Geophys. J. Int. +- 142, <??<? Department of Earth Sciences, Parks Road, Oxford UK. E-mail: [email protected] Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, USA !" # !$ !" #% ! !!" & ' '( ) !!" $! & "* ' +!> , - '!" ($!. & ! "! ' & ' . ! & / ! & ' ! " " . $" !' ' " /! ", . 0"! & '! ! "! " ! /! 10. " !! !, '" & "! at the time of loading "! ' " /$ ! !'*!$ ! 2 ! . ' " ', . ! 10. " !! !, 3. & " ! ) ! $! & 0'" 10. " !! !, & ! "! " " (! " !' '"" " !' ). '! && ', 0! (/ '" "! /! "! ' & ' & " *! . "0! /! /2 ! 4 !$! "!$ " & / $ $" '."!* ", $!"! ' " /! ! ( ." & 0 !'" 2 '! ! "! ! '"", !$ '" .. ! !$ (, "*"! ' " , ' ! !! & ' " /! / '!"! & 10. " !! !, !' / $ &. !& . '" $!!, ! !$! , ( !( "* ' '!" ($!. & ! "! ! 56 '"x )! ' ! 0"! & 10. " !! !, both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atts and S. Zhong ! +! xxx# x- / ' /! ! /! "!" ! ' !" + ,- 0!" + !&*, (! & '!- ! /! ,!"", ! x?xx x + @"! A . $ #% B/' A ! - ". " && & ! 2 ! 2/ & ' "( , . ! /! 2 ('! /2 ! ! & ' x x# x ", & . '" '. "/ ! & "!" ! ", . ((", ( ! / C & ' " !'" ' & ' . ! & /, ! /0! /! & ! " + @" ?- :. ! D "! & 0'" " & B ' ! C. / $ (, ! /! . '" ( ! ! ! ! 12! ! "!' ". & ! " !& .! . '" E. ! ! /! /" & 0'" . '" / ." .! ."!& / " / .(! ! 12! ! , '!! & ."!& .(! ' ! ' /! !! & !" ' " ' & B/! 1.! ", ! ( !(" . & (. ! $!!, .. & '" . ! & F ! +FE" 2 - D2 $!"" +4/2! A .8. < B ' ! +. A "! <- . & 0'" $!!, & rxr r !$", & /2 ! ", . "! "! ", G ' et al +<- . / ( $! & "*/$" !'* $!, 9" . (! !$ (, "! "!! !' $!!, & '" ! % ! &/ !' !" & "!" (. $! ' !& * '! ! $! "!* !1. & & '! 4 !." @"" +#<- / F ! ."!& 3.! "! "! 0 & 2' F. ' *"$" ( $! & ' " / . F!" +"& <- . "! !2 & "! & < 2' !'!" $". $ ( . & ' & (. & ! "! 7!" 8 ! *"!" "2 & B ' ! +" - F!"", ! $! A "! +- . .! !$ ! !3. ."!& ! F ! 3.! "! "! ? 2' !2 ' /! !'" & "!" . !&! , /$ !'" & "!" " ! !"" 4& '! & '! & "! !'" & ' & ' $" !' " & ' ! "! ! !" * * ,' B ", " & " . ! +> - (. , ( ' ! " ." , $ $! !& '! "* ' '!" ! & "! $ "!$", '"" !" " & ' .&." ' " ( . + =. - !( & '! & "! ! "! " ' " 4 ! ' " "! ! ! "! " $ "! !$!! .( .' , ' ! !! & ' " /! ( $! & 10. ! ! & $" !' & 0'" ! ( !(" ! "* ' "! ! & "! ! "!! ( " " + <% @" /"" A ). % @>$ et al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g( ." 9 ( $! ) "! !2 !' . (, @. , A .' +<- / ( '!"! (, ! et al +</! !". ? !' & ' '! *! ! * !" ,' ! !" '. !$ " ! ! et al +<- . , ' ? # GJI &'( <??<? Flexure and rheology of oceanic lithosphere additional !' & "! !2 $ ( .("! &/ & !' + * !" ,'- ! $!. $". /!" " "! !' (. , ( ' . * , $!, ! '", ) 'E !, & / !' /$ & ' "!" &. !". ! ! et al +<- '!"! 4 ! / . / '!"! & "! !2 !' *0'! 