The hydrologic control on shallow landslide triggering: empirical and monte carlo pysically-based approaches

THE HYDROLOGIC CONTROL ON SHALLOW

LANDSLIDE TRIGGERING: EMPIRICAL AND

MONTE CARLO PYSICALLY-BASED

APPROACHES

Ph.D. Dissertation

THE HYDROLOGIC CONTROL ON

SHALLOW LANDSLIDE

TRIGGERING: EMPIRICAL AND

MONTE CARLO PYSICALLY-BASED

APPROACHES

David Johnny PERES

Tutor:

Prof. Ing. Antonino CANCELLIERE

Coordinatore del Dottorato:

Prof. Ing. Salvatore Damiano CAFISO

Catania, Dicembre 2012

UNIVERSITÀ DI CATANIA

Dipartimento di Ingegneria Civile e Ambientale

DOTTORATO DI RICERCA IN INGEGNERIA DELLE

INFRASTRUTTURE IDRAULICHE, SANITARIO-AMBIENTALI

E DEI TRASPORTI

XXV Ciclo

Tesi per il conseguimento del titolo

UNIVERSITÀ DI MESSINA Dipartimento di Ingegneria Civile

COMMISSIONE EUROPEA FONDO SOCIALE EUROPEO

Is this the real life?

Is this just fantasy?

Caught in a landslide

No escape from reality

!"#$"#% &''

!"#$"#%

()*+,-.+ / / 01+,234.+'21 5 ! "#$%#&$' ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ( !) *&+ ,- ./$ %$0$1%2/ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3 !4 5$0$1%2/ +$./,6,7,89 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! : !; "<.7&=$ ,- ./$ 6&00$%.1.&,= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! > 6 7-13*8'39 +,'::9,'1: ); ,-'1<-88 // )! ?1=607&6$ @/$=,+$=1 1=6 %&0A +&.&81.&,= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! )!) B+@&%&217 1@@%,12/$0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ; )!4 C/90&21779DE10$6 +,6$70 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3 = $>?','.-8 ,-'1<-88 +@,9*@283* <2, +@9 A982,'+-1' B241+-'1* -,9-C 0+-8; 65 4! C%$7&+1%9 %$+1%A0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! )( 4!) F/$ C$7,%&.1=& G,<=.1&=0 210$ 0.<69 1%$1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! )( 4!4 *@@7&21.&,= ,- H?1I5 +,6$7 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! )> 4!4! G$./,6 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! )> 4!4!) J1.1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4) 4!4!4 5$0<7.0 1=6 6&02<00&,= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4) 4!; G$./,6 E10$6 ,= 1==<17 +1K&+1 %1&=-177 61.1 ! ! ! ! ! ! ! ! ! ! ! ! ! 4; 4!;! G$./,6 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4; 4!;!) J1.1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4( 4!;!4 5$0<7.0 1=6 6&02<00&,= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4: 4!( L,=27<0&#$ %$+1%A0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4M D B21+9 -,82 ?@;*'.-88;E)-*93 *'>48-+'21 >9+@23282:; D/ ;! C%$7&+&=1%9 %$+1%A0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ; ;!) N&+<71.&,= 02/$+$ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;) ;!4 I6$=.&O21.&,= ,- %1&=-177 $#$=.0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;) ;!; G$./,6,7,89 ,- 1=1790&0 ,- 0&+<71.&,= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;; ;!;! 5$.<%= @$%&,6 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ;( ;!;!) 51&=-177D?1=607&6$ ,22<%%$=2$ %$71.&,=0/&@ ! ! ! ! ! ! ! ! ! ! ! ;(

!!! "#$%&$%' !" #$%&'()* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ( $)*+,-.'/011 2)/1,-345,6 7458)8 6,!-9,55 +0:)5 ;< "!, -)*./0/1()2 )*0()34 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 5 "!6 -)$7*44 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "8 "!9 -)$:*)&/*4 $% &;* <#=- :)$7*44 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "9 "! >(./?)(&/$1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! " = >,-:85!:) 16!33)6!-3 ?@*8!/,55*.A,8): +0:)5!-3 (B +!, @;* @=AB=# 0$C*. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "D +!,!, EF*)F/*' ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "D +!,!6 B$F*)1/1G *HI(&/$14 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "5 +!,!9 J14(&I)(&*C K$1* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "5 +!,! #(&I)(&*C K$1* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! +, +!,!" A1L.&)(&/$1M =I1$NM (1C O.$' =$I&/1G ! ! ! ! ! ! ! ! ! ! ! ! ! +9 +!,!+ #.$:* 4&(?/./&2 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! +9 +!6 A1&*G)(&/$1 $% @=AB=# '/&; ( '(&*) &(?.* )*7*44/$1 0$C*. ! ! ! ! ! ! + +!9 P$C*. :*)%$)0(17* (44*440*1& ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + B C??5!/,1!0- 10 >0/0 /,1/@+)-1 !- 1@) 7)506!1,-! D04-1,!-8E F1,5* =B D!, -)*./0/1()2 )*0()34 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! +D D!6 >(./?)(&/$1 (1C F(./C(&/$1 $% &;* <#=- )(/1%(.. 0$C*. ! ! ! ! ! ! ! ! +Q D!6!, R1(.24/4 $% O/I0*C/1/4/ )(/1%(.. C(&( ! ! ! ! ! ! ! ! ! ! ! ! ! ! +Q D!6!6 P$C*. >(./?)(&/$1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! D8 D!6!9 P$C*. F(./C(&/$1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! D" D!9 R::./7(&/$1 $% &;* :;24/7(..2S?(4*C 0$C*. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! D5 D!9!, T(&( (1C :)*./0/1()2 (1(.24*4 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! D5 D!9!6 =*4I.&4 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Q9 D! R::./7(&/$14 $% &;* P$1&* >().$ :;24/7(..2S?(4*C (::)$(7; ! ! ! ! ! 58 D! !, =*&I)1 :*)/$C *4&/0(&/$1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 58 D! !6 A1&*14/&2STI)(&/$1 0$C*. *F(.I(&/$1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! 56 G "0-/548!0-8 HIH >!81 09 J!346)8 HH< >!81 09 %,A5)8 HH< 2)9)6)-/)8 HH<

!"#$%&#

!"#$$%& '#()*$+ ,%-)./ $#.*0$)*102 3')//1'1* 4+ '#).5#$$ ).6$3'#3)%.2 7#801 ,#.+ 5#3#$)3)10 #.* ,87" *103'873)%. &%'$*&)*19 :.*1'03#.*)./ 3"1 "+*'%$%/)7#$ 7%.3'%$ %. 0"#$$%& $#.*0$)*1 3')//1')./2 )0 58.; *#,1.3#$ ). $#.*0$)*1 ')0< ,)3)/#3)%.2 #3 $1#03 5%' 3&% '1#0%.09 ="1 6'03 '1#0%. )0 3"#3 $#.*0$)*1 1#'$+ &#'.)./ 0+031,0 '1>8)'1 ).5%',#3)%. %. 3"1 $).< 413&11. '#).5#$$ #.* $#.*0$)*1 %778''1.719 ="1 017%.* '1#0%. )0 3"#3 <.%&$; 1*/1 %5 3"1 "+*'%$%/)7 7%.*)3)%.0 3"#3 3')//1' $#.*0$)*10 ). # 0(#3)#$$+;*)03')4831* 5#0")%. #$$%&0 3% ,#( '138'. (1')%* %5 $#.*0$)*1 3')//1')./ &)3"). # $#.*0$)*1;('%.1 '1/)%.9 =")0 )0 %.1 %5 3"1 58.*#,1.3#$ 031(0 5%' ('%*873)%. %5 "#?#'* #.* ')0< ,#(0 3"#3 ,#+ 41 1@173)-1$+ 801* #0 #. #)* 5%' 8'4#. #.* $#.*0$)*1 ,)3)/#3)%. ($#..)./9 A. 3"1 *)001'3#3)%.2 # B%.31 C#'$% #(('%#7"2 3"#3 7%,4).10 03%7"#03)7 #.* *131',).)03)7 ,%*1$)./ #(('%#7"102 )0 801* 3% #.#$+?1 3"1 "+*'%$%/)7#$ 7%.3'%$ %. 0"#$$%& $#.*0$)*1 3')//1')./9 A. (#'3)78$#' #. ).31/'#31* 03%7"#03)7 '#).5#$$ #.* *131',).)03)7 $#.*0$)*1 0),8; $#3%' "#0 411. *1-1$%(1* 5%' 3"1 (8'(%019 ="1 0),8$#3%' )0 7%,(%01* 4+ 3"1 5%$$%&)./ 7%,(%.1.30D E)F # 01#0%.#$ G1+,#.; !7%33 H173#./8$#' I8$010 EGH!IF ,%*1$ 3% /1.1'#31 0+.3"13)7 "%8'$+ (%).3 '#).5#$$ *#3#J E))F # ,%*8$1 5%' '#).5#$$ 1-1.3 )*1.3)67#3)%. #.* 01(#'#3)%. 5'%, *'+ ).31'-#$0J E)))F 3"1 ='#.0)1.3 H#).5#$$ A.6$3'#3)%. #.* K')*;L#01* H1/)%.#$ !$%(1;!3#4)$)3+ E=HAKH!F ,%*1$2 -1'0)%. M EL#8, 13 #$92 MNNO2 MN NF 3% 0),8$#31 $#.*0$)*1 3')/; /1')./ 4+ '#).5#$$ ).6$3'#3)%.2 7%,4).1* &)3" # &#31' 3#4$1 '17100)%. EP=HF ,%*1$ 3"#3 7%,(8310 3"1 ).)3)#$ &#31' 3#4$1 "1)/"3 3% 7%.0)*1' ). 0),8$#3)./ '#).5#$$ 1-1.30 &)3" =HAKH!9

