Rai sismique - Moodle

Rai sismique

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Sismique réfraction

Nous pouvons retrouver les variations de vitesse et les épaisseurs des couches d’un milieu tabulaire grâce aux temps des premières arrivées sismiques.

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On réduit l’information d'une trace à seulement un temps d’arrivée, en pointant la position de la première ondelette visible.

Rai sismique

Identification des premières arrivées

La précision des pointés est très importante, car elle influence directement la précision des résultats.

Des données trop bruitées rendent difficile, voire impossible, un pointage précis!

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Rai sismique


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Pour y parvenir, il faut des données de qualité comportant des premières arrivées franches.

Bruits ou arrivées ?

Rai sismique

Front d’onde

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L’identification des premières arrivées consiste à tracer dans l’espace le déplacement du front d’onde parvenant aux récepteurs. Il faut donc identifier la même phase sur toutes les traces!

Front d’onde: Positions spatiales d’une onde dont la phase est équivalente (par exemple le minimum ou le maximum d’une onde).

Rai sismique

Front d’onde

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L’identification des premières arrivées consiste à tracer dans l’espace le déplacement du front d’onde parvenant aux récepteurs. Il faut donc identifier la même phase sur toutes les traces!

Front d’onde: Positions spatiales d’une onde dont la phase est équivalente (par exemple le minimum ou le maximum d’une onde).

Rai sismique

Principe de Huygens

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Pour estimer les vitesses sismiques du sol, il faut estimer quel a été le parcours du front d’onde qui est arrivé à la surface. Comment ?

Principe de Huygens: Chaque point du front d’onde agit comme une source d’une onde sphérique, de même amplitude et de même phase. L’interface constructive et destructive des sources secondaires produit un front d’onde continu et qui se déplace dans le temps.

Rai sismique

Principe de Huygens

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Pour estimer les vitesses sismiques du sol, il faut estimer quel a été le parcours du front d’onde qui est arrivé à la surface. Comment ?

Principe de Huygens: Chaque point du front d’onde agit comme une source d’une onde sphérique, de même amplitude et de même phase. L’interface constructive et destructive des sources secondaires produit un front d’onde continu et qui se déplace dans le temps.

Front de l’onde réfléchie

Front de l’onde réfractée

Front de l’onde incidente

Rai sismique

Rai sismique

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Il est plus commode d’utiliser le rai sismique pour retracer le parcours et la direction du front d’onde. Le rai est perpendiculaire au front d’onde.

Rai sismique: Vecteur perpendiculaire au front d’onde et pointant dans sa direction de propagation.

Front de l’onde réfléchie

Front de l’onde réfractée

Front de l’onde incidente

Rai réfracté

Rai réfléchi

Rai incident

Rai sismique

Il est possible de prédire le parcours des rais sismiques grâce à la loi de Snell-Descartes:

1. Loi de la réflexion:

2. Loi de la réfraction:

Lois de Snell-Descartes

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Rai réfracté

Rai réfléchi

Rai incident

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Rai sismique

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


Onde SV réfléchie


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Onde SV réfractée

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Rai sismique

Les ondes SH (polarisée horizontalement, parallèle au plan de réfraction) ne produisent pas de conversion d’onde!

La loi de la réfraction reste cependant la même!

Réfractions SH

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Onde SH réfractée

Onde SH réfléchie

Onde SH incidente



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Rai sismique

Qu’arrive-t-il si la vitesse augmente graduellement ?

Aucune réflexion n’est produite, mais le paramètre de rai reste toujours constant!

Les rais deviennent alors courbes et peuvent remonter à la surface!

Gradient de vitesse

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Rai réfracté

Rai réfléchi

Rai incident




Rai sismique

Réfraction critique

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Comment varie l’angle en fonction du contraste de vitesse entre les milieux 1 et 2 ?

Prenons V2/V1 = 5, alors:

• • • •

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Rai sismique


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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.



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Rai sismique

La réfraction

• Modèle à deux couches

• Un gradient de vitesse est présent dans chaque couche, ce qui courbe les rais

• Propagation purement acoustique, pas de conversion de mode, ni d’ondes de surface

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Tiré des notes de cours de Jean Virieux after Anne Obermann

La réfraction

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La réfraction

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• L’angle critique est atteint

• La réfraction est maintenant parallèle à l'interface

• Une réflexion totale interne est maintenant atteinte, c’est-à-dire que le coefficient de réflexion est de 1.