3.! & "* ' '* !" ! & ! "! F! / ' !' /! !! & ! "! $!* "! " ' " ' /!" ' " $ .&." . ! ' !>! ( $! & 10. , 3.", !( / "! ."", ( * "* ' " . '."!", $!"! ' " & ! "! !'!" !!"", $" (, @. , A .' +<- '! !&& (! ' !0 !3. = 8 &.! ! . "$ 10. 3.! , ' ! / '!"! & "! !2 !' /! !! & '."!", $!"! ' " / '! 7(*98 ' & !$! , & $!!, & ! "! F!"", / 0'! !'"!! & (*9 ' & .(! ."!& ! , & !$ / $"! !" ! , & ! 12! ' ' ) # ! # ) * Te :. ! / ( /" & / ' ! "! " '" ! . & , ' ! $!, ! '"! !'! 1! 9" & ( & 10 ! . !'! & ! $! & !" $"!, $ . .. ! ! & $"! !' , & " /! !! & !'" "! ' " ! ( !(" ! "* ' '!" ! & "! ''", . ' ! 10. . ! ! "! !2 & "! T ) "! !2 ! '. & ! & "! & '! +! !&&- ! '! & ' 10. " !! !, D (, D~ETe I({p ) , () / E ! J.8 ' .". s ! !8 ! )(" ! .'' , & ! T !' ' !' & ' ' (,' ! &. ' !' $ . , & "! $". F 0'" 9 !' '. ! !" ! F ",! @ , 4" / ( ", C)? 7 ! 8 & (,' ! + @"' <% F!"' A B. <- ) !' $ .(3.", ( $! += /!""! A % :K(!! et al % et al - .! / !( !' ! "! $". F 0'" ", !' !" * ,' + @" /"" et al #- ! 3.", & && & ,!" ! ! ! & ! " . $. +B. <- $ & *$". ! T "! ", $". !." &. ( ( $". $ ! "! ' ) ."! . !' /! ! 0!'", < & " .'( .("! F! / /$ . ! !"" !"", !$ (! /! ", ! !(. $ & / " 8 '! (! F! / " & T ! !&& ! (/ & . ",! 1 & Te estimates 60 60 0 0 -60 -60 Mid-oceanic TrenchSeamounts/ Fracture Zones ridges Outer Rise Ocean islands * + D! & T !' +! ) : ! )(" - . ! ! . , # GJI &'( <??<? <? Delta <?< A. B. Watts and S. Zhong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et al ?+@" /"" et al #+@" /"" et al #+@" /"" et al #+@" /"" et al #+5>! A /! #+., + et al <+ <+ <+ <+ <+ <+ <+ <+ <+ <+ <+ <+ <+ <+ <+B. A <+B. A <+B. A <+@ +@ +B. +: !2 A +@" /"" A ). +@" /"" A ). +@" /"" A ). +@>$ et al <+@>$ et al <+@>$ et al <+D'(2 <(+D'(2 <+ A !( <+ A !( <+B. <+B. <+B. <+B. <+B. <+B. <+B. <+B. <+ et al <+@>$ A :'! <+ A ! <+ A ! <+ A ! <+ A ! <# GJI &'( <??<? Flexure and rheology of oceanic lithosphere <? # + +Continued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et al <?+ et al <?+ et al <?+/! A !""! <?+F! et al <#+5. A '! <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' A @>$ <#+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' A @>$ <#+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+@"' <+B. <<+ A !2 <+ A B. <+'! et al <+'! et al <+F!"' A B. <+5 A !" +5 A !" +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al - <# A. B. Watts and S. Zhong # + +Continued- N ? # < ? # < ? # < ? # < ? ? ? ? ? ?? ?# ? ?< ? # # # # # #? ## # #< ), F F F F F F F F F F F F F F F F F ) ) ) ) ) ) ) ) ) ) F. @ .! = M @MG @MG ! ML" , !.> . !!. .! MC / @" ! @" ! @" ! @" ! @" ! @" ! @" ! @"! @"! . , . , . , . , N !