GLQ3205 Géophysique appliquée 2 Résumé de la matière · GLQ3205 Géophysique appliquée 2 Résumé de la matière Gabriel Fabien-Ouellet [email protected] Été

GLQ3205 Géophysique appliquée 2

Résumé de la matièreGabriel [email protected]

Été 2019

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mailto:[email protected]

Résistivité électrique

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La conduction ionique dans l’eau des pores est le principal mécanisme de conduction et est la source des phénomènes de polarisation provoquée.

Potentiel d’électrodes

Potentiel de membrane

Conduction ionique

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• : Porosité • : Saturation en eau

Révision des méthodes électriques

Vitesses sismiques

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Roches

Nous ferons une distinction entre matériaux granulaires et roches dans ce qui suit

Vitesses sismiques

Matériaux granulaires

• Une variation marquée de Vp entre saturation partielle et complète pour un dépôt non consolidé (de 300 m/s à 1500 m/s)

• Vs est peu influencée par la saturation et par la porosité • Les vitesses augmentent avec la pression effective, surtout pour les matériaux en surface. • La quantité de fractures et leur forme affectent grandement Vp et Vs dans les roches: les

vitesses diminuent avec un degré croissant de fracturation.

Faibles vitesses

Grandes vitesses

Méthodes Électromagnétiques

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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

Boucle émettrice

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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

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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

Forme de l’anomalie

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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

Inductance mutuelle de dispositifs communs

L’inductance mutuelle permet de déterminer la forme des anomalies pour un modèle à 3 boucles

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Détection d’anomalie conductrice

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Le champ magnétique d’un dipôle:

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Pour une petite boucle où B est constant

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surface

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Rapport du champ primaire au champ secondaire

�9

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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Détection d’anomalie conductrice

La réponse dépend du nombre d’induction:

qui est le rapport de la distance entre les boucles r et la profondeur de peau:

Réponse du circuit équivalent

�10

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Limite inductive

Limite résistive

Méthodes électromagnétiques fréquentielles

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Une f.e.m. est produite à la boucle réceptrice en présence d’un flux magnétique variant dans le temps:

Deux façon d’y parvenir: • Coupure brusque du

champ (TDEM) • Champ harmonique

(FEM)

Résumé FEM vs TDEM

�11(Legault, 2015)

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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

�12

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Conductivimètre (limite résistive)

• La plupart des équipements au sol opèrent dans la limite résistive.

• La composante en quadrature est alors proportionnelle à la conductivité

• La composante en phase est nulle.

• Les bons conducteurs sont détectés par une forte augmentation de la composante en phase.

�13

Geonics EM38

Geonics EM34

Geonics EM31

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1.Révision FEM

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Conductivité apparente (limite résistive)

�14

Pour faciliter les calculs, on utilise habituellement la courbe cumulative:

Ce qui donne:

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Conductivité apparente (limite résistive)

�15

Exemple avec 3 couches et dispositif HCP:

• hauteur du dispositif: 1 m • distance entre les boucles: 4 m • couche 1: d=1.5 m, sigma = 1 mS/m • couche 2: sigma = 10 mS/m

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Sondage en profondeur

Pour retrouver les variations de la résistivité en profondeur, il faut: • Varier la fréquence (hors de la

limite résistive) • Varier l’espacement des boucles

(pas toujours possible) • Avoir plusieurs points de mesure

par station • Procéder à l’inversion

En pratique, c’est plutôt rare, on utilise surtout les conductivimètres pour faire des cartes des variations latérales de conductivité.

�16


Propagation d’une impulsion

La distance de diffusion :

Le temps de diffusion:

La vitesse de diffusion

�17

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Méthodes en temps: Principes de base

z

Amplitude

Diffusion

Mesures TDEM

�18

Principes de base TDEM

1. On injecte un courant électrique dans une boucle pendant un certain temps.

2. On coupe le courant pendant une période dite « temps mort ».

3. Les champs secondaires sont lus pendant la période temps mort, en l’absence du champ primaire.

4. À chaque point de mesure, plusieurs lectures du champ à différents canaux de temps.

Émission Réception

Pas de mesures

Mesures

T coupureT montée

Temps

Temps

TempsPas de

mesures

Mesures

Cour

ant

F.E.M

dB/d

t

Tout comme en FEM où nous regardions les limites résistives et inductives, nous nous intéresserons à deux limites:

• Temps courts (u >> 1)

• Temps longs (u << 1)

Réponse d’un sol homogène

�19

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changement de signe!

Temps courts

Temps longs

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Les mesures en TDEM se font aux temps longs

Pour les deux configurations:

�20

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changement de signe!

Temps courts

Temps longs

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Temps longs

• Voltage ~ t-5/2 • Voltage ~ à la

conductivité • Même dépendance

dans les deux configurations

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Résistivité apparente

�21

La résistivité apparente aux temps longs:

Attention! Formule valide que pour les temps longs!

L’inversion permet de retrouver les résistivités vraies!

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On peut caractériser un bon conducteur par sa constante de temps:

Cette équation correspond à la pente du graphique semi-logarithmique du temps en fonction de l’amplitude.

La constante de temps peut être reliée à la conductivité par:

où K est un facteur géométrique propre à la géométrie du conducteur et A est une constante propre à ses dimensions.

Interprétation de conducteurs

�22

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Attention! La pente est l’inverse de la constante de temps ici!

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Profondeur d’investigation

�23

Le moment dipolaire donne la force du champ magnétique générée par le transmetteur:

Le temps de coupure donne le temps des premières mesures, qui donne la plus faible profondeur pouvant être investiguée.

Le temps de coupure donne la plus faible profondeur détectable tandis que le moment dipolaire est proportionnel à la profondeur d’investigation.

