GLQ3205 Géophysique appliquée 2 Méthodes sismiques 3

GLQ3205 Géophysique appliquée 2

Méthodes sismiques 3: Sismique réfraction (suite)Gabriel [email protected]

Été 2019 Plan du cours

1. Révision 2. Vitesses sismiques 3. Méthode du Plus-Minus 4. Mise en oeuvre et applications 5. Étude de cas

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mailto:[email protected]

Attention! En sismique, nous avons plusieurs types d’ondes (P et S). Une interface produira une 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

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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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Révision

Réfraction critique

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L’angle critique est donné par:

• La réfraction critique ne survient que si V2>V1

• L’onde 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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Révision

Exemple: Interprétation à deux couches

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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 assigner 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

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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

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S R

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Distance

Tem

ps



S R


Inversion de vitesse Couche cachée

Révision

Corrections et limitations

�7

Bref, les dromochroniques sont rarement des droites parfaites en pratique, ce qui rend l’interprétation non triviale! Effet combiné de la

topographie de surface et du roc et des

variations de vitesse!

Révision

Vitesses sismiques

�8

Ondes S Ondes P

Ondes P et ondes S

�9

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La vitesse des ondes P est toujours plus grande que celle des ondes S !

Vitesses sismiques

Coefficient de Poisson

�10

Les modules élastiques et la densité sont donc directement liés aux vitesses sismiques!

Il est possible d’obtenir le coefficient de Poisson à partir des vitesses:

Le rapport Vp/Vs est donc fondamental!

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Vitesses sismiques

Vitesses sismiques

Plusieurs facteurs affectent les vitesses sismiques: • Lithologie: D’énormes différences sont rencontrées entre roches et dépôts

granulaires, qui sont dues aux différences de rigidité de la matrice. • Minéralogie: La structure atomique des minéraux et la composition des

roches affectent leur densité et leur module élastique. • Porosité: Une grande porosité diminue les vitesses sismiques. • Saturation: La nature des fluides contenus dans les pores affecte

grandement la vitesse des ondes P. • Pression effective: Plus la pression effective est grande, plus les vitesses

augmentent. • Compaction et cimentation: Lorsque les sédiments se compactent, la

porosité diminue et la vitesse augmente. Lors de la cimentation, les grains deviennent solidaires, ce qui augmente la rigidité de la matrice et donc les vitesses sismiques.

�11

Vitesses sismiques

Lithologie

�12

Matériau Ondes P Ondes S(m/s) (m/s)

Grès saturés

2000-3500 800-1800Marne 2000 - 3000 750 - 1500Craie 2300 - 2600 1100 - 1300Charbon 2200 - 2700 1000 - 1400Sel 4500 - 5500 2500 - 3100Anhydrites 4000 - 5500 2200 - 3100Calcaires 3500 - 6000 2000 - 3300Dolomites 3500 - 6500 1900 - 3600Granite 4500 - 6000 2500 - 3300Basalte 5000 - 6000 2800 - 2400Gneiss 4400 - 5200 2700 - 3200

Matériau Ondes P Ondes S(m/s) (m/s)

Air 343 N/AEau 1450 - 1500 N/AGlace 3400 - 3800 1700 - 1900Huile 1200 - 1250 N/ASol végétal 300 - 700 100 - 300Sables secs 400 - 1200 100 - 500Sables saturés 1500 - 2000 400 - 600Argiles saturés 1100 - 2500 80 - 800

Roches

Sédiments

https://gpg.geosci.xyz/content/physical_properties/tables/index.html

La lithologie affecte grandement les vitesses sismiques. En particulier, des variations de 10x sont rencontrées entre dépôts granulaires et roches.

Vitesses sismiques

https://gpg.geosci.xyz/content/physical_properties/tables/index.html

Vitesses sismiques

�13

Matériaux granulaires Roches

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

Vitesses sismiques

Vitesses sismiques

�14


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

Vitesses sismiques

Vitesses sismiques

�15


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

• Nous considérerons les roches comme un matériau poreux contenant des fractures à toutes les échelles

• Ces deux types de porosité ont des formes différentes et réagissent différemment aux contraintes: les fissures se ferment plus facilement que les pores

• La rigidité des dépôts granulaires est fonction des contacts entre les grains

• Ce contact dépend de la forme des grains et de la pression

• Le nombre de contacts dépend du triage et de la granulométrie

Vitesses sismiques

Contrainte effective

�16

Les vitesses sismiques dépendent de la contrainte effective. Celle-ci dépend de la contrainte totale et de la contrainte du fluide:

Lorsque la pression des pores est très élevée, la cohésion des dépôts granulaires peut être perdue et la résistance au cisaillement devient nulle.

La pression effective agit sur la matrice des roches et des matériaux granulaires en augmentant leur rigidité.