="1 B%.31 C#'$% 0),8$#3%' "#0 411. #(($)1* 3% 3"1 Q%7% 7#37",1.3 ). 3"1 I1$%')3#.) B%8.3#).0 ). .%'3"1#031'. !)7)$+ %5 A3#$+2 #. #'1# &)3" ")/" $#.*0$)*1 ')0<2 #0 '171.3$+ *1,%.03'#31* 4+ 3"1 '1/)%.#$ *14')0;R%& 1-1.3 3"#3 %778''1* %. 03S73%41' MNNT2 &")7" 7#801* UV 7#08#$3)10 #.* ,)$$)%.0 %5 18'%0 %5 *#,#/19 ="1 GH!I ,%*1$ '108$31* 7#(#4$1 %5 7#(38')./ 3"1 ,%03 ),(%'3#.3 #.* ,#.+ %3"1' 03%7"#03)7 51#38'10 %5 '#).5#$$ %401'-1* .1#'4+ 3"1 038*+ 7#01 #'1#J ,%*1$ -#$)*#3)%.2 7#'')1* %83 4+ 3103)./ 3"1 '1('%*873)%. %5 '#).5#$$ 1-1.3 7"#'#731')03)70 ),(%'3#.3 &)3" '10(173 3% $#.*0$)*1 3')//1')./ 087" #0 1-1.3 ).31.0)3+ #.* *8'#3)%.2 "#0 /)-1. 0#3)05#73%'+ '108$309 !8)3#4)$)3+ 5%' ,%*1$)./ 3"1 3')//1')./ %5 $#.*0$)*10 ). 3"1 ).-103)/#31* #'1# %5 3"1 =HAKH! ; P=H ,%*1$ "#0 411. 31031* 4+ #(($+)./ )3 3% 3"1 3"'11;1-1.3

!"#$%&'$

!"#!$%! &'(& )*+,+-!. /($. /0.! +$ 1 &2%&+3!* 45567 8+.!/ )!*9+*:($%! '( 3!!$ ( ! !. 3; %+:)(*0$< :())!. /0.! 9+* &'! 1 &2%&+3!* 4556 !,!$& =0&' :+.!/ +#&)#&> (/ + 0$ &!*: +9 ?2@A3( !. B?!%!0,!* 2)!*(&0$< @'(*(%&!*0 &0%C 0$.0%! 7 8+.!/ )!*9+*: (& /!( & ( =!// ( +&'!* -$+=$ ())/0%(&0+$ +9 &'! D?EF?G :+.!/ &+ +&'!* &#.; %( ! (*!( B?2@A(%%#*(%; ($. )*!%0 0+$ (*! *! )!%&0,!/; <*!(&!* &'($ 57H5 ($. 57I5C7

D'! 8+$&! @(*/+ ())*+(%' '( 3!!$ ())/0!. 9+* ! &0:(&0+$ +9 *!&#*$ )!*0+. +9 '(//+= /($. /0.! &*0<<!*0$< ($. 9+* &'! !,(/#(&0+$ +9 &'! :+ & %+::+$/;A# !. &;)! +9 !:)0*0%(/ *(0$9(// &'*! '+/.7

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

8+$&! @(*/+ 0:#/(&0+$ '(,! (//+=!. &+ :() *!&#*$ )!*0+. +9 /($. /0.! &*0<A <!*0$< B07!7 ( 9(%&+* +9 (9!&; F S ď 1C +$ &'! %( !A &#.; %(&%':!$&7

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

D'! +3&(0$!. *! #/& (//+= &+ &(&! &'(&> (%&#(//;> &+%'( &0% &*#%&#*! +9 *!(/ *(0$9(// !,!$& %+:30$!. =0&' &'! 0$N/&*(&0+$ *! )+$ ! *!,!(/ 0$ ( %!*&(0$ !$ ! ( &'!+*!&0%(/ Q# &0N%(&0+$ &+ &'! E A K *!/(&0+$ '0)7 E +A)+*!A)*! #*! )+0$& > 0$ &'! 30A/+<(*0&':0% *(0$9(// B:!($C E$&!$ 0&; A K#*(&0+$ )/($!> /(;> =0&' *!/(&0,!/; /+= %(&&!*0$<> (*+#$. ( &*(0<'& /0$!> 0$ &'! %( ! &'(& 0$0&0(/ =(&!* &(3/! '!0<'& 0 $!</0<03/!7

D'0 :!($ &'(& &'! IAD :+.!/ *!)*! !$& ( ,(/0. :+.!/ &+ 0$&!*)*!& .(&( 0$ &'! %( ! &'(& :!:+*; +9 )+*! )*! #*! 0 $!</0<03/!7 D'0 '+/. &*#! 3( 0%(//; ='!$ &'! ';.*(#/0% %+$.#%&0,0&; +9 &'! +0/ 0 *!/(&0,!/; '0<'> 0$ *!/(&0+$ &+ *(0$A 9(// %'(*(%&!*0 &0% B*!/(&0,!/; 0 +/(&!. *(0$9(// !,!$& C ($. '0// /+)! )+ 0&0+$ 0$ &'! %(&%':!$& B/+= ,(/#! +9 #) /+)! %+$&*03#&0$< (*!(C7

!"#$!%% &'()%*

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ă 12 ,= ! )!% 3! "!6%)."#2)#-"29 ,9)2'8 !/, &!9 / '(01) ! /' )./ )--0 ) )-/'#-) %)-- 2,!# 2,) '#) "#(01)( 69 ! )12!#80%! ,9)2'8 !/, '$ 2,) -!&) :&)!#; "#2)#-"29 !#( (0 !2"'#= 7,"%) 2,) '//'-"2) '110 - $' ,"8, (0 !2"'#-* ? '& 2,) 1'&/! "-'# )%!2"3) 2' 2,) %!22) 1!-)= "2 1!# 6) -2!2)( 2,!2 "# ()/)#()#1) '$ 2,) "#"2"!% 7!2) 2!6%) ()/2, :"*)* !"#$!%% 2"&) ,"-2' 9 / )1)("#8 2,) )3)#2; )3)# !"#$!%% )3)#2- '$ %'7 "#2)#-"29 !#( (0 !2"'# &!9 2 "88) %!#(-%"()-*

!"#$%& '

!"#$%&'"($!

! "#$%#&$'

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

!"#$%&'(#)%"

!"#$ %"&'() *+( ,!-. /0$(123"-($ %"&'( 45"66(..0 (. 71)8 9::;< 7--",(- .+( =!&, I_{“ αD}β_{8 /+(&( D 0- &70#=711 $"&7.0!# 4,(7-"&($ =&!, .+( (>0##0#> != .+( ('(#.}

.! .+( 0#-.7#. != 0#%0?0(#. -1!?( =701"&(< 7#$ I “ H{D 0- ,(7# &70#=711 0#.(#-0.2 4H 0- %","17.0'( &70#=711 ! -(&'($ !# .0,( 0#.(&'71 D<)

@# .+( -(%!#$ %7-(8 17#$-10$( !%%"&&(#%( 0- 0#'(-.0>7.($ 2 ,(7#- != (A"7.0!#-7..(,?.0#> .! ?+2-0%7112 $(-%&0 ( .+( ?&!%(--(- >!'(&#0#> -1!?( =701"&( 4@'(&-!#8 9:::<) B(#%( .+(2 7&( %!,?!-($ 2 7# +2$&!1!>0%71 ,!$(1 != "#-7."&7.($ 7#$ -7."&7.($ >&!"#$/7.(& C!/8 %!"?1($ /0.+ 7 >(!,(%+7#0%71 -1!?(3=701"&( ,!$(1) *! .+0- (#$8 =&(A"(#.12 0#D#0.( -1!?( -.7 010.2 7#712-0- 0- 7??10($) *+(-( ,!$(1- 7&( "-"7112 7??10($ 0# 7 -?7.071123$0-.&0 ".($ =7-+0!# 7. 7# 7&(7 .+7. ,72 +7'( .+( (E.(#-0!# != !#( !& ,!&( $&70#7>( 7-0#-)

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

!" #$% &' ()* +*,*-+.)