$ N !$ N !$ N !$ B M . .M . B M@!" CM!9M! :" !! ='(! ! .!! ! L.! )!! L/!!M ! / = ' /! L 2! :$! :!2 : H.M@ "M H.M@ "M H.M@ "M H.M@ "M H.M@ "M? H.M@ "M# H.M@ "M @ ,M4" & 1 + < # ? ? ? # < ## ? ? < ?# #< #? # ? # ? ? < #? ? < ? # <? # # ? # ?? 1 +, ? ? ? ? ? ? ? ? ? ? # # ? ? ? < ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? & " +- D +, - T +2'- T +2'- # # ? ? < ? ? < < < ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? #? #? ?< < ?# # # # ? < ?? ?? ? ? # < # ? < # # ? ? ? ? ? ? ? ? & +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +@"' et al +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +" A L0(, +6. A B. +6. A B. +6. A B. + A @ += /!""! A += /!""! A += /!""! A += /!""! A += /!""! A += /!""! A += /!""! A += /!""! A +" +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' +L ! A @' + # GJI &'( <??<? Flexure and rheology of oceanic lithosphere <# # + +Continued- N ), # ? # < < < < < < <? <# ) ) ) ) ) ) ) ) ) ) ) F. @ ,M4" ="O ="O ".! !"" ! @!" 6 6$ 5. !" ! ! "M' ! . !""!! ).'. C MC MF"!0M!" ! & 1 +- 1 +, - & " +- D +, - ? ? ? ?#< # < # < #? ? < ? ? ? < ? ? ? ?? < ? ? T & +2'- T +2'- ? ? #< # # # ? ? # ? # ? ? ? < ? ? ? +:K(!! A @" +F! A ! +F! A ! +D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+D$! A /"" ?+4 et al ?+5 . et al +5 . et al +!."" A > - ='.I! !" ; ='.I! !" ! F ",! !% '='. 7(2 28 F ",! ! + "" '.- )= * . ! ,' := !$ " ='! *! ! F=& . > x= " $". .(3.", " (, $". ) $". $ ( " ! F! ? = $". + & . $. /"" (,' ,- " ) " 9 ' !'" "!! 9 (, +<- ( '. '"" (/ ! T & "! at the time of loading F. & ' ! + C' '.- $ "/ T &. & ' &&* ! + L/!! 4" - ) / '!"! / 0!'", & T !' &"" /!! # u@ ! ! ' ( "! " ' " ) '! 0! !' & ' & . > + ' !" * ,'- / T ( ,'* !"", ! ' '. ! !" ! F ",! ! / T ' ( "/ !' ." / ! F! ! T ! " !'! !2 & ! "! !& & ' . &*/$ . ! 4& / . & 0'" / !' & B!!'. A F , +<- /! $ ( & ! , & ,. +? - ! . & " +<# - . T ! ' ?? " !'! !2 /! ' $". (. " ""/! & !' ! 2 (.!" .(' ! !9 & ! $" T !' ! F! " " 4 !'! !* ' ( " & . ! & &/ &/ . )! . " ! !2 & "! '!"", . " '. & ' ! * ' !'! ! "* ' "! !2 ) !'" $ /! ! "0! . ! ", ! , ) ! $! ! "! ', !. "0 $ " !' F 0'" F! / " & T ! & "! & '. ! !" ) !' ". * ! /! # GJI &'( <??<? " &. (". ,. ) " . " '. ! !" $ "/ T ,. & !$ & ! "! ' &. + ? E! '.- $ "/ T (. , / & ' ,. "! !' & " ! /$ + ? "! '.- " "! / " , 3.! " !' & " ! 4& " ! F! ! !$ ! . "! ', "0 !'" " , ) !& & " *! . "0! ! ! "! .!$ & $!"! ($!. !(" 0"! & ! T !' * & ! ! $!"! " ' " !( (, B ! +#- 4 . ' " !!!" 10. ! "! (. $!. && (' ! !", !' /! !' +F! - F! ? / " & D ! " & '. ! !" / '" ! "! >< ) ( $ !' +9"" ! "- & ' "! 4 ! !9 ) "." . $ +"! "!