méthodes en fréquencesGabriel [email protected]
Été 2019Plan du cours
1. Modèle du conducteur enfoui 2. FEM: Détection de conducteur 3. FEM: Mesure de conductivité 4. Étude de cas
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Propagation dans le régime diffusif
La solution de l’équation de diffusion:
La solution est alors:
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Révision: notions de base en EM
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Profondeur de peau
Longueur d’onde Vitesse de diffusion
Propagation dans le régime diffusif
�3
Onde non-atténuée
Onde atténuée
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Révision: notions de base en EM
Boucle émettrice
�4
La loi de Biot-Savart: Production d’un champ magnétique par une boucle de courant:
À distance suffisante, le champ ainsi créé est dipolaire, c’est-à-dire qu’on peut l’assimiler au champ de petit aimant.
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Révision: notions de base en EM
Boucle réceptrice
�5
Selon la loi de Faraday, un changement de flux magnétique engendre une force électromotrice mesurable:
Le flux dépend de la direction de la boucle par rapport au champ magnétique
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Révision: notions de base en EM
Principe de base en EM
�6
1. Une boucle transmet un champ magnétique primaire variant dans le temps • Ceci produit un courant dans un object conducteur
2. Les courants de Foucault produisent un champ magnétique secondaire • Ceci produit un courant à la boucle réceptrice
Révision: notions de base en EM
Modèle du conducteur enfoui
�7
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 conductrice dans la sous surface ?
�8
Modèle du conducteur enfoui
Modèle du conducteur enfoui
�9
Conducteur
Niveau du sol
Courants deFoucault
Champ primaire
Champ secondaire
Récepteur
Transmetteur
• L’émetteur émet un champ magnétique, que l’on nomme champ primaire.
• Le champ primaire induit un courant dans le conducteur enfoui, selon la loi de Faraday.
• Le courant induit crée à son tour un champ magnétique que l’on nomme champ secondaire.
• Le récepteur mesure la somme du champ primaire et du champ secondaire.
Modèle du conducteur enfoui
Modèle du conducteur enfoui
�10
Modèle du conducteur enfoui
Le circuit équivalent
On utilise un système simplifié afin de comprendre la dynamique du système. Le sol est assimilé à une troisième boucle de courant.
�11
Réponse de la sous-surface
(Butler, 2005)
Modèle du conducteur enfoui
Forme de l’anomalie
�12
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
Modèle du conducteur enfoui
Forme de l’anomalie
�13
Convention des signes:
Rx
+
Rx
-
Champ primaire
Champ secondaire
Modèle du conducteur enfoui
Forme de l’anomalie
�14
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Modèle du conducteur enfoui
Forme de l’anomalie
�15
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Tx Rx
Modèle du conducteur enfoui
Forme de l’anomalie
�16
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Modèle du conducteur enfoui
Forme de l’anomalie
�17
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Tx Rx
Modèle du conducteur enfoui
Forme de l’anomalie
�18
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Modèle du conducteur enfoui
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Forme de l’anomalie
�19
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
Tx Rx
Modèle du conducteur enfoui
Forme de l’anomalie
�20
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Modèle du conducteur enfoui
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Forme de l’anomalie
�21
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
Tx Rx
Modèle du conducteur enfoui
Forme de l’anomalie
�22
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Modèle du conducteur enfoui
Forme de l’anomalie
�23
Tentons d’expliquer la forme de l’anomalie grâce au flux magnétique.
+ -
+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Tx Rx
Modèle du conducteur enfoui
Quelle serait la forme des profils ?
�24
Tx Rx
Tx Rx
Tx Rx
Modèle du conducteur enfoui
Résumé
• Une boucle émet un champ magnétique (le champ primaire)
• Le champ primaire se propage dans le sol
• Le champ primaire induit un courant dans le sol
• Le courant produit un champ magnétique secondaire
• La boucle émettrice mesure les champs primaires et secondaires
• La mesure dépend du couplage entre les boucles et entre les anomalies présentes dans le sol.
�25
Modèle du conducteur enfoui
Méthodes électromagnétiques fréquentielles
�26
Méthodes en fréquence
�27
Loi de Faraday: Une force électromotrice causée par la variation d’un champs magnétique dans une boucle. C’est le principe d’induction.
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Les méthodes en fréquence utilisent un champ magnétique sinusoïdale de fréquence entre 10 et 104 Hz.
Méthodes électromagnétiques fréquentielles
Appareils en FEM
�28
Systèmes au sol et aéroporté.