Angle critique

La réfraction

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La réfraction

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• La réflexion atteint maintenant la surface

• On discerne maintenant une onde « conique » causée par la réfraction critique montante

Onde conique


La réfraction

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• Les ondes réfractées par le gradient de vitesse (les rais courbes jaunes) arrivent maintenant avant l’onde directe

• À ce moment, la distance critique du gradient est atteinte

Onde conique

Distance critique


La réfraction

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La réfraction

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La réfraction

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• La réfraction critique rejoint maintenant l’onde réfractée par le gradient de vitesse

• Un brusque changement de pente est observé, car l’onde conique se propage à la vitesse du milieu 2

• La distance de croisement de la réfraction au milieu 2 est alors atteinte.


La réfraction

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La réfraction

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La réfraction

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• À long déport, les ondes réfléchies et les ondes courbées par le gradient de vitesse ont le même temps de propagation

• Une seule arrivée est alors observée sur le sismogramme

Onde guidée


La réfraction

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Milieu tabulaire à 2 couches horizontales

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Parcours des rais sismiques

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S RL’énergie peut voyager de la source au receveur selon plusieurs parcours:

• Onde directe

• Onde réfléchie

• Onde réfractée

2 couches horizontales

Réciprocité

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S RRéciprocité en sismique: Les temps d’arrivée entre deux points fixes sont équivalents, peu importe si les positions du tir et du receveur sont interverties.

• Ceci permet de vérifier la précision du pointage des arrivées (tSR = tRS)

• Permet de vérifier des erreurs sur le positionnement du temps 0 lors de l’acquisition

• Les méthodes d’interprétation se basent sur le principe de réciprocité


Dromochronique

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S RR R



Distance

Tem

ps

La dromochronique est le graphique des temps d’arrivées en fonction de la distance. Elle permet d’interpréter les levés de sismique réfraction.


Onde directe

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S RR R

Distance

Tem

ps

L’onde directe voyage sur un parcours direct entre la source et les receveurs. Son temps d’arrivée est:

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Onde réfléchie



S R R

Distance

Tem

ps

L’onde réfléchie subit une réflexion au point milieu de S et R. Son temps d’arrivée est:

M

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Onde réfractée



S R R

Distance

Tem

ps

L’onde réfractée suit une droite dont la pente est donnée par l’inverse de la vitesse du milieu 2.

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<latexit sha1_base64="O//cXY9sYb0ZxRjzvrZrtD00T4o=">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</latexit>



Temps d’intercepte



S R R

Distance

Tem

ps

L’ordonnée à l’origine de la droite de la réfraction s’appelle le temps d’intercepte:

<latexit sha1_base64="uu/sNIvMs2b7MFkQtMQzsj7R61M=">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</latexit> <latexit sha1_base64="uu/sNIvMs2b7MFkQtMQzsj7R61M=">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</latexit>


<latexit sha1_base64="pvCo4+qsaM5jgFdJSOiiBPLGZ2w=">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</latexit>


<latexit sha1_base64="wJnr1ZFdJJTYqvf1+/AQW+091kc=">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</latexit>



Distance critique



S R R

Distance

Tem

ps

Attention! Aucune réfraction ne peut arriver avant la distance critique! L’ordonnée à l’origine ne représente pas une arrivée physique!



R


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Distance de croisement



S R

Distance

Tem

ps

Une autre distance importante est la distance de croisement, le point où l’onde réfractée rejoint l’onde directe:



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Interprétation deux couches horizontales

�40

Distance

Tem

ps

1. Calculer les vitesses des milieux 1 et 2 grâce à l’inverse des pentes des ondes directes et réfractées

2. Estimer l’épaisseur soit:

• par les temps d’intercepte:

• par les distances de croisement


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Exemple: Interprétation à deux couches

�41

Distance(m) Temps(ms)

0 0.0

5 16.7

10 33.3

15 49.2

20 52.5

25 55.9

30 59.2

35 62.5

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



�42


1. Tracez la dromochronique



�43





�44



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



�45


V1 = 300 m/s

V2 = 1500 m/s


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

3. Obtenir les vitesses par l’inverse des pentes



�46





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

V1 = 300 m/s

V2 = 1500 m/s

xi = 14.7 m

t0 = 39 ms



�47





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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Interprétation de n couches horizontales

�48

Dans le cas de n couches horizontales, le temps d’arrivée est donné par:

On voit que la pente dépend de la vitesse de la couche N.