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Vitesses sismiques

Roches: Pression effective

�17

• Les vitesses augmentent avec les contraintes effectives

• Cette dépendance provient de la fermeture des fractures qui rigidifie la matrice

• L’amplitude du changement est proportionnelle au niveau de fracturation

• La forme des fractures régit la pression à laquelle l’asymptote est atteinte

Vitesses sismiques

Dépôts granulaires: Pression effective

�18

Les vitesses dans les dépôts meubles dépendent fortement de la pression effective!

Vitesses sismiques

Dépôts granulaires: Taille des grains et consolidation

�19

La taille des grains et leur triage affectent dans une moindre mesure les vitesses.

Vitesses sismiques

Dépôts granulaires: Compaction

�20

Pour un même dépôt, la compaction augmente sensiblement les vitesses sismiques pour une même pression effective.

Vitesses sismiques

Dépôts granulaires: Porosité

�21

Les vitesses des ondes P sont plus sensibles aux changements de porosité que les ondes S.

Vitesses sismiques

Dépôts granulaires: Porosité

�22

Le rapport Vp/Vs est beaucoup moins sensible aux effets de porosité et est plus lié à la pression effective.

Vitesses sismiques

Dépôts granulaires: Saturation

�23(Domenico, 1977)

La saturation en eau influence grandement les vitesses sismiques:

• Variation non-linéaire de Vp avec la saturation: brusque augmentation autour de 1

• Affecte peu les vitesses des ondes de cisaillement (légère diminution de la vitesse avec une augmentation de la saturation).

Vitesses sismiques

Température

�24

La température affecte peu les vitesses sismiques, sauf lorsque la viscosité du fluide contenu dans les pores varient fortement en fonction de la température:

• Peu de variations pour de l’eau ou de l’air

• Variations notoires en présence d’huile.

Vitesses sismiques

Résumé: vitesses sismiques

Pour interpréter les variations de vitesse sismique dans les sols, les points importants sont:

• 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 influencé 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.

�25

Vitesses sismiques

Méthode du Plus-Minus

�26


�27

Comment tenir compte des variations de vitesse et de la topographie des réfracteurs ?

Effet combiné de la topographie de surface et du

roc et des variations de vitesse!

Méthode de Plus-Minus

�28

AP

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<latexit sha1_base64="s/5MyT1RsZhGmoGsZSLLA0irkJI=">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</latexit>

<latexit sha1_base64="WdJF5UnUnDRH5sNcGTI8rOq7N8c=">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</latexit>

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

Elle se base sur deux temps, le Plus et le Minus:

<latexit sha1_base64="lmuHFNcTeX8Lbw0d3+AiMV4ioXk=">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</latexit>

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Parcours entre les deux tirs en bout de ligne

�29

AP






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�30

AP









�31

AP







<latexit sha1_base64="Nr4MZjz28eXuCpEvAYfsC+y+flw=">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</latexit>



�32

AP







<latexit sha1_base64="Nr4MZjz28eXuCpEvAYfsC+y+flw=">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</latexit>

<latexit sha1_base64="43hVa5vHfQkbFYSvMNYJK2JaSHI=">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</latexit>



�33

AP






<latexit sha1_base64="BT23NQ60EXLlJcPtpiO+RO8/iH8=">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</latexit>

<latexit sha1_base64="joi3jfASsg/PDS7QrKFd8Xkjxdo=">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</latexit>

<latexit sha1_base64="vq5Ro9vkN5nKV2OPumNPSL7G7fA=">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</latexit>


Le Plus

�34

Le temps Plus est défini comme:

Grâce aux expressions précédentes:


<latexit sha1_base64="M1w1UYkcgzMrA/MQFNQkOhzhwzc=">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</latexit>


<latexit sha1_base64="M1w1UYkcgzMrA/MQFNQkOhzhwzc=">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</latexit>

Le Plus

�35





Le Plus

�36




<latexit sha1_base64="CAF95oVRaXO3RxH55VeDGj8hUYU=">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</latexit>


Le Plus

�37

AP






<latexit sha1_base64="yQyfBE3vn67y2QbqSk3QqjACwJ0=">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</latexit>

<latexit sha1_base64="VvOVKq1USt3btWTPpfM4+CCu7Lo=">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</latexit>


Le Plus

�38

AP






<latexit sha1_base64="yQyfBE3vn67y2QbqSk3QqjACwJ0=">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</latexit>

<latexit sha1_base64="VvOVKq1USt3btWTPpfM4+CCu7Lo=">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</latexit>





Temps d’intercepte


Le Plus

�39

AP






Le temps Plus est le temps d’intercepte au point P. Il est relié à la profondeur sous le géophone.