EM-31 de Geonics
• Espacement TX-RX: 3.66 m
• Fréquence: 9.8 kHz
• Profondeur approximative: 4m
• Mesures: Composantes en phase et en quadrature
Méthodes électromagnétiques fréquentielles
Appareils en FEM
�29
Systèmes au sol et aéroporté.EM-34 de Geonics
• Espacement TX-RX: variable de 10m, 20m,40m
• Fréquence: 6.4 1.6 et 0.4 kHz
• Profondeur approximative: jusqu’à 60m
• Mesure: Conductivité
Méthodes électromagnétiques fréquentielles
Appareils en FEM
�30
Systèmes au sol et aéroporté.GEM-2 de Geophex
• Fréquence: 25 Hz à 96 kHz kHz
• Profondeur approximative: 10 m (selon le fabricant)
• Mesure: Parties en phase et en quadrature
Méthodes électromagnétiques fréquentielles
Appareils en FEM
�31
Systèmes au sol et aéroporté.
Resolve de CGG
• Séparation entre 7 et 9 m
• Fréquence: 6 fréquences entre 400 Hz et 140 kHz
• Mesure: Parties en phase et en quadrature
Méthodes électromagnétiques fréquentielles
Détection d’anomalie conductrice
�32
Le circuit équivalent
Analysons plus en détails le circuit équivalent vu précédemment.
�33
Réponse de la sous-surface
(Butler, 2005)
Détection d’anomalie conductrice
Inductance mutuelle Inductance Condensateur Résistance
Rappel: analyse de circuit
La loi d’Ohm généralisée utilise une impédance complexe:
Principaux composants en analyse de circuits
�34
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Détection d’anomalie conductrice
Inductance mutuelle
�35
L’inductance mutuelle simplifie le couplage entre deux inductances.
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<latexit sha1_base64="16IhSh3VVqD39iBvoaiazTlEwEo=">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</latexit>
TxRx
Détection d’anomalie conductrice
Inductance mutuelle
�36
L’inductance mutuelle simplifie le couplage entre deux inductances
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TxRx
• Géométrie des boucles • Distance entre les boucles • Orientation des boucles
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Détection d’anomalie conductrice
Inductance mutuelle de dispositifs commun
Quel est l’inductance mutuelle des configurations communes de boucle ?
�37
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Horizontal coplanaire
(HCP)
Vertical coplanaire
(VCP)
Vertical coaxial (VCX)
Détection d’anomalie conductrice
Impédance mutuelle de dispositifs commun
Quelle est l’inductance mutuelle des configurations communes de boucle ?
Le champ en z d’une source dipolaire:
Au receveur, le champ du transmetteur est:
�38
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Horizontal coplanaire
(HCP)
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Détection d’anomalie conductrice
Quelle tension est mesurée au receveur ?
Pour connaître la réponse à la boucle réceptrice, on peut résoudre le circuit équivalent.
�39
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<latexit sha1_base64="DQREzf+vsXHi7A/7HU91piiIPq0=">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</latexit>
<latexit sha1_base64="VVuuwjMgDZZ54hm3qgmjSXYSAO4=">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</latexit>
<latexit sha1_base64="nEdzRNvVbkGlB7nRCn2999Uoq94=">AAADbXiclVJNT9RQFD0z9QPHD0DjCmMaJ0bjYtIaE11OwsYFCwgOkOCEtOXN2NCvtK+jZMJPcCu/zX8gK/4C514eBiFEfU2n9517znn33nlxlaWNDYKfna536/aduwv3evcfPHy0uLT8eKsp2zoxo6TMynonjhqTpYUZ2dRmZqeqTZTHmdmOD1Ylvz0zdZOWxSd7WJlxHk2LdJImkSW0ubYX7i31g0Ggy78ehC7ow631crnzBp+xjxIJWuQwKGAZZ4jQ8NlFiAAVsTHmxGpGqeYNjtCjtiXLkBERPeDvlLtdhxbci2ej6oSnZHxrKn28pKYkr2Ysp/mab9VZ0Ju85+optR3yGzuvnKjFF6J/010w/1UnvVhM8EF7SNlTpYh0lziXVqcilfuXurJ0qIhJvM98zThR5cWcfdU02rvMNtL8L2UKKvvEcVucuCoLIl91WrnWX9B9TlyYM1Yk/9lYEfGZ6BniG1PxTXFxbLRK83sCgs+U+f/KPk88uvT0eA/Dq7fuerD1dhAGg3DjXX84dDdyASt4gdf0e48hPmIdI1YwxXf8wHH31HvqPfOen1O7Had5gj+W9+oMfVywmw==</latexit>
<latexit sha1_base64="jJ+6sF1tIyFOlQXRDaI5ITh2hfg=">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</latexit>
Détection d’anomalie conductrice
Quelle tension est mesurée au receveur ?
Soit un courant au transmetteur:
La tension au récepteur:
La f.e.m. du champ primaire:
La f.e.m. champ secondaire:
Quel est le courant dans le sol ?