*+( 70, != .+( $0--(&.7.0!# 0- .! %!#.&0 ".( .! 7# 0,?&!'($ "#$(&-.7#$0#> != .+( +2$&!1!>0% %!#.&!1 !# -+711!/ 17#$-10$(-)

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

• .! 0#'(-.0>7.( .+( 10#I (./((# &70#=711 ('(#. %+7&7%.(&0-.0%- 7#$ 17#$-10$( !%3 %"&&(#%( 0# !&$(& .! ?&!'0$( 0#-0>+.- =!& .+( $('(1!?,(#. != &70#=711 .+&(-+!1$-=!& 17#$-10$( .&0>>(&0#>N

!" #$%$&'() *$+),-,.,/0 1

• ! "!#$%&' (' ')'" !* +#' ,%&+%-+.+ / !* $&'"+$+ % +!0 !0 .%012.+1' &+33'&+03 $! '0 +%. 4+ ( (% +015"'1 -/ &'" %035.%& (/' !3&%$(2 6"!02 %0 +0 '02+ /78 • ! '2 +#% ' &' 5&0 $'&+!1 !* .%012.+1' !""5&&'0"'2 (52 $&!,+1+03 % !!. *!&

.%012.+1' &+29 #%$$+03:

;(' 1+&'" .+09 -' 4''0 &%+0*%.. ','0 "(%&%" '&+2 +"2 %01 .%012.+1' !""5&&'0"' (%2 -''0 +0,'2 +3% '1 -/ 2','&%. &'2'%&"('&2 52+03 (' <0 '02+ /=>5&% +!0 #!1'. I_{“ αD}β _{'?5% +!0 ! +0 '&$&' 2+#5. %0'!52 !-2'&,% +!02 !* &%+0*%.. %01 .%012.+1'2}

%01 1' '&#+0' '#$+&+"%. &%+0*%.. (&'2(!.12 !* .%012.+1' &+33'&+03:

<0 2$+ ' !* + 2 "!02!.+1% '1 52'@ 0! $%& +"5.%& ('!&' +"%. A52 +B"% +!0 *!& (' 52' !* (% '?5% +!0 'C+2 2 6D5EE' + ' %.:@ FGGH7: ;(52@ (' %+# !* (' 1+22'& % +!0 !0 (+2 +225' +2 ! ',%.5% ' *&!# % ('!&' +"%. $'&2$'" +,' '#$+&+"%. #!1'.2@ +:': ! 501'&2 %01 +* (' 2 !"(%2 +" 0% 5&' !* &%+0*%.. "!#-+0'1 4+ ( (' $(/2+"%. $&!"'22'2 !* 2!+.=4% '& #!,+#'0 $&!,+1'@ +0 % "'& %+0 #'%25&'@ % ('!&' +"%. A52 +B"% +!0 ! (' #!2 4+1'./ 52'1 '#$+&+"%. #!1'.2@ 25"( %2 (' I=D #!1'.:

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

!" #$%$&'() *$+),-,.,/0

;(' T!0 ' U%&.! 2+#5.% +!0 '"(0+?5' 1','.!$'1 +0 (+2 1+22'& % +!0 +2 -%2'1 !0 (' "!#-+0% +!0 !* % 2 !"(%2 +" &%+0*%.. #!1'. 4+ ( % 2$% +%../=1+2 &+-5 '1 $(/2+"%../= -%2'1 (/1&!.!3+"%. #!1'.:

<0 $%& +"5.%&@ (' V'/#%0=R"! J'" %035.%& W5.2'2 6VRJW7 #!1'. +2 5 +.+E'1 ! 3'0'&% ' (!5&./ &%+0*%.. % % $!+0 : VRJW #!1'. +2 "(!2'0 -'"%52' + &'$&'2'0 2 % "!#$&!#+2' -' 4''0 X'C+-+.+ / %01 "!#$.'C+ / 6!0./ B,' $%&%#' '&2 $'& 2'%2!07 %01 05#'&!52 %$$.+"% +!02 "!&&!-!&% ' + 2 ,%.+1+ / 6"*:@ ':3: J!1&+35'E=< 5&-' ' %.:@ NOSH-8 U!4$'& 4%+ ' %.:@ NOOQ8 U%.'01% %01 V%$!.+ %0!@ NOOO7:

;(' ;&%02+'0 J%+0*%.. <0B. &% +!0 %01 D&+1=Y%2'1 J'3+!0%. R.!$'=R %-+.+ / #!1'. 6;J<DJR7@ ,'&2+!0 F 6Y%5# ' %.:@ FGGS@ FGNG7@ 1','.!$'1 -/ % &'2'%&"( 3&!5$ !* (' Z0+ '1 R % '2 D'.!3+"%. R5&,'/@ +2 5 +.+E'1 *!& (' 2$% +%../=1+2 &+-5 '1 $(/2+"%../=-%2'1 (/1&!.!3+"%. #!1'.: ;(' 502% 5&% '1 ,'&2+!0 !* (' #!1'. +2 "!0= 2+1'&'1@ 4(+"( 2!.,'2 (' N=> 6,'& +"%.7 J+"(%&12L '?5% +!0 $%& +"5.%&+E'1 *!& (' 'C$!0'0 +%. R!+. [% '& J' '0 +!0 U5&,' $&!$!2'1 -/ D%&10'& 6NOPS7: ;(+2 *!&#5= .% +!0 +2 "(!2'0 *!& + 2 "!#$5 % +!0%. '\"+'0"/@ -'+03 %0%./ +"%. 2!.5 +!02 %,%+.%-.' *!& (+2 "%2'@ %* '& R&+,%2 %,% %01 ]'( 6NOON7:

!"#$%&'(#)%"

! "#$%#& '!!()*! +*,-./'0 .120-,'-.314 .- .! '1 event ´ based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“ 1 7,3+.5* 0'15!0.5* -,.GG*,.1G .1!-'1-!4 -9'- ',* (!*5 -3 /3)7(-* ,'.1;'00 Y('1-.-.*!4 !(/9 '! )*'1 .1-*1!.-: I '15 5(,'-.31 D4 '15 -3 .1+*!-.G'-* 31 -9* 5.,*/- ,*0'-.31 3; -93!* Y('1-.-.*! @.-9 0'15!0.5* -,.GG*,.1G> "9.! '003@! -3 *+'0('-*4 ;,3) ' !-3/9'!-./ 79:!./'00:F6'!*5 7*,!7*/-.+*4 -9* @.5*0:F(!*5 I´ D *)7.,./'0 )35*0>

!" #$%&'() *+ %,) -'..)/%0%'*(

"9.! 5.!!*,-'-.31 .! 5.+.5*5 .1 *.G9- /9'7-*,! .1/0(5.1G -9* 7,*!*1- .1-,35(/-.31> $1 /9'7-*, C 0.-*,'-(,* 31 0'15!0.5* -,.GG*,.1G 6: ,'.1;'00 .! ,*+.*@*5> L9'7-*, V 7,*!*1-! -9* '770./'-.31 3; *)7.,./'0 )35*0! ;3, 5*-*,).1'-.31 3; ,'.1;'00 -9,*!9305! ;3, 0'15!0.5* *',0: @',1.1G4 @.-9 ,*;*,*1/* -3 -9* P*03,.-'1. K3(1-'.1! ',*'4 .1 13,-9*'!-*,1 &./.0:> $1 7',-./(0',4 -9* NO'$# )35*0 <&.,'1G*03

!" #$%&'() *+ %,) -'..)/%0%'*( 1

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

7! '3 .2$% G 23$ H1!2$ E %01 &/-50 2/1! -$231"101=8 /& /005&2% 2$" /! "$2 /0: E3 .2$% I /005&2% 2$& 23$ "1.2$" &21'3 &2/' J$8- !<K'122 L$'2 !=50 % D50&$& .1/!2 % /!4 00 -1"$0:

E3 .2$% M "$&'%/9$& 23$ .38&/' 008 9 &$" -1"$0: 7! 23/& '3 .2$% 23$ >L7NLK 6:+ -1"$0 /& &5-- %/O$" 2 '$%2 /! 0$6$0 14 "$2 /0( 952 23/& "$&'%/.2/1! ' !!12 '$%2 /!08 &59&2/252$ %$ "/!= 14 23$ - !5 0 14 23$ .%1=% - CP 5- $2 0:( +FFQ, !" 23$ %$0 2$" A15%! 0 %2/'0$ CP 5- $2 0:( +F)F,:

7! '3 .2$% R ..0/' 2/1!& ' %%/$" 152 ?/23 %$4$%$!'$ 21 23$ S1'1 ' &$<&25"8 ' 2'3-$!2 %$ /005&2% 2$":

!"#$%& '

!"#$%&#' ()&**')&"* +, )!&"-!%%

!" #$%&'()&* +,*%-.*%$ $%& /)'0 .)1)2$1)-%

!"#$%&#'$ (!)$' ! %*+ *, #!-!.' !"# #'!+/$ &" -!"0 (*)"+1&'$2 3*1%#4&#'5 %!"#$%&#'$ *(()1 !"# (!)$' +/*)$!"#$ *, (!$)!%+&'$ !"# 6&%%&*"$ &" -*"'+!10 %*$$'$ !"")!%%0 78&./%!"# !"# 9*61*4$:05 ;<<=>2 9'&". 6*+/ 1'%!+'# +* &"+'"$' *1 ?1*@ %*".'# ?1'(&?&+!+&*"5 %!"#$%&#&". !"# A**#&". !1' (%*$'%0 !%%&'#5 !"# &+ &$ (*"$'@ B)'"+%0 #&C()%+ +* (!110 *)+ $'?!1!+' B)!"+&D(!+&*"$ *, #!-!.'2