<latexit sha1_base64="noFFLxh2OKE1KY/l2eoCrdqcvN0=">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</latexit>

<latexit sha1_base64="QBDOc3pYwAlkInfCoTQ7AnFnMqg=">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</latexit>


Le Minus

�40

<latexit sha1_base64="joi3jfASsg/PDS7QrKFd8Xkjxdo=">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</latexit>

<latexit sha1_base64="vq5Ro9vkN5nKV2OPumNPSL7G7fA=">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</latexit>

<latexit sha1_base64="BT23NQ60EXLlJcPtpiO+RO8/iH8=">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</latexit>

Le temps Minus est défini comme:




Le Minus

�41



<latexit sha1_base64="vX5wPw9ewdCATDZ0TVxdJhA5iMg=">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</latexit>





Le Minus

�42

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Le Minus

�43

AP






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Le Minus

�44

AP






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Temps d’intercepte pour A

Le Minus

�45

AP






x

Le temps Minus est le temps entre la source et un point au droit du géophone. Il dépend de la vitesse près du géophone.


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

Parcours des Plus et Minus

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AP






x





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



�47

TAP

TBP

Les temps Plus-Minus peuvent être mesurés directement sur la dromochronique!




1. On peut déterminer la vitesse du réfracteur grâce à la pente du temps Minus:

2. À l’aide des temps Plus, on peut déterminer la profondeur en dessous de chaque géophone:

où Dp est le délai, donné par


�48


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�49

Méthode du Plus-Minus:



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1. Mesurer la vitesse 1

A BPosition

Tem

ps



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A BPosition

Tem

ps



�52



2. Déterminer

3. Déterminer Minus et Plus

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A BPosition

Tem

ps





�53



2. Déterminer


4. Calculer


A BPosition

Tem

ps






�54



2. Déterminer


4. Calculer

5. Calculer les épaisseurs


A BPosition

Tem

ps





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Variations de vitesse

�55

Les variations de vitesse peuvent être mesurées sur la courbe minus par des pentes différentes.

On peut donc identifier des vitesses différentes en prenant la pente des différents segments du Minus.

Lorsqu’on calcule les profondeurs avec les délais, il faut choisir la vitesse du réfracteur correspondant à la station pour laquelle on calcule la profondeur.


Exemple

�56

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.84 20 49.4 86.75 25 50.6 84.66 30 52.5 83.17 35 55.2 82.68 40 59.5 82.19 45 63.8 81.610 50 67.3 80.411 55 70.1 78.412 60 71.3 76.313 65 72.6 74.214 70 74.5 72.715 75 77.3 72.316 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100

TirA TirB

Exemple

�57

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.84 20 49.4 86.75 25 50.6 84.66 30 52.5 83.17 35 55.2 82.68 40 59.5 82.19 45 63.8 81.610 50 67.3 80.411 55 70.1 78.412 60 71.3 76.313 65 72.6 74.214 70 74.5 72.715 75 77.3 72.316 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100

TirA TirB

Mesurer V1

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Exemple

�58

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

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0 50 100

TirA TirB Minus

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0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.84 20 49.4 86.75 25 50.6 84.66 30 52.5 83.17 35 55.2 82.68 40 59.5 82.19 45 63.8 81.610 50 67.3 80.411 55 70.1 78.412 60 71.3 76.313 65 72.6 74.214 70 74.5 72.715 75 77.3 72.316 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100

TirA TirB

Identification de TAB

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Exemple

�59

0102030405060708090100

0 50 100

TirA TirB Minus

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0 50 100

TirA TirB Minus

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0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

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0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

0102030405060708090100

0 50 100

TirA TirB Minus

G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.8 49.84 20 49.4 86.7 53.15 25 50.6 84.6 56.56 30 52.5 83.1 59.87 35 55.2 82.6 63.18 40 59.5 82.1 67.99 45 63.8 81.6 72.710 50 67.3 80.4 77.411 55 70.1 78.4 82.212 60 71.3 76.3 85.513 65 72.6 74.2 88.814 70 74.5 72.7 92.215 75 77.3 72.3 95.516 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100

TirA TirB Minus


Calcul du temps Minus

Exemple

�60

G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.8 49.8 46.54 20 49.4 86.7 53.1 45.65 25 50.6 84.6 56.5 44.76 30 52.5 83.1 59.8 45.27 35 55.2 82.6 63.1 47.38 40 59.5 82.1 67.9 51.19 45 63.8 81.6 72.7 54.910 50 67.3 80.4 77.4 57.311 55 70.1 78.4 82.2 58.112 60 71.3 76.3 85.5 57.213 65 72.6 74.2 88.8 56.314 70 74.5 72.7 92.2 56.715 75 77.3 72.3 95.5 59.216 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100