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Temps de coupure pour le NanoTEM

Interprétation: Résultat des inversions

�24

Les levés FEM (hors de la limite résistive) et TDEM sont inversés en 1D et assemblés pour faire des modèles 3D.

Propagation sismique

�25

On applique brusquement une large force sur le sol.

Cette force fera varier les contraintes dans le sol, ce qui provoquera des déformations momentanées du volume de sol à proximité.

Ces déformations peuvent être mesurées par le déplacement d’une surface.

Les contraintes, déformations et déplacements se propagent dans l’espace sous la forme d’une onde.

https://teara.govt.nz/en/photograph/9759/seismic-survey

Propagation des ondes: Théorie

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https://teara.govt.nz/en/photograph/9759/seismic-survey

Ondes S

avec .

Ondes P

avec .

Ondes P et ondes S

�26

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Attention! En sismique, nous avons plusieurs types d’ondes (P et S). Une interface produira un conversion de mode, et chaque type d’onde répond à l’équation de réfraction généralisée:

où p est le paramètre de rai.

Réfractions en sismique

�27

Onde P réfractée

Onde P réfléchie

Onde P incidente

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Onde SV réfléchie

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Onde SV réfractée

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Rai sismique

Réfraction critique

�28

L’angle critique est donné par:

• La réfraction critique ne survient que si V2>V1

• L’angle se propage à la vitesse V2 le long de l’interface

• Selon le principe de Huygens, une onde est réémise vers le haut, à un angle égal à l’angle critique.

Réfraction critique

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Rai sismique

Exemple: Interprétation à deux couches

�29

Exemple: Interprétez les temps d’arrivées suivants selon un modèle à deux couches horizontales.

1. Tracez la dromochronique

2. Identifiez les brisures de pente et assignez les arrivées à un réfracteur

3. Obtenir les vitesses par l’inverse des pentes

4. Déterminez le temps d’intercepte et la distance de croisement

5. Déterminez la profondeur sous le tir:

V1 = 300 m/s

V2 = 1500 m/s

xi = 14.7 m

t0 = 39 ms

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Révision

Couches inclinées

�30

A B

Les vitesses apparentes du réfracteur dépendent maintenant de la direction du tir!

Il faut toujours un tir direct et un tir inverse en sismique réfraction !



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Tem

ps

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Révision

Interprétation d’un réfracteur incliné

�31

1. Déterminer les vitesses V1, V2+ et V2-

directement sur les dromochroniques

2. Déterminer l’angle critique et le pendage à l’aide de:

3. Déterminer la vitesse vraie du deuxième milieu:

4. Déterminer les profondeurs grâce aux distances de croisement ou aux temps d’intercepte:

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dA =

t�02 cos ✓c cos↵

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Couche inclinée

Le temps Plus Dépend de la profondeur et de la vitesse locale du réfracteur.

Méthode du Plus-Minus

�32

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AP

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x

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Le temps Minus Sa pente ne dépend que de la vitesse du réfracteur.


La méthode de Plus-Minus permet une interprétation d’un réfracteur ondulé dont la vitesse est variable!

Configuration d’un levé

La longueur d’un levé doit permettre d’observer la distance de croisement

L’espacement des géophones devrait permettre d’observer la pente de chaque arrivée ( au moins 3 receveurs par segments de droite).

Le nombre de tirs minimal est 2: un tir direct et un tir inverse de part et d’autre de la ligne.

�33

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Mise en oeuvre et applications

Profondeur du Plus-Minus

Méthode de Plus-Minus

�34

Méthode du Plus-Minus:

1. Mesurer la vitesse 1

2. Déterminer Minus et Plus pour chaque receveur valide

5. Calculer

6. Calculer les épaisseurs

A BPosition

Tem

ps


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Difficultés

�35

Distance

Tem

ps

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S R

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Distance

Tem

ps

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S R

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Inversion de vitesse Couche cachée

Révision

Dispersion

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Dispersion: Une onde dispersive est une onde dont la vitesse dépend de la fréquence (ou de la longueur d’onde)

La dispersion provoque l’étalement du train d’ondes dans le temps.

Propagation dispersive Propagation sans dispersion

Ondes de surface

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• Les ondes de surface sont les arrivées prépondérantes pour les levés sismiques de faible profondeur.

• Pourquoi ? Leur amplitude décroit comme mais l’énergie des ondes S et P décroit comme .

• La vitesse des ondes de surface est fortement reliée à la vitesse des ondes de cisaillement.

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Dispersion et modes

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• Les différents modes des ondes de Love et de Rayleigh sont causés par l’interférence des ondes SH et des ondes P et SV, respectivement.

• Pour un mode, la vitesse varie selon la fréquence: à haute fréquence VL tend vers V1 et à basse fréquence VL tend vers V2.

• Les modes possèdent une fréquence de coupure, et donc n’existe pas au-delà d’une certaine fréquence

V1

modes

V2

Coupure

Inversion modèle initial

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On peut faire une approximation de Vs directement grâce à la courbe de dispersion. Ceci correspond au modèle initial lors de l’inversion.

Estimation de Vs Pour un milieu homogène, on peut approximer que . On peut donc estimer directement Vs à partir de la vitesse de phase du mode fondamental.

Estimation de la profondeur La profondeur de pénétration augmente avec la longueur d’onde. On peut approximer que d est entre et .

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Inversion des ondes de surface

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En mesurant les vitesses de phase des différents modes à plusieurs fréquences, il est possible de retrouver les variations de vitesse en profondeur par inversion.

Documents

GLQ3205 Géophysique appliquée 2 Résumé de la matière · GLQ3205 Géophysique appliquée 2 Résumé de la matière Gabriel Fabien-Ouellet [email protected] Été