E)FF'++& '+ !%2 7;<<G> (*-?&%'# #!+!6!$'$ *" %!"#$%&#' !"# A**# *(()11'"(' !"# #!-!.' &" H+!%02 H" ?!1+&()%!15 !"!%0$&$ *, +/' #!+!6!$' &"#&(!+'$ +/!+ -*1' +/!" G<GIJ ?'*?%' #&'#5 4'"+ -&$$&".5 *1 4'1' &"K)1'# &" ;G=< A**# !"# %!"#$%&#' 'L'"+$5 &" +/' M;N@0'!1 ?'1&*# ,1*- OP Q;MI +* ;<<;2 O+ %'!$+ MJJ<<< ?'*?%' 4'1' 'L!()!+'# &" +/!+ $!-' ?'1&*#2 O" !"!%0$&$ 60 R!/" 7;<<G> *" +/' +/' 1*%' *, &"(*-'5 .'*.1!?/05 !"# &"$+&+)+&*"$ *" +/' #'!+/ +*%% ,1*- "!+)1!% #&$!$+'1$5 1'L'!%'# +/!+ +/*)./ 1&(/'1 "!+&*"$ #* "*+ 'S?'1&'"(' ,'4'1 "!+)1!% #&$!$+'1$ +/!" ?**1'1 "!+&*"$5 1&(/'1 "!+&*"$ #* $)T'1 %'$$ #'!+/ ,1*- #&$!$+'15 !"# (*"$'B)'"+%0 +/!+ '(*"*-&( #'L'%*?-'"+ ?1*L&#'$ &-?%&(&+ &"$)1!"(' !.!&"$+ "!+)1'U$ $/*(:$2

!"#$%&#' 1&$: -&+&.!+&*" $+!1+$ ,1*- )"#'1$+!"#&". +/' +0?'$ *, %!"#$%&#' +/!+ +/1'!+'" +/' !1'! )"#'1 $+)#05 6'(!)$' +/&$ :"*4%'#.' #'+'1-&"'$ -!"0 ,)"#!-'"@ +!% !$?'(+$ +/!+ !1' &-?*1+!"+ +* ?%!" !"# !#*?+ !??1*?1&!+' -&+&.!+&L' !(+&*"5 $)(/ !$ +/' ?*+'"+&!% $?''# *, -*L'-'"+5 %&:'%0 L*%)-' *, #&$?%!('-'"+5 #&$+!"(' *, 1)"@*)+5 !$ 4'%% !$ +/' ?*$$&6%' 'T'(+$ *, +/' %!"#$%&#'2

O %!"#$%&#' -!0 6' #'D"'# !$ ! #*4"$%*?' -*L'-'"+ *, 1*(: *1 $*&%5 *1 6*+/5 *(()11&". *" +/' $)1,!(' *, 1)?+)1' &" 4/&(/ -)(/ *, +/' -!+'1&!% *,+'" -*L'$ !$ ! (*/'1'"+ *1 $'-&@(*/'1'"+ -!$$ 4&+/ %&++%' &"+'1"!% #',*1-!+&*" 78&./%!"# !"# 9*61*4$:05 ;<<=>2

V/' -*$+ 4&#'%0 )$'# (%!$$&D(!+&*" *, %!"#$%&#'$ &$ +/' *"' 60 W1)#'" !"# X!1"'$ 7QIIY> 7-*#&D'# ,1*- X!1"'$ 7QIM=>>2 O((*1#&". +* +/!+ (%!$$&D(!+&*"5 %!"#$%&#'$ -!0 6' (%!$$&D'# *" +/' 6!$&$ *, +/' +0?' *, -*L'-'"+ !"# +/' +0?' *, -!+'1&!% &"L*%L'#2 V/' ,*1-'1 -!0 6'Z fall5 topple5 slide *1 flow5 4/&%' +/' %!++'1 -!0 6' '&+/'1 1*(: *1 $*&% 7*1 6*+/>2 [*&% (!" +/'" 6' (%!$$&D'# !$ earth &,

! "#$%&'(%) *+(,,)+($, -. +#($/#''

!"#$% &' (')*+ ', )!#+-)".*+ '/ 0#* (!/1"&$*) !#+ debris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

D!#+)$"+* /")C "1"3!1"'# *!)6/*) &!# 2* &!1*3'/".*+ "#1' 1<' &$!))*)E )1/6&-16/!$ !#+ #'#-)1/6&)1/6&-16/!$4 F9* ,'/ */ &'#)")1 "# )1/6&16/*) !" *+ 1' )$'(* )1!2"$".!-1"'# !#+ +*2/") /*1!"#"#3A !#+ 196) 19*% (/*:*#1 $!#+)$"+* ,/' '&&6//"#3 '/ 1/!:*$ "#1' 6/2!#".*+ !/*!)A <9"$* 19* $!11*/ !% &'#)")1 "# !&1"'#) 19!1 !% "#:'$:* $"11$* )1/6&16/* &'#)1/6&1"'#4

B1/6&16/!$ *!)6/*) !/* 3*#*/!$$% '/* *G*&1":*A 261 9!:* !# 9"39 &')1 (*/ 6#"1 ', (/'1*&1*+ !/*!A )' !&16!$$% '#$% !/*!) 19!1 9!:* 2**# 19/*!1*#*+ 2% +*:!)1!1"#3 $!#+)$"+*) !/* "#1*/*)1*+ 2% 19*)* *!)6/*)4

F9* ')1 " ('/1!#1 #'#-)1/6&16/!$ *!)6/* ") $!#+)$"+* *!/$% <!/#"#34 D!#+)$"+* *!/$% <!/#"#3 !% $*))*# +! !3* !#+ :"&1" )A 261 6)6!$$% +' #'1 (/*:*#1 $!#+)$"+* '&&6//*#&*4 H*1 "1 9!) ! $'< &')1 (*/ 6#"1 ', (/'1*&1*+ !/*!A <9*# &' (!/*+ 1' )1/6&16/!$ *!)6/*)4

D!#+)$"+* *!/$% <!/#"#3 )%)1* ) !/* 2!)*+ '# 19* "+*#1"0&!1"'# ', /!"#,!$$ 19/*)9'$+) ', $!#+)$"+* 1/"33*/"#3 IH!#' !#+ B*#''A 8JKLM N**,*/ *1 !$4A 8JKOM P!(-(!/*$$" !#+ F"/!#1"A 7Q8QM 5!19!#" *1 !$4A 7QQJM F!C!/! !#+ R("( S!3"!<!#A 7QQJM S!6 !#+ T'+1A 7Q8QU4 F96) 6#+*/)1!#+"#3 19* 1" "#3 !#+ 19* $'&!1"'# ', $!#+-)$"+* 1/"33*/"#3 ") " ('/1!#1 ,/' ! )&"*#1"0& !#+ (/!&1"&!$ (*/)(*&1":*4

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•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• ()*+#%&''*,-&+./ E $!#+)$"+* '&&6//*#&* ") "#:*)1"3!1*+ 2% *!# ', *?6!1"'#)

!" #$%&'()&* +,*%-.*%$ $%& /)'0 .)1)2$1)-% "3

! "#$%&'(%) *+(,,)+($, -. +#($/#''

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

! "#$%&%'()

($$&*('+,-H 1#($% 0'+6 B"6*)$// AFIJKG ".# B"(.$ AFILEG "'$ "6+., !$ 7'% +.$% '$/" $# + #$ $'6(." (+. +0 '"(.0"// !'$%!+/#% +0 /".#%/(#$ '(,,$'(.,2

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“ 14.82D´0.39 AD2FG )$% #$7.$# 0+' '"(.0"// #1'" (+.% )$ ?$$. FE 6(.1 $% ".# FE #"4%2 3!$ %+8&"//$# Intensity´ Duration model A<=G (. '+#1&$# )4 B"(.$ !"% )$&+6$ !$ 6+% &+68 6+. 4*$ +0 !'$%!+/# 1%$# (. !$ /( $'" 1'$5 ?!+%$ ,$.$'"/ 0+'6 (% A:1VV$ ( $ "/25 DEEJGU

I_{“ c ` aD}´β AD2DG H(.&$ B"(.$ AFILEG 0+'61/" !"% )$$. *1)/(%!$#5 */$. 4 +0 % 1#($% !"-$ 0+&1%$# +. !$ #$ $'6(." (+. +0 /".#%/(#$ !'$%!+/#%5 6+% +0 !$6 %( $8%*$&(7&5 (2$2 '$/" (-$ + " %6"// /".#%/(#$8*'+.$ '$,(+.5 %+6$ (6$% '$%1/ (., (. W1% " %/(,! 6+#(7&" (+. +0 !$ &+$X&($. ".# $>*+.$. +0 $Q1" (+. D2F5 A&025 $2,2 :1VV$ ( $ "/25 DEEJG2

Y )()/(+,'"*!(& '$-($? )4 !$ < "/(". Z" (+."/ B+1.&(/ +0 ;$%$"'&!5 <.% ( 1 $ +0 ;$%$"'&! 0+' M4#'+8,$+/+,(&"/ ['+ $& (+. ABZ;8<;[<G A:1VV$ ( $ "/25 DEEJG 4($/#$# " /(% +0 FDK '"(.0"// !'$%!+/#%5 ?!(&! (% "/%+ "-"(/")/$ " !$ ?$)%( $ !!"# $$%&'()&**! %+, -*.,/'%"'/0(%/'!$2 Y6+., !$ FDK !'$%!+/#%5 KP "'$ '$/" (-$ + "'$"% ?( !(. < "/42

! "#$%&%'() ($$&*('+,- ./

!!"#$%&' (" ()* +(,$- ". /,00*((% *( 123 4566789 *:;%#%!12 ()#*+)"2$+ %& ()* !"22*!(%"& !1& <* $%+(%&',%+)*$ %& .",# +,<=!1(*'"#%*+>

• %&(*&+%(-=$,#1(%"& ()#*+)"2$+?