TirA TirB Minus Plus

Calcul du temps Plus


Exemple

�61

G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.8 49.8 46.5 3.04 20 49.4 86.7 53.1 45.6 3.05 25 50.6 84.6 56.5 44.7 3.06 30 52.5 83.1 59.8 45.2 3.07 35 55.2 82.6 63.1 47.3 3.08 40 59.5 82.1 67.9 51.1 2.19 45 63.8 81.6 72.7 54.9 2.110 50 67.3 80.4 77.4 57.3 2.111 55 70.1 78.4 82.2 58.1 2.112 60 71.3 76.3 85.5 57.2 3.013 65 72.6 74.2 88.8 56.3 3.014 70 74.5 72.7 92.2 56.7 3.015 75 77.3 72.3 95.5 59.2 3.016 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100



Calcul des vitesses 2

Exemple

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G x(m)

TA(ms)

TB(ms)

Minus(ms)

Plus(ms)

v(km/s)

h(m)

0 0.0 90.51 5 16.7 90.72 10 33.3 90.23 15 48.1 88.8 49.8 46.5 3.0 7.04 20 49.4 86.7 53.1 45.6 3.0 6.95 25 50.6 84.6 56.5 44.7 3.0 6.76 30 52.5 83.1 59.8 45.2 3.0 6.87 35 55.2 82.6 63.1 47.3 3.0 7.18 40 59.5 82.1 67.9 51.1 2.1 7.79 45 63.8 81.6 72.7 54.9 2.1 8.310 50 67.3 80.4 77.4 57.3 2.1 8.711 55 70.1 78.4 82.2 58.1 2.1 8.812 60 71.3 76.3 85.5 57.2 3.0 8.613 65 72.6 74.2 88.8 56.3 3.0 8.514 70 74.5 72.7 92.2 56.7 3.0 8.615 75 77.3 72.3 95.5 59.2 3.0 8.916 80 80.9 66.717 85 84.5 50.018 90 87.3 33.319 95 89.2 16.7

100 90.5 0.0

0102030405060708090100

0 50 100


Calcul des épaisseurs

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Résumé méthode de Plus-Minus

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AP






B

La méthode du Plus-Minus permet:

• Une interprétation de la topographie d’un réfracteur

• Permet d’identifier les variations de vitesse le long du réfracteur

• Produit une estimation de l’épaisseur et de la vitesse sous chaque capteur ayant observé la réfraction sur les tirs direct et inverse

• L’épaisseur obtenue est perpendiculaire à l’interface

Mise en oeuvre et applications

�64

Longueur d’un levé

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

Pour V1 = 1500 m/s et V2 = 2000 m/s: • xi = 5.3 h

Règle de pouce: La longueur de la ligne devrait être autour de 6x la profondeur de la cible

�65

Distance

Tem

ps



S R




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Espacement des géophones

L’espacement des géophones devrait permettre d’observer la pente de chaque arrivée:

Pour V1 = 300 m/s et V2 = 4500 m/s et h = 1m:

• xi = 2.14 m

Règle de pouce: Chaque réfracteur devrait produire une arrivée sur au moins 3 capteurs

�66

Distance

Tem

ps



S R




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Positionnement des tirs

�67

Profondeur du Plus-Minus mal contrainte

• Au minimum 2 tirs doivent être utilisés, placés de part et d’autre de la ligne.



�68

Profondeur du Plus-Minus mal contrainte


• Des tirs internes permettent d’avoir une redondance des données et de mieux estimer la vitesse de la première couche



�69


• Des tirs internes permettent d’avoir une redondance des données et de mieux estimer la vitesse de la première couche

• Des tirs au loin permettent d’étendre l’estimation des profondeurs à toute la ligne et de mieux estimer les temps d’intercepte (Distance: 1.5x xi du dernier géophone)


Profondeur au roc

�70

L’application naturelle de la sismique réfraction est l’estimation de la profondeur au roc!


Évaluation de la qualité du roc

�71

En géotechnique, la sismique réfraction est souvent utilisée pour estimer la qualité du roc!

(Barton, 2007)

• RQD: % de fraction de roc compétent dans une carotte dont la longueur est de plus de 10 cm

• Ja: dépend du nombre de fractures

• Jr dépend de la rugosité des fractures

• Ja dépend du degré d’altération • Jw dépend de la pression de

l’eau • SRF dépend du relâchement du

aux failles


Évaluation de la qualité du roc

�72

En géotechnique, la sismique réfraction est souvent utilisée pour estimer la qualité du roc!

(Barton, 2007)

Faible qualité Q

Grande qualité Q


Évaluation de la rippabilité

�73

La sismique réfraction permet d’évaluer les moyens nécessaires lors du terrassement de roc.


�74

Caractérisation des aquifères


Documents

GLQ3205 Géophysique appliquée 2 Méthodes sismiques 3