GLQ3205 Géophysique appliquée 2 Méthodes EM: Méthodes en

GLQ3205 Géophysique appliquée 2

Méthodes EM: Méthodes en fréquencesGabriel Fabien-Ouelletgabriel.fabien-ouellet@polymtl.ca

Été 2019Plan du cours

1. Modèle du conducteur enfoui 2. FEM: Détection de conducteur 3. FEM: Mesure de conductivité 4. Étude de cas

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

Onde non-atténuée

Onde atténuée

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Boucle émettrice

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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Boucle réceptrice

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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Principe de base en EM

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

Modèle du conducteur enfoui

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 ?

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.

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.

Réponse de la sous-surface

(Butler, 2005)

Forme de l’anomalie

P, Q %

Traverse

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.

Convention des signes:

Champ primaire

Champ secondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

Quelle serait la forme des profils ?

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.

Méthodes électromagnétiques fréquentielles

Méthodes en fréquence

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.

Appareils en FEM

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

Appareils en FEM

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

Appareils en FEM

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

Appareils en FEM

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

Détection d’anomalie conductrice

Le circuit équivalent

Analysons plus en détails le circuit équivalent vu précédemment.

Réponse de la sous-surface

(Butler, 2005)

Inductance mutuelle Inductance Condensateur Résistance

Rappel: analyse de circuit

La loi d’Ohm généralisée utilise une impédance complexe:

Principaux composants en analyse de circuits

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Inductance mutuelle

L’inductance mutuelle simplifie le couplage entre deux inductances.

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Inductance mutuelle

L’inductance mutuelle simplifie le couplage entre deux inductances

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• Géométrie des boucles • Distance entre les boucles • Orientation des boucles

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Inductance mutuelle de dispositifs commun

Quel est l’inductance mutuelle des configurations communes de boucle ?

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Horizontal coplanaire

Vertical coplanaire

Vertical coaxial (VCX)

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:

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Horizontal coplanaire

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<latexit sha1_base64="/RSSws/7krjASlVCfy0Uj2PWdxA=">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</latexit>

<latexit sha1_base64="m11uAVXD+WwCBiGXBtOC5VGXU8c=">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</latexit>

<latexit sha1_base64="eVi2Ns/o52XYGgxzPrA0XqoETmw=">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</latexit>

<latexit sha1_base64="ZZEHjZyGs4dA4QqXadLMk8h4Oj8=">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</latexit>

Quelle tension est mesurée au receveur ?

Pour connaître la réponse à la boucle réceptrice, on peut résoudre le circuit équivalent.

<latexit sha1_base64="5UWs2zsuAq9EhMBwMVywMr1YvGw=">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</latexit>

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<latexit sha1_base64="jJ+6sF1tIyFOlQXRDaI5ITh2hfg=">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</latexit>

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 ?

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La loi de boucles de Kirchoff:

Si on applique au circuit représentant le sol:

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<latexit sha1_base64="VBy1xiulPigzG3ifqOTbml+nZkk=">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</latexit>

<latexit sha1_base64="sO0GKGtaTBcFEdX/rufEwSMpwlc=">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</latexit> Nombre d’induction

<latexit sha1_base64="YbDzA5N230Jb18/7+GB2MOSoJoQ=">AAADxHiclVJda9RAFL3b+FHr11Yf9WFwEXxaEinoi7CgSB8Uq7htoVnKJJ1sQycfTJLVEtYHf42v+m/8B/ovPPd2KtUi6oTd3Dn3nDP33kxS27xpw/DrYCW4cPHS5dUra1evXb9xc7h+a7upOpeaaVrZyu0mujE2L820zVtrdmtndJFYs5McPeX8zsK4Jq/Kt+1xbWaFnpd5lqe6BbQ/vBtrWx9q9UTFVWHmWsWZ02n/Ytm/War94Sgch7LU+SDywYj82qrWB5sU0wFVlFJHBRkqqUVsSVODZ48iCqkGNqMemEOUS97Qktag7cAyYGigR/ifY7fn0RJ79mxEneIUi5+DUtF9aCrwHGI+TUm+E2dG/+TdiyfXdox34r0KoC0dAv2b7pT5rzrupaWMHksPOXqqBeHuUu/SyVS4cnWmqxYONTCOD5B3iFNRns5ZiaaR3nm2WvLfhMko71PP7ei7r7IE8k6mVUj9Jdx74MxcoCL+ZjNB2CeTM9g3geK94OzYSJXm5wQYXwjz/5UjnLg883CVz0RrpS9DLz33lZ8I7/gmxLLL4HHyhhZ3OPr9xp4Pth+Oo3Acvd4YTSb+Nq/SHbpHD1DLI5rQJm3RFBV8pE/0mb4EzwMbNEF3Ql0ZeM1t+mUFH34ApnfG+Q==</latexit>

Soit un courant au transmetteur:

La tension au récepteur:

Le champ primaire:

Le champ secondaire:

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<latexit sha1_base64="DNTvmDpGc3Akwv97DDvgsV+l49M=">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</latexit>

<latexit sha1_base64="TzVMkMdE3Y9pfyCwylthl5tuklo=">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</latexit>

<latexit sha1_base64="L572JFafUaTuKsS/Uj9i1BD86CQ=">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</latexit>

<latexit sha1_base64="pfbzHINZd9Fdt2e/6ysbNrtXYDU=">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</latexit>

Rapport du champ primaire au champ secondaire

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>

Dépend du couplage

Dépend de la fréquence et des propriétés du sol.

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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Dépend du couplage

Dépend de la fréquence et des propriétés du sol

P, Q %

Traverse

Conducteur

Composante en quad.

Composante en phase

Lecture négative

Champ EMprimaire

Champ EMsecondaire

Effet du facteur géométrique G

Déphasage

Les champs primaires et secondaires sont déphasés l’un par rapport à l’autre.

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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

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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

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Mesure du champ secondaire

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

Induction: Circuit équivalent

L’amplitude et la phase varient de façon marquée en fonction du paramètre d’induction.

Paramètre d’induction

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