fold mechanics
TRANSCRIPT
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A
TERM PAPER
ON
FOLD MECHANICS
COMPILED BY
SERIKI OLUWASEGUN OLUWASEYI
CVE/07/0368
AS PART OF THE REQUIREMENT FOR THE
COURSE AGY 20
SUBMITTED TO
THE APPLIED GEOLOGY DEPARTMENT!
COURSE LECTURER" MR #! OWOSENI
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Contents
!0 I$%&'()*%+'$
2!0 L+,% '- . %&1,
3!0 F*%'&, --*%+$/+$-4)$*+$ -'4( -'&1%+'$
3! L& %5+*.$,, +,*'),+% $( ,5
3!2 F+$ 41$% *'$%$%
3!3 R'*. (%
3!9 V+,*',+% &%+'
9!0 D,*&+%+'$ '- -'4(,
9! D,*&+%+'$ '- ,+$4 -'4(( ,)&-*,
9!2 D,*&+%+'$ '- 1)4%+4 -'4(( ,)&-*,
:!0 F'4( *4,,+-+*%+'$
:! K+$1%+* $4,+, '- -'4(, +$ *&',, ,*%+'$
:!2 F'4( ,5
:!3 F'4( %+5%$,,
:!9 F'4( ,11%&
:!: D-'&1%+'$ ,%4 *4,,,
6!0 F'4( %,7!0 M*5$+*, '- -'4(+$
8!0 S)11&
R-&$*,
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!0 INTRODUCTION
T5 %&1 -'4( +, ),( +$ '4' ;5$ '$ '& ,%*. '- '&++$44 -4% $( 4$& ,)&-*, ,)*5 , ,(+1
,%&% & <$% '& *)&( , &,)4% '- 4,%+* =+!! &1$$%> (-'&1%+'$! S$,(+1$%& -'4(, & %5', ()
,4)1+$ '- ,(+1$%& 1%&+4 <-'& +% +, 4+%5+-+(! F'4(, +$ &'*., & +$ ,+? -&'1 1+*&',*'+* *&+$.4, %'
1')$%+$@,+?( -'4(,! T5 '**)& ,+$4 , +,'4%( -'4(, $( +$ %$,+ -'4( %&+$, '- (+--&$% ,+?, '$ &+
,*4,! F'4(, -'&1 )$(& &+( *'$(+%+'$, '- ,%&,, 5(&',%%+* &,,)& '& &,,)& $( %1&%)& @
5(&'%5&14 &(+$% , +($*( < %5+& &,$* +$ ,'-% ,(+1$%, %5 -)44 ,*%&)1 '- 1%1'&5+* &'*.,
$ , &+1& -4'; ,%&)*%)&, +$ ,'1 +$'), &'*.,! A ,% '- -'4(, (+,%&+<)%( '$ &+'$4 ,*4 *'$,%+%)%,
<4% *'11'$ -%)& '- '&'$+* ?'$,!
T5 '<*%+ '- %5+, %&%+, +, %' 54 ), )$(&,%$( ,'1 <,+* 1*5$+,1, %5% '&% ()&+$ -'4(
-'&1%+'$! T5& & ,&4 &'*,,, +$'4( +$ -'4( -'&1%+'$ $( 1'1$%! T5+, +$*4)(, P,,+ -'4(+$"
4 $' 1*5$+*4 &'4 +$ (4'+$ -'4(,!
A*%+ -'4(+$" L& %5+*.$,, $( +,*',+% (%&1+$ -'4( ,5
A*%+ -'4(+$ +$'4, <)*.4+$ '& <$(+$ '- ,%+-- =1'& +,*'),> 4&,!