�40
<latexit sha1_base64="oaywZWWDxtMmC+MpeOBvkJ4xNgk=">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</latexit>
<latexit sha1_base64="5UWs2zsuAq9EhMBwMVywMr1YvGw=">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</latexit>
<latexit sha1_base64="DQREzf+vsXHi7A/7HU91piiIPq0=">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</latexit>
<latexit sha1_base64="VVuuwjMgDZZ54hm3qgmjSXYSAO4=">AAADbXiclVLbTtRQFF0z9QLjBdDwpDGNE6PxYdIaE32chBcfAR0gwQlpy5mxobe0p6Nkwif4Kt/mH8gTv8Dam4NBCFFP0+k+a6+1zt57TlxlaWOD4Gen6926fefuwmLv3v0HD5eWVx5tNWVbJ2aUlFlZ78RRY7K0MCOb2szsVLWJ8jgz2/HBmuS3Z6Zu0rL4ZA8rM86jaZFO0iSyhD5u7oV7y/1gEOjyrwehC/pwa71c6bzGZ+yjRIIWOQwKWMYZIjR8dhEiQEVsjDmxmlGqeYMj9KhtyTJkREQP+DvlbtehBffi2ag64SkZ35pKHy+oKcmrGctpvuZbdRb0Ju+5ekpth/zGzisnavGF6N90F8x/1UkvFhO81x5S9lQpIt0lzqXVqUjl/qWuLB0qYhLvM18zTlR5MWdfNY32LrONNP9LmYLKPnHcFieuyoLIV51WrvUXdJ8TF+aMFcl/NlZEfCZ6hvjGVHxTXBwbrdL8noDgM2X+v7LPE48uPT3ew/DqrbsebL0ZhMEg3HjbHw7djVzAEzzHK/q9wxAfsI4RK5jiO37guHvqrXpPvWfn1G7HaR7jj+W9PAOPkrCh</latexit>
<latexit sha1_base64="nEdzRNvVbkGlB7nRCn2999Uoq94=">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</latexit>
<latexit sha1_base64="jJ+6sF1tIyFOlQXRDaI5ITh2hfg=">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</latexit>
<latexit sha1_base64="DNTvmDpGc3Akwv97DDvgsV+l49M=">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</latexit>
<latexit sha1_base64="TzVMkMdE3Y9pfyCwylthl5tuklo=">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</latexit>
Détection d’anomalie conductrice
<latexit sha1_base64="TR07SsgGV0nLgMyKKnvzaXRxvGE=">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</latexit>
<latexit sha1_base64="0nDjxtpmrAAhaGZfchKFx+SbGTM=">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</latexit>
<latexit sha1_base64="HbHnTch1C2yiRP3Vf+GHRvD5mgU=">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</latexit>
<latexit sha1_base64="pfbzHINZd9Fdt2e/6ysbNrtXYDU=">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</latexit>
Quelle tension est mesurée au receveur ?
La loi de boucles de Kirchoff:
Si on applique au circuit représentant le sol:
�41
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<latexit sha1_base64="5UWs2zsuAq9EhMBwMVywMr1YvGw=">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</latexit>
<latexit sha1_base64="DQREzf+vsXHi7A/7HU91piiIPq0=">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</latexit>
<latexit sha1_base64="VVuuwjMgDZZ54hm3qgmjSXYSAO4=">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</latexit>
<latexit sha1_base64="nEdzRNvVbkGlB7nRCn2999Uoq94=">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</latexit>
<latexit sha1_base64="jJ+6sF1tIyFOlQXRDaI5ITh2hfg=">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</latexit>
<latexit sha1_base64="VBy1xiulPigzG3ifqOTbml+nZkk=">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</latexit>
<latexit sha1_base64="sO0GKGtaTBcFEdX/rufEwSMpwlc=">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</latexit> Nombre d’induction
Détection d’anomalie conductrice
<latexit sha1_base64="TR07SsgGV0nLgMyKKnvzaXRxvGE=">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</latexit>
<latexit sha1_base64="0nDjxtpmrAAhaGZfchKFx+SbGTM=">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</latexit>
<latexit sha1_base64="HbHnTch1C2yiRP3Vf+GHRvD5mgU=">AAADrHiclVLLTtxAEKzFeRDygnDMxcoqUk4rG0Uix5WSAxcUkNgFaVkh24yJg1+yxwtotf+Qa/Jn+YPkL1LdDAiCoiRj7bqnuqqmuz1xnWetDYLvvSXv3v0HD5cfrTx+8vTZ89W1F+O26prEjJIqr5qDOGpNnpVmZDObm4O6MVER52Y/Pn0v+f2ZadqsKvfsRW2mRXRSZmmWRJbQePtoHm4sjlb7wSDQ5d8NQhf04dZOtdbbwiGOUSFBhwIGJSzjHBFaPhOECFATm2JOrGGUad5ggRVqO7IMGRHRU/6fcDdxaMm9eLaqTnhKzl9DpY/X1FTkNYzlNF/znToL+ifvuXpKbRd8x86rIGrxiejfdFfMf9VJLxYp3mkPGXuqFZHuEufS6VSkcv9GV5YONTGJj5lvGCeqvJqzr5pWe5fZRpr/oUxBZZ84boefrsqSyJlOq9D6S7rPiQtzxorkm00VEZ9UzxDfmIpzxcWx1SrN9QQEnynz/5V9nri48UiVH1Sba18G24770U1EdnITDnWX0uPyTS3vcPj7jb0bjDcGYTAId9/2h0N3m5fxEq/whrVsYogt7GDECj7jC77imzfw9ryJN72kLvWcZh23lpf+Av6Kvek=</latexit>
<latexit sha1_base64="YbDzA5N230Jb18/7+GB2MOSoJoQ=">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</latexit>
Quelle tension est mesurée au receveur ?