Distance

Tem

ps



S R

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<latexit sha1_base64="b7dCAbiRAvSMm5TW9PWkhuvgk5g=">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</latexit>



�49

1. Identifier chaque bris de pente sur les dromochroniques, et en tirer les vitesses des n couches ainsi que leur temps et leur distance d’intercepte.

2. Trouver itérativement les épaisseurs de chaque couche:

<latexit sha1_base64="4DR4bLSqpHcA4yS/DEoVIT4SipE=">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</latexit>

<latexit sha1_base64="nF/YHRu4fjrekdlG8dHNe+MFe8I=">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</latexit>

<latexit sha1_base64="cFbG7p8oFnRJdUO9olF1O3GjJYQ=">AAAEN3iclVJNb9NAEB3XfJTylcKxlxWhEhJqZFdIcACpEhwqIUSRSFqpCZHtboobf2GvA5Xl38Dv4adw4obKkQN33ky2qFDKh61kZ9+893ZmvGGRxJXxvI/Ognvu/IWLi5eWLl+5eu16Z/nGoMrrMtL9KE/ycicMKp3Eme6b2CR6pyh1kIaJ3g6njzm/PdNlFefZS3NY6FEa7GfxJI4CA2jcef903BxMW/VIqeGkDKJGDas3pWn8NbsfjA9erbdYmuldv0XYqrU/cOaMtpkzfps+27lVatzpej1PHnU68G3QJfts5cvOJg1pj3KKqKaUNGVkECcUUIV3l3zyqAA2ogZYiSiWvKaWlqCtwdJgBECn+N/HbteiGfbsWYk6wikJfiWUilahycErEfNpSvK1ODN6lncjnlzbIdbQeqVADb0G+jfdMfNfddyLoQk9kB5i9FQIwt1F1qWWqXDl6kRXBg4FMI73kC8RR6I8nrMSTSW982wDyR8Jk1HeR5Zb0xdbZQbkrUwrlfozuDfAmTlDRfzNRoKwz0TOYN8QineCs2MlVeofE2B8Jsz/V3ZxYnvi5SqfiDaRvjQ9s9zndiK845swlN0EHvMVWtxh/9cbezoYrPd8r+e/uNfdeGhv8yKt0C26g1ru0wZt0hb1UcE3Z8W57ay6H9xP7mf3aE5dcKzmJv30uF+/A15w8qw=</latexit>

Distances de croisement Temps d’intercepte

<latexit sha1_base64="bJlUTLjMrARyGsE1zAbGAVoxHoQ=">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</latexit>



�50

S R

3. Trouver le déplacement sous le tir pour lequel la profondeur est valide

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<latexit sha1_base64="iTb0qbGUIpe8ivp+6GXFNnzRQQk=">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</latexit>

<latexit sha1_base64="BC4Qn0VUrMj+F1/54k4z148H6z0=">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</latexit>


Milieu tabulaire avec une couche inclinée

�51

Couches inclinées

�52

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

Distance<latexit sha1_base64="Al/BQTwOYzwLGTH3qglQ4qeYQaE=">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</latexit>

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x

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Couche inclinée

Couches inclinées



A B

Le temps de propagation entre A et B:




hA

hB

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Couche inclinée

Couches inclinées

�54


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<latexit sha1_base64="e5yhFA3NsudOxWoorP4xwKjIFwA=">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</latexit>

<latexit sha1_base64="eKVxmSU51cysG92yZJ1VPecqgS4=">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</latexit>

<latexit sha1_base64="NuaT60pTYv6NoPLRTx4e3NYRLsY=">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</latexit>

Couche inclinée

Couches inclinées

�55


<latexit sha1_base64="NuaT60pTYv6NoPLRTx4e3NYRLsY=">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</latexit>

<latexit sha1_base64="0O0UGOsjVmohmKIfCG8ditohyN0=">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</latexit>

<latexit sha1_base64="XvuLPYOT99XX+oq3WhdWw84k7Eg=">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</latexit>

<latexit sha1_base64="8Ah7xrGNd98MRDl10PzVl1frFDQ=">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</latexit>

Couche inclinée

Couches inclinées

�56

Le temps de A à B est bien sur égal au temps de B à A.