• ()#*+)"2$+ <1+*$ "& ()* ("(12 *@*&( #1%&.122? • #1%&.122 *@*&(=$,#1(%"& ()#*+)"2$+?

• #1%&.122 *@*&(=%&(*&+%(- ()#*+)"2$+3

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

• )%') $*;*&$*&!* ". ()* ()#*+)"2$ "& ()* !)1#1!(*#%+(%! O,1&(%(%*+ !)"+*& ."# ()* ."#:,21(%"& ". ()* :"$*2 1&$ "& ()* ()* ."#: ". ()* *:;%#%!12 #*21(%"&+)%; ,+*$?

• )%') ,&!*#(1%&(- %& ()* $*M&%(%"& ". ()* (#%''*#%&' (%:* %&+(1&(9 1&$ )*&!* ". #1%&.122 $,#1(%"& 4,+*$ %& :"+( ". ()* *:;%#%!12 :"$*2+8?

• #*2%1<2* $1(1 ".(*& %+ &"( 1@1%21<2*?

• %:;"++%<%2%(- ". )1@* %&."#:1(%"& 1<",( ()* :1'&%(,$*9 ()* 2"!1(%"& ". ()* 21&$+2%$* *@*&( (#%''*#*$?

• L)*& "&2- ()* (#%''*#%&' #1%&.122 *@*&(+ 1#* !"&+%$*#*$ %& ()* +(1(%+(%!12 1&12= -+%+9 ()* !1+* ". .12+* ;"+%(%@*+ %+ &"( 1!!",&(*$ ."# 4.12+* 121#:+8?

• #"2* ". 1&(*!*$*&( ;#*!%;%(1(%"& %+ &"( .,22- ,&$*#+(""$3

& 1((*:;( (" '*&*#12%0* *:;%#%!12 :"$*2+ )1+ <**& !"&$,!(*$ <- U%#1&'*2" 1&$ V*#+1!* 4HII589 ()1( )1@* ;#";"+*$ ()* WX1BY 4F "#*!1+(%&' ". La&$+2%$*+

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ptq9 83$ ,-%(*(8& )" #8(- Y ptq (4 <(5$ %& 83$ #- 5-*"8(- ( 8$<6'* -) Iptq K(83 ' filter function ψptq:

Y_{ptq “} żt 0 ψ_{pt ´ τqIpτqdτ}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

V #$ 83$ 4$8 -) 7'6',$8$649 ' ! 3$ #$ 83$ ,-%(*(8& )" #8(- 9 (4 " (5-#'**& !$O 8$6,( $!9 $'6*& K'6 ( < -) *' !4*(!$4 ,'& %$ %'4$! - #-,7'6(4- -) 83$ ,-%(*(8& )" #8(- K(83 ' #6(8(#'* 5'*"$9 "4"'**& '44",$! '4 83$ ,( (,", 5'*"$ -) 83$ #'*(O %6'8$! ,-%(*(8& )" #8(- )-6 K3(#3 *' !4*(!$ 86(<<$6( < 3'4 %$$ -%4$65$!. J$6)-6,' #$4 -) $'6*& K'6 ( < 4&48$,4 %'4$! - 83$ /0'12 ,-!$*9 (,7*$,$ 8$! ( 83$ ;'*'%6(' 6$<(- =18'*&+9 3'5$ %$$ ( 5$48(<'8$! 6$#$ 8*& ( 8$6,4 -) ( !(#'8-64 %'4$! - 83$ ",%$6 -) #-66$#8 '*'6,4 CA9 ,(44$! '*'6,4 MA ' ! )'*4$ '*'6,4 F A. W(8 6'8$ HR “ F A{pCA ` F Aq ' ! /'*4$ J-4(8(5$ 2'8$ F P R “ F A{pCA ` F Aq 5'6($! ( 83$ 6' <$ G.?H O G.AA ' ! G.QH O G.XA9 6$47$#8(5$*& =C$64'#$ $8 '*.9 FG?F+.

!" #$%&'()**%+,)&-. /0.-*&

M3$4$ '776-'#3$4 '6$ %'4$! - 83$ #-,7"8'8(- -) ' )'#8-6 -) 4')$8& F S K(83 6$47$#8 8- 4*-7$ 48'%(*(8&. M3$ 6$<(- -) ' '*&4(4 "4"'**& #- 4(484 ( ' #'8#3,$ 89 K3(#3 (4 4"%!(5(!$! ( $*$,$ 84 -6 #$**49 - ' 47'8('**&O!(486(%"8$! Y21T -6 #- 8-"6 %'4(4.

M3$ )'#8-6 -) 4')$8& $L7*(#(8*& !$7$ !4 - 83$ 4-(* K'8$6 76$44"6$. M3"4 ' 3&O !6-*-<(#'* ,-!$*9 )-#"4$! ,'( *& - 4"%4"6)'#$ K'8$6 !& ',(#49 83'8 '**-K4 #-,O 7"8'8(- -) 7-6$ 76$44"6$4 )6-, 6'( )'** ( 7"89 (4 ' )" !',$ 8'* 7'68 -) 83$4$ 8&7$

!" #$%&'()**%+,)&-. /0.-*& 12

! " #$%&' ()$ &% *$ &+,-.%.+/ " #$% .& 0&0,%%/ $1*2$&&$# ,& 3$ ! 2"0%, ! 2 +)$ &,!$+/ !,4+ 25 ,3# 03&+,-%$ 4$%%& ,2$ .#$3+.6$# ,& +)$ 3$& ! 2 7).4) F S ă 1'

83 +)$ ! %% 7.39 &$4+. 3&5 +)$ *2.34.*,% &% *$ &+,-.%.+/ ,3# ).%%&% *$ )/#2 % 9/ " #$%& 0&$# -/ 2$&$,24)$2& ,2$ 2$:.$7$#' ()$ #$+$2".3,+. 3 ! 2$+023 *$2. # ! %,3#&%.#$& .& +)$3 ! 40&$#'

3*04- &5),'*'5% )6)*%&'&

83 ",3/ ! +)$ " #$%.39 ,**2 ,4)$&5 .+ .& ,&&0"$# +),+ +)$ * +$3+.,% !,.%02$ &02!,4$ %.$& ,+ , #$*+) dLZ -$% 7 +)$ &02!,4$ +),+ .& &",%% .! 4 "*,2$# 7.+) +)$ %$39+) !

+)$ &% *$5 & +),+ +)$ $#9.39 $;$4+& ,2$ 3$9%.9.-%$' ().& ,%% 7& 3$ + 0&$ +)$ inf inite<slope &+,-.%.+/ ,3,%/&.& =>,$!$%.5 ?@ABC (,/% 25 ?@ABD' 83 +).& 4,&$5 +)$ !,4+ 2 ! &,!$+/ .& #$+$2".3$# !2 " +)$ ,3,%/&.& ! , &%.4$ ! ",+$2.,% ! 03.+ 7.#+) ,3# +).4E3$&& =&$$ 6902$ F'FD'

G.902$ F'FH I4)$"$ ! 2 .363.+$ &% *$ $J0.%.-2.0" ,3,%/&.& =,#,*+$# !2 " K && $+ ,%'5 FLLMD' N3 +)$ %$!+5 +)$ 4 2#.3,+$ &/&+$" 0&$# -/ 8:$2& 3 =FLLLD

G,4+ 2/ ! &,!$+/ .& .3 9$3$2,% #$63$# ,& +)$ 2,+. -$+7$$3 &)$,2 &+2$39+) τf

,3# &)$,2 &+2$&& τH

F S_“ τf

τ . =F'AD

O44 2#.39 + +)$ *2.34.*%$ ! $;$4+.:$ &+2$&&5 +)$ &)$,2 &+2$39+) ",/ -$ $1*2$&&$# ,&H

τf“ c1` pσ ´ ψq tan δ =F'PD

7.+) c1_{#$3 +.39 & .% 4 )$&. 35 σ +)$ 3 2",% + +,% &+2$&&5 ψ +)$ * 2$ 7,+$2 *2$&&02$5}

! "#$%&'(%) *+(,,)+($, -. +#($/#''

! γ "#$"#%#&'% '(# )*#")+# ,-./ -&0' 1#0+(' 2! %20. ),2*# '(# +"2-&31)'#" .#*#. )&3 γsat '(# %)'-")'#3 -&0' 1#0+(' 2! %20. -&3#" '(# +"2-&31)'#" .#*#.4 '(#

#5$"#%%02&% 2" σ4 τ )&3 ψ )"#6

σ “ rp1 ´ ωqγ ` ωγsatsdLZcos 2

δ

τ _{“ rp1 ´ ωqγ ` ωγ}satsdLZsin δ cos δ 789:;