Soit un courant au transmetteur:
La tension au récepteur:
Le champ primaire:
Le champ secondaire:
�42
<latexit sha1_base64="oaywZWWDxtMmC+MpeOBvkJ4xNgk=">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</latexit>
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<latexit sha1_base64="TzVMkMdE3Y9pfyCwylthl5tuklo=">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</latexit>
<latexit sha1_base64="L572JFafUaTuKsS/Uj9i1BD86CQ=">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</latexit>
Détection d’anomalie conductrice
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<latexit sha1_base64="pfbzHINZd9Fdt2e/6ysbNrtXYDU=">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</latexit>
Rapport du champ primaire au champ secondaire
�43
One mesure souvent le champ secondaire par rapport au champ primaire:
Dépend du couplage
entre le sol, Tx et Rx
Facteur d’amplitude qui dépend de la fréquence et des propriétés du sol
Déphasage entre les signaux primaires et secondaires.
Dépend de la fréquence et des propriétés du sol.
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<latexit sha1_base64="IhoMmQy9Z0sXrDuMsEGbata60Ys=">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</latexit>
Détection d’anomalie conductrice
Rapport du champ primaire au champ secondaire
�44
One mesure souvent le champ secondaire par rapport au champ primaire:
Dépend du couplage
entre le sol, Tx et Rx
Facteur d’amplitude qui dépend de la fréquence et des propriétés du sol
Déphasage entre les signaux primaires et secondaires.
Dépend de la fréquence et des propriétés du sol.
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<latexit sha1_base64="IhoMmQy9Z0sXrDuMsEGbata60Ys=">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</latexit>
La f.e.m. est proportionnel au champ magnétique selon la loi de Faraday.
Traditionnellement, on parle des rapports de champ magnétique, et donc:
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Détection d’anomalie conductrice
Rapport du champ primaire au champ secondaire
�45
One mesure souvent le champ secondaire par rapport au champ primaire:
Dépend du couplage
entre le sol, Tx et Rx
Facteur d’amplitude qui dépend de la fréquence et des propriétés du sol
Déphasage entre les signaux primaires et secondaires.
Dépend de la fréquence et des propriétés du sol
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+10
-10
-20
-30
0
P, Q %
T TT
Traverse
R RR
+
++
Conducteur
Composante en quad.
Composante en phase
Lecture positiveLecture positive
Lecture négative
Champ EMprimaire
Champ EMsecondaire
Effet du facteur géométrique G
Détection d’anomalie conductrice
Déphasage
�46
Les champs primaires et secondaires sont déphasés l’un par rapport à l’autre.
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<latexit sha1_base64="IhoMmQy9Z0sXrDuMsEGbata60Ys=">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</latexit>
Détection d’anomalie conductrice
Selon l’identité trigonométrique:
Le déphasage peut être exprimé selon une partie en phase P et une partie en quadrature Q.
Mesures: parties en phase et en quadrature
�47
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Détection d’anomalie conductrice
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En notation réelle:
En notation phaseur:
La mesure de P (partie en phase ou partie réelle) et Q (partie imaginaire ou en quadrature) est équivalente à mesurer l’amplitude et la phase du signal:
Mesures: parties en phase et en quadrature
�48
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Détection d’anomalie conductrice
Mesure du champ secondaire
�49
Pour mesurer le champ secondaire, il faut annuler le champ primaire au receveur, ce qui se fait par une boucle de compensation.
La référence est transmise au receveur
Une boucle de compensation émet un champ de même amplitude, mais de signe contraire
Détection d’anomalie conductrice
Induction: Circuit équivalent
L’amplitude et la phase varient de façon marquée en fonction du paramètre d’induction.
�50
Paramètre d’induction
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Détection d’anomalie conductrice
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