Cependant, la vitesse apparente sera différente!

A



B1 B2 B3 B4x

Le parcours réfracteur surface se rallonge en x

hA

hB

Couche inclinée

Couches inclinées

�57

Le temps de A à B est bien sur égal au temps de B à A.

Cependant, la vitesse apparente sera différente!



A1 A2 A3 BxA1

Le parcours réfracteur surface se raccourcit en x

hB

hA

Couche inclinée

Couches inclinées

�58

Pour trouver les vitesses, il faut exprimer les hauteurs en A et B en fonction de x:


BxA1

hB

hA


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<latexit sha1_base64="3m95BqHxpiWwTdwwJuAJNV5HH4I=">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</latexit>

<latexit sha1_base64="pfODB2hk6q+ep15wyOOoHLv/Y3w=">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</latexit>

Couche inclinée

La vitesse est la dérivée de la distance en fonction du temps. Sachant:

La vitesse pour un tir en A:

Couches inclinées

�59


<latexit sha1_base64="QZ2/t/irpnVOTNc1hbP7mMKrd8w=">AAAENXiclVJNb9NAEB3XfJTy0RROiMuqEVIRIrIrJDiAVASHXhBFImmlOERrdx2vurGt9TqksvwT+D38Fg7cEIITB/4As+NtVagQsFbs2TfvvZ2ZbFwqWZkg+Oit+BcuXrq8emXt6rXrN9Z7GzdHVVHrRAyTQhX6IOaVUDIXQyONEgelFnweK7EfHz23+f2F0JUs8jfmuBSTOZ/lMpUJNwhNe++jVPOkCdtmNN1++6BlT1mHRCXXRnLVnkZs2UZKpGbsCElRNZHJhOHTpLX6sN3Kps/Yfda9lyyqZN5EXJUZb+8h0gkRJ2mH08FtpOUsM5Nprx8MAlrsfBC6oA9u7RUb3i5EcAgFJFDDHATkYDBWwKHCZwwhBFAiNoEGMY2RpLyAFtZQWyNLIIMjeoTvGe7GDs1xbz0rUid4isKfRiWDu6gpkKcxtqcxytfkbNE/eTfkaWs7xm/svOaIGsgQ/ZvuhPmvOtuLgRQeUw8SeyoJsd0lzqWmqdjK2ZmuDDqUiNn4EPMa44SUJ3NmpKmodztbTvmvxLSo3SeOW8M3V2WOyDua1pzqz9G9QdwyF1iR/c8mhFiflM6wvjEqloRbx4qqFKcTsPiCmP+v7OOJ7ZnHVvmCtIr6EvDScV+5ididvQkR7VL06L6oxTsc/n5jzwej7UEYDMLXD/s7T9xtXoU7sAlbWMsj2IFd2IMhVvDDu+1ten3/g//J/+x/6agrntPcgl+W//0nFMjy4g==</latexit>

<latexit sha1_base64="V6H1sy2xMJR2H7hnI2UmK/h+kmo=">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</latexit>

<latexit sha1_base64="k4ESl1+X2nqiaIRPC41iqqDV+OY=">AAADzniclVJNb9NAEJ3UfJTylcKRi0UEKkKK7AqJHopUCQ69IIJE0kp1FK2368aqY1v2OlBZFlcO/Bqu8Ef4B/AveDPdokKFgLUSz7557+3MeOMyS2sbBF97K96ly1eurl5bu37j5q3b/fU7k7poKm3GusiKaj9WtcnS3IxtajOzX1ZGLeLM7MXHzzm/tzRVnRb5G3tSmulCHeVpkmplAc36D/1nfpRUSrdRnebtRqSycq4eR3ZurJrp7lHXTmZhN+sPgmEgy78YhC4YkFujYr23SxEdUkGaGlqQoZws4owU1XgOKKSASmBTaoFViFLJG+poDdoGLAOGAnqM/yPsDhyaY8+etag1Tsnwq6D06QE0BXgVYj7Nl3wjzoz+ybsVT67tBO/YeS2AWpoD/ZvujPmvOu7FUkJb0kOKnkpBuDvtXBqZClfun+vKwqEExvEh8hViLcqzOfuiqaV3nq2S/DdhMsp77bgNfXdV5kDeyrQWUn8O9xY4M5eoiL/ZVBD2SeQM9o2heCc4O9ZSpfk5AcaXwvx/5QAnducervKFaDPpy9BLx33lJsI7vgmR7BJ4nL6hxR0Of7+xF4PJ5jAMhuHrJ4OdbXebV+ke3acN1PKUdmiXRjRGBR/pE32mL97IW3qd9/6UutJzmrv0y/I+/AB75stK</latexit>