ψ “ ωdLZγwcos 2

δ

1(#"# ω “ h{dLZ )% %(21& 0& 8984 )&3 "#$"#%#&'% '(# !"#!$$ !)<'2"9

=-,%'0'-'02& 2! '(# ),2*# !2">-.)% 0& 89? )&3 89@ A0#.3% '(# !2..210&+ #5$"#%%02& !2" '(# %)!#'A !)<'2"4 -%#3 0& '(# >23#. ,A B2%%2 #' ).9 78CC:;6

F S“ c

1_{` rp1 ´ ωqγ ` ωγ}1_sd

LZcos2δ tan φ1

rp1 ´ ωqγ ` ωγsatsdLZsin δ cos δ

. 789D;

E2&'+2>#"A )&3 F0#'"0<( 7GHH@; -%#3 '(# ) %0>$.0I#3 *#"%02& 2! '(0% !2">-.)4 1(0<( <2&%03#"% ) <2(#%02&.#%% %20. >)&'.# 7c1_{“ 0; )&3 γ “ γ}

sat6

F S_“ γsat´ ωγw γsat

tan φ1

tan δ. 789J;

K >2"# +#&#"). #5$"#%%02& '()& #L-)'02& 89D4 '()' ()% ,##& -%#3 10'(0& >23#.% '()' $"2*03# '(# $2"# $"#%%-"# 30%'"0,-'02& ).%2 0& '(# -&%)'-")'#3 M2&# 7#9+9 N)-> #' ).94 8CGCO P)$$)"#..0 )&3 Q#"%)<#4 8CGG; )<<2-&'% !2" '(# 3#+"## 2! %)'-")'02& 0& '(# -&%)'-")'#3 M2&# ,A >-.'0$.A0&+ $2"# $"#%%-"# !2" '(# )$$"250>)'02& +0*#& ,A Q)&)$)..0 )&3 R"#3.-&3 78CCC; 2! '(# N0%(2$S% N0%(2$ #T#<'0*# %'"#%% $)")>#'#" χ“ pθ ´ θsq{pθs´ θrq4 ,#0&+ θ “ Vw{Vt '(# )<'-). %20. 1)'#" <2&'#&' 7*2.-># 2!

1)'#" Vw$#" -&0' *2.-># 2! %20. Vt;9

U(# 0&I&0'# %.2$# %<(#># '#&3#&'02-%.A .#)3% '2 -&3#"#%'0>)'02& 2! '(# )<'-). !)<'2" 2! %)!#'A4 ,#0&+ '(# #3+0&+ #T#<'% &#+.#<'#39 K<'-)..A4 (#'#"2+#&#0'0#% 0& '(# %20. <()")<'#"0%'0<% >)A )33 ) 3#+"## 2! -&<#"')0&'A '()' >)A .#)3 ).%2 '2 2*#"#%'0>)'02&% 2! F S4 3-# !2" #5)>$.# '2 2*#"#%'0>)'02& 2! '(# %20. >#<()&0<). $"2$#"'0#% c1 _{)&3 φ}1₉

N)-> #' ).9 78CG8; -%#3 ).%2 ) !)<'2" 2! %)!#'A ,)%#3 2& ) I&0'# VWF %.2$# %<(#>#4 2,')0&0&+ ,#''#" "#%-.'% '()& 10'( '(# GWF %.2$#4 10'( '(# %)># $2"# $"#%%-"# 30%'"0,-'02& <).<-.)'#3 10'( '(# *#"'0<). 0&I.'")'02& >23#. UB XB= *9 89C 7N)-> #' ).94 8CCJ;4 3#%<"0,#3 )!'#"9

0(''&'12) 3.%+1'1,.

Y)".A >23#.% )"# ,)%#3 2& >)%% <2&%#"*)'02& 2! +"2-&31)'#" 0& '(# %<(#># .0/# '(# 2&# 2! I+-"# 89V4 1(#"# ) 0>$#">#),.# ,#3 0% )' 3#$'( dLZ9 E)%%W<2&%#"*)'02&

#L-)'02& >)A ,# #5$"#%%#3 )% '(# !2..210&+ 7B2%%2 #' ).94 8CC:;6 Ap_{´ q “} dS

dt, !2" h ď dLZ 789H; )&3

!" #$%&'()**%+,)&-. /0.-*& 12

!"#" t $% &"'%(#") *#+& ,!" -".$//$/. +* ,!" %,+#&0 S ,!" ',"# %,+#'." $/ ,!" "1"&"/,0 '/) r ,!" +2"#1'/) 3+ )$%4!'#." +44(##$/. !"/ %+$1 $% %',(#',") 5$6"6 Sr“ 176

8$.(#" 96:; <4!"&" +* 4+/,+(#=-'%") &+)"1% 5')'>,") *#+& ?+%%+ ", '160 9@@A7 ?+%%+ ", '16 59@@A7 "B>#"%%") ',"# %,+#'." '% S “ Vwptq´Vwp0q “ Vwptq´V_Vt wp0qVt“ e

1_`ep1 ´ SrqAh0 !"/4" 4+/%$)"#$/. ' /+/=/(11 $/$,$'1 )".#"" +* %',(#',$+/ Sr6

C!" D'#4E 1' ,!"/ >#+2$)"% ,!" %"">'." 3+ $/ ,!" .#+(/) ',"# ,'-1" '%; q_{“ pBh cos δqK}stan δ“ BhKssin δ, 596FF7

-"$/. Ks,!" %',(#',") !E)#'(1$4 4+/)(4,$2$,E +* ,!" %+$1 '/) tan δ !"') .#')$"/,0

'%%(&") ,+ -" >'#'11"1 ,+ ,!" 1+4'1 .#+(/) %1+>"6 G/,".#',$+/ +* ,!" )$H"#"/,$'1 "I(',$+/ 96J E$"1)% ,+; h“ p p˚dLZ „ 1´ exp ˆ ´ 1 A1 p˚ t dLZ ˙ ` hiexp ˆ ´ 1 A1 p˚ t dLZ ˙ , *+# p p˚ ď 1 596F97 !"#" hi “ hp0q $% ,!" $/$,$'1 ',"# ,'-1" !"$.!,0 A1“<sub>1`e</sub>e p1´Srq '/) p˚ “TsB sin δ_A

! "#$%&'(%) *+(,,)+($, -. +#($/#'' ! "#$ !%"&'%" () *'$+ * "%" () '%"$ ,Ts“ Ksz -$)("$! #.-'%&/ + "'%)!0 !! 1 ". (2 "#$ !( / 0%)"/$34 52 )$" '% )2%// $6+$$-! "#$ !%"&'%" () *'$+ * "%" () '%"$ p˚_{7 ()$ (8"% )! !%"&'%9} " () (2 "#$ !( / 0%)"/$ %2"$' % +$'"% ) " 0$ t˚_: h_“ " $;)4 2.12 2 t ď t˚ dLZ 2 t ą t˚ ,<4=>3 %)-t˚“ ´A1 z p˚log ¨ ˝ zp1 ´ pp˚q hi´ppz˚ ˛ ‚ ,<4=?3 @ *'$1 (&!7 %)- ! 0*/$'7 0(-$/ 8. A()"B(0$'. %)- C $"' +# ,=DD?37 +()! -$'$-"#$ !"$%-. !"%"$ +%!$7 4$4 -$'$-"#$ *'$1 (&! $;&%" () E "# -$'$-"#$ " 0$9-$*$)-$)" "$'0 dS dt “ 07 %)- 2%+"('. (2 !%2$". F S B 1$) 8. $;&%" () <4F7 E# +# . $/-! "#$ 2(//(E )B 2% /&'$ +' "$' ()7 ) "$'0! (2 G+' " +%/G E$")$!!: ωCR“ γsat γw „ 1´ tan δ tan φ1  , ,<4=H3 E# +# 0*/ $! "#%" "(*(B'%*# + $/$0$)"! E#$'$

A{B ě pTs{pq sin δpγsat{γwqr1 ´ tan δ{ tan φ1s ,<4=I3

%'$ *'$- +"$- "( 8$ &)!"%8/$4

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

51$'!() ,<PPP3 *'(1 -$- %) )! B#" (2 *#.! +%/ 0$+#%) !0 &)-$'/. )B /%)-!/ -$ "' BB$' )B 8. '% )2%//7 8%!$- () "#$ !(/&" () (2 *%'" +&/%' +%!$! (2 "#$ O +#%'-!R $;&%" ()4

51$'!() ,<PPP3 %'B&$- "#%" !$/29+()"'%- +"('. '$!&/"! %'$ . $/-$- 8. &" / S )B %*9 *'(%+#$! 8%!$- () !/(*$ *%'%//$/ T(E %)- 0%!! +()!$'1%" () (2 B'(&)-E%"$' ) % !+#$0$ (2 T(E -(0% ) 8(&)-$- 8. %) 0*$'0$%8/$ 8$- %" -$*"# dLZ7 !&+# %! "#$

0(-$/! U&!" //&!"'%"$-4 N#&! 51$'!() ,<PPP3 *( )"! (&" "#%" 1$'" +%/ )M/"'%" ()7 0(-$/$- 8. O +#%'-!R $;&%" () 0%. 8$ %**'(*' %"$ 2(' &)-$'!"%)- )B !#('"9"$'0

!" #$%&'()**%+,)&-. /0.-*& 1

!"#$%"! $& '(! ()**"*$#! '$ ' +%")!%' +)%&+**, )% $ -! '$ +""!"" (.- $*$/)0+* 0$%-)1 ')$%" '(+' ' )//! *+%-"*)-!"2