2.0 List of key terms:
• -'4( %," *4+$(&+*4 *'$*$%&+* *'$+*4 +&&)4& *'1',+%
• -'4( *&,% -'4( 5+$ -'4( +, -'4( 4+1<,
• +4 4$ +4 ,)&-* +4 %&*
• &$*
• -'4( ,*4
• +$%&4+1< $4
• -'4( *)&%)& @ &')$(( %' *5&'$ *),%
•
$4'+$ ,)&-*, $( ; *5&*%&+,%+*,• $%+-'&1 $%+*4+$ ,$-'&1 $( ,$*4+$
• 1'$'*4+$, $( ,%&)*%)&4 %&&*,
• &444 ,! ,+1+4& -'4(,
• &,+%+* '& ,*'$(& -'4(,
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• -'4( +$%&-&$* %%&$,
• -'4( %&$,',+%+'$
• -4)&4 ,4+
• <)*.4 -'4(,
• -4'; '& +,*'), -'4(,
• 4& &444 *'1&,,+'$
The adjacent photo is of folds evident in ice and debris material in Malaspina glacier, St Elias Mountains of Ala
The folds reflect deformation, flowage in the ice, although another factor in the appearance here is that this is n
orthogonal cross section view, but a very obliue slice provided by a melting surface, and thus layer thicknesses
not true layer thicknesses. !ndeed, given that moraine material is often of a stripe, character, the geometry
simply that of folded layers
.
3.0 Factors affecting the formation of folds
3! L& %5+*.$,, +,*',+% $( -'4( ,5"
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• T5+*.& 4& &%& &* 4$%5
• G&%& +,*',+% *'$%&,% &%& &* 4$%5
Figure 1.1
Another evidence of the factors affecting the formation of folds is shown ictorially in fig. 1.2! showi
elastic and lastic deformation rocess as simulated in the la"oratory.
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3!2 Finite element content
Fig. 2.1
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3.3 #ock data
3.$ %iscousity ratio of rocks
fig. 3.$.1 &igh viscousity ratio of rocks affect folding
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Fig. 3.$.2 Low viscousity ratio of rocks result in high folding
$.0 'escri"ing folds
$.1 'escrition of single folded surfaces
A *'11'$ ,,)1%+'$ +, %5% 4&, ,%&% ')% , 4$& $( 5'&+?'$%4 ,%&%! T5+, +, ''( ;'&.+$ ,,)1%+'$
1$ ,%&%! "hen might it not be a good assumption# W ;+44 ,%&% ')% 4'&+$ 5'; %' (,*&+< %5 *5&*%&
,+$4 -'4(( ,)&-*! S)*5 ,)&-* 1+5% < &&,$%( < ,)&-* *'$%')& 1!
cylindrical geometry:
• +(4+?( -'4( ,)&-* %5% *$ < &*'$,%&)*%( < &++( %&$,4%+'$ '- 4+$ %5&')5 ,*! T5% 4+$ +, %5
a(is $ +1'&%$% ,11%& 41$%!
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• vergence -'4( ,11%& &4%( %' '&%+*+% $( +$ ,'1 ,+%)%+'$, %' ,+14 ,5& ,$,! I$*4+$%+'$
+4 %&* %' $4'+$ ,)&-*, short vs. long lim" asymmetry!
$olds in carbonate strata in Montana showing a clear vergence. %iew is northward. &hoto source'
http'((libraryphoto.cr.usgs.gov(cgi)bin(show*picture.cgi#!+!+.-/Mudge,-/M.0.-/123ct .
D,*&+%+'$ **'&(+$ %' ,+? =;'&., ;+%5 '%5& ,%&)*%)&,>!
• microscoic.
• mesoscoic*megascoic.
• macroscoic *'&+$ <'(+, %' 4& '& %'' ''&4 ',( %' < 1+$( (+&*%4 +$ %5+& $%+&%
T)&$& $( W+,,!
• ($($% '$ &,*%+ $( '$ % '- ')%*&',!
• 4%&$%+" thin section scale! hand secimen scale! outcro scale! and ma scale.
D,*&+%+'$ **'&(+$ %' %+5%$,, '& interlim" angle "
• R1, *4,,+-+*%+'$ ),( +$ 4+%&%)&"
o 1+0*120 , gentle.
o 120*-0 , oen.
o -0*30 , closed.
o 30*0 , tight.
o 0 or arallel lim"s * isoclinal!
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• ;5 $'% ),% + +$%&4+1< $4
• ,+$+-+*$* @ +, ,'1 % '- +$-'&1%+'$ <')% (& '- ,%&+$ $( 4& &444 ,5'&%$+$!
D,*&+%+'$ **'&(+$ %' &'-+4 *)&%)&"
• rounded.
• angular.
• chevron.
• cusate.
• conugate fold <' -'4( 1)4%+4 5+$, $( +4 4$,!
• 1%51%+*4 @ ,+$ -)$*%+'$, 5&1'$+*, $( ,)**,,+ &'+1%+'$,! P&'+(, *'14% (,*&+%+'$
$'% ,+4 **,,+<4 $( )+% %+1 *'$,)1+$!