Couche inclinée

Les vitesses apparentes sont données par:

Couches inclinées

�60

A B






<latexit sha1_base64="gOngDottK/7/PLDB6wfKSALBtXo=">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</latexit>

Tem

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<latexit sha1_base64="7iPUPDWD53PL1dYrjvkI3eblBh0=">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</latexit>

Couche inclinée

Comment déterminer le pendage et la vitesse vraie ?

Couches inclinées

�61

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<latexit sha1_base64="Dc73VxiITZr6OYtc/d1VApus0U0=">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</latexit>

<latexit sha1_base64="7iPUPDWD53PL1dYrjvkI3eblBh0=">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</latexit>

Couche inclinée

Quels sont les temps d’intercepte ?

Le temps de parcours était:

Temps d’intercepte

�62

Tem

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<latexit sha1_base64="y9i4OF81o/HQSibA8tuMPnQ276g=">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</latexit>

<latexit sha1_base64="vtTSjCEuL/2dU2ip1uHEoM2s+AI=">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</latexit>

<latexit sha1_base64="/4FpehCkarx8DcGfwZyrO+lkw4w=">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</latexit>

<latexit sha1_base64="tJX4So+U/vdDaU+b+ePfdMN6R/w=">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</latexit>

Pour les tirs en A et en B:

Couche inclinée

Quelles sont les distances de croisement ?

Le temps de parcours était:

Distances de croisement

�63

Tem

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<latexit sha1_base64="JtfsA/+Suz1gBMQkZ3Kh2twwgU4=">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</latexit>

<latexit sha1_base64="7cDu8NSclinADeX7/EPnYynPJuo=">AAAD5HiclVJNTxRBEK1lVBC/Fj16mbAxwRg2M1zkAAlGD1yMmLBAwqyTnqaH7TBfme5ZIJP5B96MVw/+Gq968x/ov7Cq6DUoMWpPdqf61Xuvq2o6qTJtbBB87c15167fmF+4uXjr9p279/pL9/dM2dRSjWSZlfVBIozKdKFGVttMHVS1EnmSqf3k5Dnl96eqNrosdu15pca5OC50qqWwCMX9jbNYv1n1N/0orYVs1ybxs0iWpo3sRFkRy65rw9XI6KJdmUFPIpFVE/G46+L+IBgGvPyrQeiCAbi1Uy71tiGCIyhBQgM5KCjAYpyBAIPPIYQQQIXYGFrEaow05xV0sIjaBlkKGQLRE/w/xt2hQwvck6dhtcRTMvzVqPThEWpK5NUY02k+5xt2JvRP3i17Um3n+E6cV46ohQmif9PNmP+qo14spLDOPWjsqWKEupPOpeGpUOX+pa4sOlSIUXyE+RpjycrZnH3WGO6dZis4/42ZhNJeOm4D312VBSKnPK2c6y/QvUWcmFOsiL7ZmBHySfkM8k1QccY4ORquUv2cAOFTZv6/coAndpceqvIFazPuS8FLx33lJkI7ugkR71L0uHijFu9w+PuNvRrsrQ3DYBi+DgZbG+42L8BDWIYVrOUpbME27MAIK/gIn+AzfPFS7633znt/QZ3rOc0D+GV5H34AadjUbA==</latexit>

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<latexit sha1_base64="/ItzA+WVIzHv1o0YUM71xw/XjjM=">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</latexit>

Pour les tirs en A et en B:

Couche inclinée

Attention! Les hauteurs hA et hB sont les longueurs perpendiculaires à l’interface sous les tirs en A et B! Pour retrouver les profondeurs au droit des tirs, il faut:

Couches inclinées

�64

A






hA

hB

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<latexit sha1_base64="toSQv202js1nzvLEiw61IoGrxI8=">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</latexit>