300$ -)%/ '$ 45! "$%67778" 45! "$%6777 +%+*.")" '(! &$**$9)%/ '( !! '):! "0+*!", $% 9()0( #(.")0+* # $0!"" /$5! %)%/ *+%-"*)-!" $#! +'!", :+. ;! -)"')%/<)"(!-=

• A{D0 +" '(! :)%):<: '):! "0+*! %!0!""+ . &$ !"'+;*)"(:!%' $& "'!+-. ;+0>1

/ $<%- 9+'! # !""< !" '(+' -!5!*$# +' px, y, Hq )% !"#$%"! '$ +)%&+** +51 ! +/!- $5! #! )$-" '(+' 0$::$%*. +%/! & $: -+." '$ -!0+-!" ?*$%/1'! : !"#$%"!@2 A(!"! "'!+-. / $<%-9+'! # !""< !" )%B<!%0! '(! # $#!%")'. &$ *+%-"*)-)%/ +' px, y, Hq ;<' '(!. -$ %$' ' )//! "*$#! &+)*< !2 • H2{D0+" + 0(+ +0'! )"')0 '):! +""$0)+'!- 9)'( ' +%")!%' #$ ! # !""< ! ' +%"1 :)"")$% -< )%/ +%- &$**$9)%/ "'$ :" ?"($ '1'! : !"#$%"!@2 C+)*< ! !"<*'" &$ : +)%&+** $5! '()" '):! "0+*!, '(+' 0$::$%*. +%/!" & $: :)%<'!" '$ :$%'("2

• aH{g +" '(! '):!"0+*! $% 9()0( #$"'1&+)*< ! *+%-"*)-! :$')$% $00< ", +% +%$'(! ):#$ '+%' +"#!0' $& *+%-"*)-! !*+'!- !"!+ 0( ?0&2, !2/2 45! "$%, DEEFG H1 _{!"#$ #% &'() *++,- .!/&$"$" #% &'() 011+2(}

3"%4 !#5#!#$6# %7 %4# 677!8"$&%# 9:9%#/ px, y, zq "'';9%!&%#8 "$ <=;!#9 0(0 &$8 0(,) >"64&!89 ?*+,*2 #@;&%"7$ /&: A# B!"%%#$ &9 ?65() #(=( !&9) *++12 C

Bψ Bt dθ dψ “ B Bx „ KLpψqˆ Bψ Bx ´ sin δ ˙ ` B By „ KLpψqˆ Bψ By ˙ ` ` B Bz „ Kzpψqˆ Bψ Bz ´ cos δ ˙ , ?0(*D2

"$ B4"64 ψ "9 =!7;$8B&%#! E!#99;!# 4#&8) θ "9 97"' F7';/#%!"6 B&%#! 67$%#$%) t "9 %"/# &$8 δ "9 %4# 9'7E# &$='#) 0 ď δ ă 90( GF#!97$ ?01112 %4#$ 8#<$#9 %4# !&%"7 ε A#%B##$ E!#99;!# 8"H;9"7$ %"/#96&'#9 H2

{D0 &$8 A{D0C ε_“ d H2 D0 AD0 “ H ? A. ?0(*I2

J4"9 !&%"7 E'&:9 & K#: !7'# "$ &$&':L"$= E!#99;!# 4#&8 !#9E7$9#9 %7 !&"$5&'' 7$ 9'7E#9) &$8 GF#!97$ ?01112 /&8# 9"/E'"<6&%"7$9 75 %4# >"64&!89M #@;&%"7$ A&9#8 7$ %4# 4:E7%4#9"9 %4&% ε ! 1(

J7 &$&':L# '7$=N%#!/ A#4&F"7! #@;&%"7$ 75 >"64&!89M /&: A# B!"%%#$ "$ %#!/9 75 %4# 8"/#$9"7$'#99 %"/# t˚_“D0

At( G$ %4# 6&9# 75 ε ! 1) >"64&!89M #@;&%"7$ 9"/E'"<#9

%7C B Bz˚ „ Kz˚ˆ Bψ ˚ Bz˚ ´ cos α ˙ “ 0 ?0(*+2

B4#!# ψ˚_{“ ψ{H) z}˚_{“ z{H) x}˚_{“ x{}?_{A&$8 y}˚_{“ y{}?_{A&!# $7!/&'"L#8 F&!"&A'#9(}

O!#@;#$%': "$ &EE'"6&%"7$9) %4# '7$=N%#!/ &F#!&=# "$<'%!&%"7$ !&%# "$ %4# z 8"N !#6%"7$ &% =!7;$8 9;!5&6# pIzqLT "9 9E#6"<#8 A: & 67$9%&$% P;Q A7;$8&!: 67$8"%"7$

!"#$%&'$( )*'++(*'#+ ,- *"'#."&&

pIzqLT “ ´KzpBh{Bzq !" #$% &'() (& &&*+%" $'+',%!%'*& -./%0&'!1 233345 .!

#$% 6 &% #$ # (!7)#0 #('! (& &*86(%!#)9 &)': #$ # pIz{KzqLT ! cos δ #$% ;0%/('*&

%<* #('! "%&60(=%& &)';%>; 0 ))%) ,0'*!": #%0 ?':@

ψ“ pz ´ dwq cos δ, -25234

:$%0% dw(& #$% : #%0 # =)% "%;#$ +% &*0%" !'0+ ) #' #$% ,0'*!" &*0A 6%5

B$% &$'0#>#%0+ ;;0'C(+ #('!1 + 9 =% "%0(/%" %C;0%&&(!, D(6$ 0"&E %<* #('! 25FG (! #%0+& 'A #$% &$'0#>#%0+ "(+%!&('!)%&& #(+% t˚ _“ D0

H2t5 H'0 ε ! 11 (! #$(&

6 &% %<* #('! 0%"*6%& #' #$% &# !" 0" D(6$ 0"&E %<* #('! A'0 /%0#(6 ) (!7)#0 #('! (! $())&)';% 'A &)';% δ@ C_pψq C0 Bψ˚ Bt˚ “ 1 cos2 δ B BZ˚ „ K_z˚ˆ Bψ ˚ BZ˚ ´ 1 ˙ , -252F4 :$%0% Cpψq “ dθ{dψ !" C0#$% +(!(+*+ / )*% 'A Cpψq1 #9;(6 ))9 '=&%0/%" :$%!

#$% &'() (& & #*0 #%"1 !" K˚

z “ Kzpψq{Ks5

I<* #('! 252F (& &#()) !'!>)(!% 01 !"1 (! ,%!%0 )1 0%<*(0%& !*+%0(6 ) +%#$'"& A'0 (#& (!#%,0 #('!1 !" #$% &*;%0(+;'&(#('! 'A &')*#('!& (& !'# ;'&&(=()%1 :$(6$ + J%& 'A "(86*)# 6 )6*) #('! 0%&;'!&%& #' 0% ) 0 (!A )) &%<*%!6%&5 .! #$% 6 &% 'A :%# (!(#( ) 6'!"(#('!&1 '!% + 9 &&*+% Kz« Ks !" pψq “ dθ{dψ « C01 !" "%0(/% #$% A'))':(!, )(!% 0 %<* #('!@ Bψ Bt “ D0 cos2 δ B2 ψ BZ2 -25224

.! #$% 6 &% 'A (!7!(#% = & ) ='*!" 09 "%;#$ !" 6'!&# !# $9%#',0 ;$ 'A (!#%!&(9 IZ !" "*0 #('! T 1 2522 $ & #$% A'))':(!, &')*#('!@

ψ ZpZ, t ď T q “ βp1 ´ d{Zq ` IZ KZrRpt ˚<sub>qs -252K4</sub> ψ ZpZ, t ą T q “ βp1 ´ d{Zq ` IZ KZrRpt ˚_{q ´ Rpt}˚_{´ T ˚qs -252L4} (! :$(6$

Rpt˚_{q “apt}˚_{{πq expp´1{t}˚_{q ´ %0A6p1{}?_t˚_{q -252M4}

(& ;0%&&*0% $% " 0%&;'!&% A*!6#('!1 :$(6$ "%;%!"& '!)9 '! !'0+ )(N%" #(+% t˚_“

t{pZ2

{ ˆDq1 T˚_{“ T {pZ}2

{ ˆDq (& !'0+ )(N%" "*0 #('!1 ˆD“ 4D0{ cos 2

δ(& ! %O%6#(/% $9"0 *)(6 "(O*&(/(#91 %0A6 (& #$% 6'+;)%+%!# 09 %00'0 A*!6#('! !" pβ “ cos2

δq (! #$% 6 &% 'A &)';%>; 0 ))%) ,0'*!": #%0 ?':5

P *+ %# )5 -23324 %C#%!"%" ./%0&'! -23334 &')*#('! -%<* #('!& 252K´252M4 A'0 #$% 6 &% 'A 7!(#% = & ) ='*!" 091 ;0'"*6(!, !" "(&#0(=*#(!, 0%) #%" &'A#: 0% #' ;;)9 #$(& +'"%) '! 0%,('! ) &6 )% !" QD.R>= &(&1 ! +%" BD.QDS -T 0 !&(%!# R (!A )) I!7)#0 #('! !" G0(">= &%" R%,('! ) S)';%>S# =()(#9 T'"%)41 /%0&('! F535 B$(& +'"%) )&' 6'!&("%0& (!&# !# !%'*& 0*!'O 0'*#(!,1 #$ # '66*0& :$%! 0 (!A )) (!#%!&(#9 %C6%%"& (!7)#0 #('! 6 ; 6(#9 'A &'()5 B$(& 0'*#(!, (& 66'*!#%" (! #$% +'"%)