• wavelength amlitude '1%& '- enveloing surfaces!
• 1*5$+*4 ,+$+-+*$* '- <'
&hoto of fold from 4S5S in 6retaceous strata of 6hile. "hat term might you use for the geometery of this fo
D,*&+%+'$ **'&(+$ %' '&+$%%+'$ $( &4%+'$,5+,"
• antiform vs. synform.
• anticline vs. syncline.
• antiformal synclines $( synformal syncline $( + 4 *'$-),+'$!
• (& '- 4)$ $( (& '- +4 4$ +$*4+$%+'$ @ F4)% (+&1!
• '&%)&$( -'4(, %5', ;+%5 $ '&%)&$( 4+1<!
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• monoclines $( structural terrace.
P+*%)& '- $ A$%+*4+$ @ USGS
• A$%+*4+$" 4+$& ,%&% $'&144 (+ ; -&'1 +4 *$%& '4(,% ,%&% +$ *$%&!
• S$*4+$" 4+$& ,%&% $'&144 (+ %';&( +4 *$%& ')$,% ,%&% +$ *$%&!
• A$%+-'&1" 4+$& ,%&% (+ ; -&'1 +4 *$%& )$.$';$ '& +$&%(!
• S$-'&1" 4+$& ,&% (+ %';&( +4 *$%& )$.';$ '& +$&%(!
• D'1" $'$4+$& ,%&% (+ ; -&'1 *$%& +$ 44 (+&*%+'$, '4(,% ,%&% +$ *$%&!
• B,+$" $'$4+$& ,%&% (+ %';&( *$%& +$ 44 (+&*%+'$, ')$,% ,%&% +$ *$%&!
• M'$'*4+$" 4+$& ,%&% (+ +$ '$ (+&*%+'$ <%;$ 5'&+?'$%4 4&, '$ *5 ,+(!
• C5&'$" $)4& -'4( ;+%5 ,%&+5% 4+1<, $( ,144 5+$,
• R*)1<$%" 4+$& -'4( +4 4$ '&+$%( % 4'; $4 &,)4%+$ +$ '&%)&$( ,%&% <4'; %5 -'4(
• S4)1" %+*44 1'$'*4+$4 &,)4% '- (+--&$%+4 *'1*%+'$ '& (+,,'4)%+'$ ()&+$ ,(+1$%%+'$ $(
4+%5+-+*%+'$!
• P%1%+*" F'4(, & *5'%+* &$('1 $( (+,*'$$*%(! T+*4 '- ,(+1$%& ,4)1 -'4(+$ 1+1%+%
(*'441$% (%*51$% ?'$,!
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M'$'*4+$ % C'4'&(' N%+'$4 M'$)1$% A -'4( +$ S4+*5';+* $%)& &,& +$ K+4*
R+$<'; B,+$ S$*4+$ $& B&,%'; C4+-'&$+
$.2 'escrition of mutlile folded surfaces and fold style
• a(ial lane: %5 4+1< <+,*%'& 4$ -'& ,+14 '1%&+,!
• a(ial surface: %5 4$ -'&1( < %5 ,)1 '- 44 %5 -'4( 5+$ 4+$,! B%%& (,*&+%'& %' ), 5, (+,%+$
,+$-+*$*!
•
a(ial trace on surface: %5 4+$ -'&1( < %5 +$%&,*%+'$ '- %5 +4 ,)&-* $( %5 &%5, ,)&-* +!1 %&* '- %5 +4 ,)&-*!
arallel folds "
• 4,' .$';$ , *'$*$%&+* -'4(,!
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• %5+*.$,, &$(+*)4& %' 4& <')$(&+, +, 1+$%+$(!
• /usk reconstruction method @ '$ ; '- &*'$,%&)*%+$ -'4( &'-+4 '1%&+,!
• disharmonic character @ &'-+4 '1%& *5$, 4'$ +4 4$!
similar folds"
• % +, *'$,%$% -'& +$ 4& , 1,)&( &444 %' %5 +4 4$! F'4( 5+$, & %5+*.$( &4%+
%5+$$( 4+1<,!
• 5&1'$+* +(44 (+--&$% 4&, ,5'; %5 ,1 &'-+4 '1%&!