Couche inclinée

Interprétation d’un réfracteur incliné

�65

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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<latexit sha1_base64="rbzJskkzzI2DMfeGsNsWiRGYKcU=">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</latexit>

<latexit sha1_base64="KURWIUAFcLkw+EMdLJz2h8kZigI=">AAAD/3iclVJNb9NAEJ3UfJTy0RSOXCwipFSokd0LCAmpCA69oBaJNJXqYK0362RVf8leh1aWD/wabogrB34IZy5Fgv/AzGSDChUC1ko88/a9tzPjjYpEV8bzPndWnEuXr1xdvbZ2/cbNW+vdjdsHVV6XUg1lnuTlYSQqlehMDY02iTosSiXSKFGj6PgZ7Y/mqqx0nr0yp4Uap2Ka6VhLYRAKu6NJ+NR94gZxKWRzEurXW31/K6h01gSJik0/MDNlRCgfBCIpZsINSj2dmc3W3Wyb7UDmVbNktIuMaW0bdnvewOPlXgx8G/TArv18o7MLAUwgBwk1pKAgA4NxAgIqfI7ABw8KxMbQIFZipHlfQQtrqK2RpZAhED3G/ylmRxbNMCfPitUST0nwV6LShfuoyZFXYkynubxfszOhf/Ju2JNqO8V3ZL1SRA3MEP2bbsn8Vx31YiCGR9yDxp4KRqg7aV1qngpV7p7ryqBDgRjFE9wvMZasXM7ZZU3FvdNsBe+fMZNQyqXl1vDVVpkh8oanlXL9Gbo3iBNzjhXRNxszQj4xn0G+ESpOGCfHiqtUPydA+JyZ/6/s4YntuYeqfM7ahPtS8MJy9+xEKKObEHAWo8fijVq8w/7vN/ZicLA98L2B/9Lr7Ty2t3kV7sI96GMtD2EHdmEfhljBJ/gC3+C789Z557x3PiyoKx2ruQO/LOfjD/gM34E=</latexit>

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Couche inclinée

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Corrections et limitations

�66

Correction topographique

La topographie change le parcours des rais. Pour la source:

Après un peu d’algèbre:

e: Élévation h: Profondeur de la source d: Élévation de référence

�67

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Correction topographique

La correction topographique totale est la somme des corrections de la source et du géophone:

Connaissant:

es: Élévation de la source er: Élévation du géophone h: Profondeur de la source d: Élévation de référence

�68

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Que se passe-t-il lorsqu’une couche intermédiaire s’amincit ?

Couche cachée

�69

Distance

Tem

ps

S R







Couche cachée

�70

Distance

Tem

ps

S R







Couche cachée

�71

Distance

Tem

ps

S R





Couche cachée

Une couche cachée est une couche dont la réfraction ne devient jamais une première arrivée!

Les causes: • Contraste de vitesse trop faible • Épaisseur trop faible • Espacement des géophones trop

grands

Dans ce cas, la profondeur du réfracteur visible sera erronée!

�72

Distance

Tem

ps



S R






Couche cachée: correction

On peut corriger pour une couche cachée dans le cas simple d’un milieu à 3 couches horizontales.

Pour cela, il faut connaître la vitesse V2 et une des épaisseurs.

�73

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V2 et hr = h1 + h2 V2 et h1 V2 et h2

Facteur de correction


En présence d’une inversion de vitesse (V2 < V1):

• Aucune réfraction critique n’est possible

• La dromochronique ne peut donc montrer un bris de pente pour cette couche

• L’interprétation sera un modèle à 2 couches

• La profondeur du réfracteur sera exagérée

La sismique réfraction n’est pas applicable dans ce cas!

Inversion de vitesse

�74

Distance

Tem

ps



S R




Faille

�75

Distance

Tem

ps

S R

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Une faille ou une dépression brusque du roc causera des discontinuités de la dromochronique.

Lorsque la hauteur de la discontinuité est faible par rapport à la profondeur du réfracteur, la hauteur peut être approximée par:


Anomalies courantes

Quelques anomalies courantes observées sur les dromochroniques:

A. Variations topographiques rapides ou changement local de vitesse de la couche 1

B. Lentille de vitesse anormale

C. Topographie localisée du réfracteur

D. Changement de vitesse locale du réfracteur

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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!


Documents

Rai sismique - Moodle