!" #$%&'()**%+,)&-. /0.-*& "

!"# ! $%& '()$ $%($ $%& *+! , '* - !& )&"" -(# $ $(""# * .(*$/(""# /!0"$*($& /! 1 2!3" .& )&""34

5 "($&* - 1&" 6# $%& 3(-& (+$% *3 78(+- &$ ("49 :;;<9 :;=;9 :;==>9 %(3 6&&! 6(3&1 ! $%& (!("#$/)(" 3 "+$/ ! ' ?/)%(*13@ &A+($/ ! :4:= 2/$% $%& &B. !&!$/(" 3 /"C2($&* *&$&!$/ ! )+*D& ' E(*1!&* 7=FG<>9 ' * 2%/)% ( )" 3&1 ' *- 3 "+$/ ! $ $%& *&3+"$/!H "/!&(*/I&1 &A+($/ ! /3 (D(/"(6"&9 .* D/1&1 6# J*/D(3$(D( (!1 K&% 7=FF=>4

L%& L?ME?J9 D&*3/ ! :4; - 1&" /3 1&3)*/6&1 /! /$3 1&$(/"3 /! )%(.$&* N9 6&/!H $%/3 - 1&" +3&1 /! $%& *&3&(*)% 1&D&" .&1 /! $%/3 $%&3/34

O!& (1D(!$(H& ' $%& .%#3/)(""#C6(3&1 (..* ()% /3 $%($ /$ ("" 239 ($ "&(3$ /! .*/!)/."&9 $ ()) +!$ ' * (!$%* . H&!/) ()$/ !9 "(!1 +3& (!1 )"/-($& )%(!H&4

P+ (!1 J/1"& 7=FFG> /3 !& ' $%& 0*3$ 2 *Q3 $%($ (!("#I&1 $%& * "& ' * $ 3$*&!H$% (!1 %(*D&3$/!H ! 3%("" 2 "(!13"/1&3 $*/HH&*/!H4 O$%&* 2 *Q3 /!D&3$/H($& ! $%& * "& ' (!$%* . H&!/) ()$/ !9 3+)% (3 * (13 (!1 2/"10*& 7M3$(!6+""+ H"+ &$ ("49 :;;RS ?+""/ (!1 ? 33 9 :;;GS ?+""/ &$ ("49 :;;NS T(*/3& (!1 U(!! !9 :;=:>

M$ %(3 $ 6& ! $/)&1 $%($9 /! .*/!)/."&9 &D&*# %#1* " H/)(" - 1&" $%($ ("" 23 &,&)$/D& &3$/-($/ ! ' H* +!12($&* . *& .*&33+*&3 /3 /! .*/!)/."& 3+/$(6"& ' * "(!1C 3"/1& (!("#3/3 /' $%& $*/HH&*/!H -&)%(!/3- /3 1+& $ *(/! /!0"$*($/ ! 7)'49 &4H4 J/- !/ &$ ("49 :;;<>4

1-2-3/'4'&2'( 3)'45)** 2$3-&$0*.& )4. 3-2634 7-3'0. 05 *)4.&*'.'48 T%#3/)(""#C6(3&1 - 1&"3 1&3)*/6&1 /! $%& .*&D/ +3 3&)$/ !9 &!(6"& $ 1&$&*-/!& 1&$&*-/!/3$/) $*/HH&*/!H $%*&3% "13 /! $&*-3 ' $ . H*(.%/)9 %#1*(+"/) (!1 H& -&C )%(!/)(" .(*(-&$&*34 V * $%& W !$H -&*# (!1 X/&$*/)% 7=FFR> - 1&"9 $%& $%*&3% "1 *&3+"$3 /! $&*-3 ' ( 3$&(1# 3$($& *(/!'("" *($&Y

pCR“ rT sin δpγs{γwqpA{Bqsr1 ´ tan δ{ tan φqs 7:4:N>

K&$ $%/3 *&3+"$ 1 &3 ! $ ("" 2 $ (33&33 $%& *&$+*! .&*/ 1 ' "(!13"/1& $*/HH&*/!H9 6&)(+3& $%& *&$+*! .&*/ 1 ' .*&)/./$($/ ! 1&.&!13 6 $% ! 3$ *- /!$&!3/$# (!1 1+*($/ ! 7X@O1 */) &$ ("49 =FFG>4 L%& .* 6(6/"/3$/) - 1&"3 $%($ ("" 2 &3$/-($/ ! ' *&$+*! .&*/ 1 ' .*&)/./$($/ !9 /4&4 $%& 2&""CQ! 2! (!1 ) -- !"# +3&1 M!$&!3/$#C X+*($/ !CV*&A+&!)# 7MXV> )+*D&39 *&A+/*& 6 $% *(/! /!$&!3/$# (!1 1+*($/ !4 7)'4 J$&1/!H&* &$ ("49 =FFZS 8+*"(!1 (!1 ? 33 9 =FFN>

L%& *&3+"$ ' ? 33 &$ ("4 7:;;N>9 ()) +!$3 ' * $*(!3/&!$ .*&)/./$($/ !9 (!1 %&!)& ' * *(/!'("" *($& pCR (!1 1+*($/ ! t9 (!1 $%& ' "" 2/!H 1&$&*-/!/3$/) $%*&3% "1 /3

#/&"1&1Y pCRptq “ TsB_Asin δ „ _pG s`eSrq ´ 1<sub>´</sub>tanδ tanφ1 ¯ 1<sub>`e´ep1´Srq</sub>´1_´tanδ tanψ1 ¯´ hi z exp ´ ´ 1_{`e</sub> e´eSr TsB sin δ Az t ¯ 1<sub>´ exp</sub>´<sub>´</sub> 1<sub>`e} e´eSr TsB sin δ Az t ¯ , 7:4:[> V * 3% *$ 1+*($/ !39 $%/3 *&"($/ !3%/. /3 .*()$/)(""# "/!&(* /! ( logpDq ´ logpIq ." $ 9 $%&! /$ 3$(*$3 1&.(*$/!H '* - /$ *&()%/!H A+/$& *(./1"# $%& % */I !$(" (3#-.$ $& ωCRp˚9 6&/!H ωCR )*/$/)(" 2&$!&33 ' * $%& ? 33 &$ ("4 7:;;N> - 1&"4 J(")/(*/!/

! "#$%&'(%) *+(,,)+($, -. +#($/#''

! "#$ %&''() *"+ ,"- ". "."#/0/1+ 2.3 +!20"!2/. /4 5/++/ ! "#$ %&''6)7 1+2.0 !* 859:5; 3$< ,/- # %="1, ! "#$7 &''&)$

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

9. 4"B! A !1A. I A2/- - I .-+7 2. 0 . A"#7 /. !* N*/# !2, *2+!/AF /4 A"2.4"##7 N*2B* - ! A,2. "#+/ !* 2.2!2"# B/.-2!2/.+7 !*"! +*/1#- ./! M . 0# B! - /A M "AM2!A"A#F "++1, -7 "+ /BB1A+ 2. !* "M/3 B2! - +!1-2 +$

!

!"#$%& '

!"#$#%&' $&#()&''

*+$,-+.'/-).$ *+, 0,'.$#*&(#

1.2(*&#(-&$,&3 4*&'5

!" #$%&'()$* $%()$+,

!"# $!%&'() *+$,#(# +- (.&")"$%/ .+0(/ +* )%"-*%// '!)(#!+/0# '!%' .%1 2( ,#(0 *+) /%-0#/"0( (%)/1 3%)-"-45 6-%/1#(# %)( *+$,#(0 +- '!( $%#( #',01 %)(% +* 7(/+)"'%-" 8+,-'%"-#9 0(#$)"2(0 "- *+//+3"-4 #($'"+- :5;5

<- &%)'"$,/%)9 =)#'/1 '!( >?%<@ .+0(/ AB")%-4(/+ %-0 C()#%$(9 DEE;F "# %&&/"(05 !(- % -(3 .('!+0 "# &)+&+#(0 %-0 %&&/"(05 <' (-%2/(# $+.&,'%'"+- +* % '!)(#!+/0 "- '().# +* $,.,/%'"G( )%"- +- % .+G"-4 '".( 3"-0+3 +* 0,)%'"+- d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

!- ./% #%&0$'1)2' 30421)'2, 5),% ,146* )$%)

!( 7(/+)"'%-" %)( % .+,-'%"- )%-4( +* -+)'!I(%#'()- B"$"/19 "- #+,'!()- <'%/19 (J'(-0"-4 *+) %2+,' ST U. %/+-4 '!( <+-"%- $+%#'/"-(5 !( )%-4( "# .%0( ,& 21 % /+-4 #()"(# +* &(%U#9 3"'! %- %G()%4( !("4!' +* VQQIDQQQ .5 !( '+&+4)%&!1