Comosite fold forms are the most common! with some layers retaining layer thickness! and others not.
due to differences in rock cometency.
$olds of chert layers in the marble matri7 of the 8ruce 9limestone9 from the :uronian seuence. ;ote how it is d
to trace for certain the delicately fold layers across the photo. <ne might describe the layering as show incipi
mild transposition. Also doe the brittle behavior evident in the thicker chert layer near the base. See below for f
e7planation.
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Fold transosition:
•
*'1',+%+'$4 4&+$ %5% ;, '&++$44 <((+$ <)% ;5& +$%$, (-'&1%+'$ 5, '<4+%&%(,%&%+&5+* &4%+'$,5+, $( *'$%+$)+%!
• *'11'$ +$ 1&<4, )&%?+%, $( 1+*@ &+*5 1%,(+1$%,!
• &*'$+%+'$ *&+%&+"
o -4'%+$ +,'*4+$4 -'4( 5+$, @ +$%&-'4+4 -'4(,!
o *4 $(/'& -'4+%+'$ &444 %' <((+$!
o %&1 -4%%$+$ '& 4'$%+'$ '- ,%&+$ 1&.&,!
o +,'4%( <')(+$, '& '(, '- 1'& *'1%$% 1%&+4!
o (& -'4(, '- '',+% &$* +$ *4', &'+1+%!
o &&,4, '- ')$+$ *&+%&+ +$ ,5'&% (+,%$*!
o 4&, (+,*'$%+$)'), , ') %&* %51!
!f you e7amine the detailed version of this photograph from the ;" coast of !reland, you can see that the a7ial t
of an earlier fold phase =some shown with red dots> are folded around a later phase fold with its appro7imate a7
trace shown with yellow dots. These are +alradian marbles that have seen comple7 polphase deformation includ
major 6aledonian phase.
olyhase deformation and fold interference atterns!
• !! *&',, -'4(+$ $( ('1, $( <,+$, $( ,((4," *% '1%& -)$*%+'$ '- ;4$%5 $( 14+
'- %;' -'4( 5,,!
• *'+4 -'4(+$ @ '%$%+44 &% '- '$ 5, , *'$%+$))1! R'%%+'$ ,),%, ,+$+-+*$% ,+14 ,5
*'1'$$% %' %5 (-'&1%+'$ 5+,%'&!
• $'$*'+4 -'4(+$ @ +$-+$+% ',,+<+4+%+,!
• ,5%5 -'4(,"
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o 5'; %' (%*%
o +&(4 %%&$ '- -'4( , '$ ,%&'$% =-'4(+$ '- $ &4+& 4+$>! G&% *+&*4 +, ,5& 4$! A,,
;+%5 ,+$+-+*$% $'$@4$& ,%&+$!
• 14 +$ D4&(+$ &'*., '- NW I&4$(!
.0 FL' CLA4F4CA45
F'4(, *$ < *4,,+-+( < %5+& ,+? -'4( ,5 %+5%$,, (+ '- %5 +4 4$!
2' fold terms
L''.+$ % -'4( ,)&-* +$ &'-+4 %5 -'4( *$ < (++(( +$%' 5+$ '&%+'$ $( %5 4+1<,! T5 4+1<, & %5
'- %5 -'4( $( %5 5+$ +, ;5& %5 -4$., '+$ %'%5&! T5 5+$ '+$% +, %5 '+$% '- 1+$+1)1 &(+), '- *)&-'& -'4(! T5 *&,% '- %5 -'4( +, %5 5+5,% '+$% '- %5 -'4( ,)&-* $( %5 %&')5 +, %5 4';,% '+$%! T5 +$-
'+$% '- -'4( +, %5 '+$% '$ 4+1< % ;5+*5 %5 *'$*+% &&,, '$ &)4& -'4(, %5+, +, %5 1+(@'+$% '- %5
3' fold terms
T5 5+$ '+$%, 4'$ $ $%+& -'4(( ,)&-* -'&1 5+$ 4+$! T5 %&$( $( 4)$ '- 4+$& 5+$ 4+$ +
+$-'&1%+'$ <')% %5 '&+$%%+'$ '- %5 -'4(! T' *'14%4 (,*&+< %5 '&+$%%+'$ '- -'4( '$ 1),% ), %5
,)&-*! T5 +4 ,)&-* +, %5 ,)&-* (-+$( < *'$$*%+$ 44 %5 5+$ 4+$, '- ,%*.( -'4(+$ ,)&-*,! I- %+4 ,)&-* +, 4$& ,)&-* %5$ +% +, *44( %5 +4 4$ $( *$ < (,*&+<( < %5 ,%&+. $( (+ '- %5
T5 +4 %&* +, %5 4+$ '- +$%&,*%+'$ '- %5 +4 ,)&-* ;+%5 $ '%5& ,)&-* =&')$( ,+( '- 1')$%+$
'4'+*4 *&',,@,*%+'$>! F+$44 -'4(, *$ 5 <)% ('$% $*,,&+4 5 -'4( +,! A -'4( +, J+, %5 *4',
&'+1%+'$ %' ,%&+5% 4+$ %5% ;5$ 1'( &444 %' +%,4- $&%, %5 -'&1 '- %5 -'4(! =D+, $(
R$'4(, 6 -%& D'$%5 $( P&.& 69 R1, 67>! A -'4( %5% *$ < $&%( < -'4( +, +, *4
*4+$(&+*4 -'4(! T5+, %&1 5, <$ <&'($( %' +$*4)( $&@*4+$(&+*4 -'4(,!
.1 6inematic analysis of folds in cross section
B,+* ,,)1%+'$, -'& ,+14 $4,+,"
• '&%5''$4 *&',,@,*%+'$!
• $' ')% '- %5 4$ =*&',, ,*%+'$ 4$> 1'1$%, =4$ ,%&+$>!
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• &444 -'4( '1%& 54,!
• '&++$4 '1%& 1),% < -+&4 ;44 *'$,%&+$(
S544'; *&),%4 44 -'4( $( %5&),% <4%, '-%$ 1% %5, &)+&1$%,!
S+$)'), <( 1%5'("
• 1')$% '- ,5'&%$+$ '&++$4 4$%5 @ &,$% 1 ;+(%5!
• &*$% '- ,5'&%$+$ @ &,$% 4$%5/'&++$4 4$%5!
• ''( +( %' (' ,&4 5'&+?'$, % (+--&$% ,%&%+&5+* 44, +$ *&',, ,*%+'$!
E)4 & 1%5'("
• *$ %. +$%' **')$% )$+% +$%&$4 (-'&1%+'$!
• $( '&++$4 ,%&%+&5+* %5+*.$,,!
• &,$% & / '&++$4 ,%&%! %5+*.$,, '&++$4 4$%5 %5$ ,%+*. +$%' <'!
• *4*)4%+'$ %' (%5 '- <,4 (*'441$% =, '&5(> % A / =4 @ 4*>!
T+*4 1')$%, '- ,5'&%$+$ +$ -'4(@$(@%5&),% <4%, 0, %' 00, '- .1!
.2 Fold shae
I% +, $*,,& %' *'$ ,$, '- %5 ,5 '- %5 -'4(! A -'4( *$ < ,5( , *5&'$ ;+%5 4$& 4+1<, 1
% $ $)4& +, , *),% ;+%5 *)&( 4+1<, , *+&*)4& ;+%5 *)&( +, '& , 44+%+*4 ;+%5 )$)4 ;
.3 Fold tightness
F'4( %+5%$,, +, (-+$( < %5 $4 <%;$ %5 -'4(, 4+1<, *44( %5 +$%&4+1< $4! G$%4 -'4(, 5 $
+$%&4+1< $4 '- <%;$ 70 $( 80 '$ -'4(, &$ -&'1 70 %' 0 %+5% -'4(, -&'1 0 %' 0 $( +
-'4(, 5 $ +$%&4+1< $4 '- <%;$ 0 $( ?&' ;+%5 ,,$%+44 &444 4+1<,!
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.$ Fold symmetry
N'% 44 -'4(, & )4 '$ <'%5 ,+(, '- %5 +, '- %5 -'4(! T5', ;+%5 4+1<, '- &4%+4 )4 4$%5 & %&1
,11%&+*4 $( %5', ;+%5 5+54 )$)4 4+1<, ,11%&+*4! A,11%&+*4 -'4(, ;+44 $&44 5 $ +,
+, % $ $4 %' %5 '&++$4 )$-'4(( ,)&-* ;5+*5 %5 -'&1( )'$!
. 'eformation style classes
F'4(, ;5+*5 1+$%+$ )$+-'&1 4& %5+*.$,, & *4,,( , *'$*$%&+* -'4(, %5', ;5+*5 (' $'% & *44( ,+1+
-'4(,! S+1+4& -'4(, %$( %' (+,4 %5+$$+$ '- %5 4+1<, $( %5+*.$+$ '- %5 5+$ ?'$! C'$*$%&+* -'4(, & *
< ;&+$ ;5+*5 &,)4%, -&'1 (-'&1%+'$ '- %5 4&, ;5&, ,+1+4& -'4(, ),)44 -'&1 < ,'1 -'&1 '-
(+,4'*%+'$ <%;$ %5 4&, =,4+(+$> ;+%5 %$,+'$ $( *'$%&*%+'$ '- %5 %5+*.$,, '- &'*. 4&, (+--&$%4
4+1< $( 5+$ ?'$,!
7.0 Fold tyes
! N)%&4 ,)&-* -'4(+$" F'4(( 4& *'$%+$, '$4 '$ 4$ ;+%5 $' +$%&$4 (-'&1%+'$ %5 $)%&4 ,)&-*
2! S5& -'4(" #ocks are sheared unevenly like a deck of cards.
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JT5 &+<4 11 S5&
F)4% &'%+'$ -'4(," 4,' *44( %&+,5& -'4(, *'&( < -)4% ;5', %+ &'%, +$%' %5 '&4+$ -'4( ;
%+1! Q)$%+%%+ 1'(4, < A441$(+$& ,5';+$ %&+,5& -'4( '4)%+'$!
,4+ '$ (+,*&% -)4% <*'1, (+,%&+<)%( %' ,4+ '$ <((+$ $( ,144& ,*4 -)4%,!
+iagram from 4S5S site ) ) showing development of fault propagation fold. Such folds can be important in seis
risk assessment, because the fold reflects a hidden earthuake generating fault hidden at depth.
Folding mechanisms
F'4(+$ '- &'*., 1),% <4$* %5 (-'&1%+'$ '- 4&, ;+%5 %5 *'$,&%+'$ '- '4)1 +$ &'*. 1,,! T5+, '*
< ,&4 1*5$+,1,!
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E14 '- 4&@,*4 *&$)4%+'$ G4$&& B,+$ W!A! $ 14 '- *5&'$@% -4)&4@,4+ -'4(,!
Fle(ural sli
F4)&4 ,4+ 44';, -'4(+$ < *&%+$ 4&@&444 ,4+ <%;$ %5 4&, '- %5 -'4(( ,%&% ;5+*5
4%'%5& &,)4% +$ (-'&1%+'$! T5 <,% $4' +, <$(+$ 5'$ <''. ;5& '4)1 &,&%+'$
**'11'(%( < ,4+ <%;$ %5 , '- %5 <''.! L&, ,4+ ,% '$ $'%5& ()&+$ -'4(+$! G$&
-'&1, &444 -'4(, '& *5&'$ -'4(,
S%+44 &)+&, (-'&1%+'$ +$ %5 5+$ ?'$, '- +$(++()4 4&,
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#eferences
• D+, G'& H! R$'4(, S%5$ #! =6>! F'4(,! Structural 5eology of 0ocks and 0egions! N;
#'5$ W+4 S'$,! ! 372929! ISBN 0@97@:262@:.
• D'$%5 F!A! $( P&.& R!B! 69 F'4(, $( F'4(+$" G'4'+*4 S'*+% '- A1&+* B)44%+$ ! 7:
62
• G'5,+*4 R,&*5 A<,%&*%, V'4! 8 0268 2006 SR-@ID" 607@762/&/EGU06@A@0268 E)&
G',*+$*, U$+'$ 2006
• http'((usgs.gov(research(deformation(fold mechanics(papers(scientam(scientam.html
• http'((libraryphoto.cr.usgs.gov(cgi)bin(show*picture.cg
• M*K$+5% T'1 L H,, D&&4 =2000>! T5 I$%&$4 P&'*,,," F'4(+$! &hysical 5eography' A ?and
Appreciation! U& S((4 R+& N#" P&$%+* H44! ! 909! ISBN 0@3@020263@0. • R1, #!G! 67 F'4(+$ $( -&*%)&+$ '- &'*.," M*G&;@H+44 B''. C'1$ N; Y'&. :60!