- ( ! $!"! " ' " /! !!!" "! !2 T & 2' ! $". (. ! ! '! */, (/ & !' & !'! !2 + 2'- & >< ! "! ( . &*/$ . ! +B!!'. A F , <- ) 9. / ! $!"! " ' " 0"! " ! ( $ ! D /! ! ! " L/$ !" "0! !' 0"! all F. ' "0! !' 0"! ! " ' 4 !." ( $ ! D + !"". (, /- ( " ! .! 10 " ! * '+ " & "! !2 & ! "! T ! & "! !' & " ! ) ! ' ( "!*" ' " & A " +- ) !'! !2 ! ( B!!'. A F , +<- D ! / '!"", !"". && T & * ' + , - "0! ! "! * ,+ " & "! !2 & ! "! T ! & "! '. ! !" 3. / '. ! !" ! F ",! E! "! '. !. ! 0 @! " / '. ! !" 0". ! ! F ",! ) 3. ! " $ ( ". * & & " /! ! !! ,. (". " ) " . $ / , "! '!"", !"". && T & "* ' + , "0! ! "! <# A. B. Watts and S. Zhong # GJI &'( <??<? Flexure and rheology of oceanic lithosphere <# Load 0 Bulge Bulge Depth (km) 5 10 t/τ =1 Airy Elastic ( To = 90 km) Viscoelastic plate 15 Flexure t/τ = 10 Single Layer E = Maxwell relaxation time = viscosity E = Young's modulus 20 t/τ = 50 25 -800 -600 -400 -200 0 200 ρw = 1030 kg m-3 ρc = 2800 ρinfill = 2800 ρm = 3330 400 600 800 Distance (km) * &+ F"0. & ! $!"! " $ "! !$!! 1.! .( .' ) 10. ( '. & .' !!!" "! !2 T & 2' J.8 ' .". & = " ! !(.! / !! & " ' !" !" (, " !9"" !, '" & < < 2 'x !$", ! & tIt= ? / t ! 0/"" "0! !' t ! & " "!'! & /2 ! 9! L/$ $ / $!"! " ' " ! . /! !". !!!" /"" 9" "! !2 +5 <- ( $! !"" ( 0"! , -.%"!% .$!"/ * .#!.))$ -!%).#!% .!#010)) ) ! "! $!"! " ' " ", 0!* '! "* ' '!" ($!. & "!* ), ! , & "/ & ( !" .!" & '! & 2 '! (, ." & 0 !'" 2 '! B! , 0"!!", 2 ! . '" .. & "! ( ' " & /." ( ! ." & 0 !'" 2 '! /! / 2 ($ (, ( !" & '! ! . . ! .(! '" ! '"", !$ ! et al +<- . ' " ! & ' 0 !'" 2 '! '" .. "$ & 10. . (! !", " ), '. '' ! /! ,!" $" /! => +<- . & ' , "8 "/ & ( !" & '! : / "/ & .!" & '! &. 3.!$" 10. & . ", "! " &""/ /$ & @. , A .' +<- ! ( !" & * '! 9" . & ! ! /*&" F! ( !" & '! 9" ! !"" ", . ! "!" $! ! 10. " ' 12 '. ! !" & ,!" ! ! & ' & '" &."! ! ' . $ ! *"! ", /! ! "! "! $!!, ! &.! & ' . ("' & . (! (" "." # GJI &'( <??<? 10. & multilayered $!"! " ' " /! ! .(E (! !", " ,+ 1 2 3 ) & '."!", $!"! " " ( !( + - (, &""/! $ ! 3.!; pij, j zogdi ~ , () ui,i ~ , () / r ! !, g ! $!!" " ! uÅi ! $"!, + !"' ! / / 9 "!" 3.!- sij ! C3 +- +- 3.! & '! !.!, !$", ) "!" 3.! & !' !(" $!"! ' !.' + 0/"" ( ,- ( / ! pij z g p_ ij ~Pdij zg_eij , k () / m g ' .". $!!, !$", P ! ,'! . e ! ! ! ! !$!$ & $ !(" /! !' .' ! "$! 3 +-+- ( (' . & & & ' " & . & F !$ "! " & '!" ! + $!!, ' .".- / "$ 3.! ! ",!"", .' !"", "." / & '! " $ ! /! !' 4 ! ",!" .' !" ( &""/ )! ! (. / . "! ", /! !"* ' '"" ' /! " !2 !'!" / &""/ (, +- ! ! . , & $".! & "*/$" , & ! (" <# A. B. Watts and S. Zhong * 4+ @' ! & ( $ ! 10. " !! !, D '. ! !" & ' >< ! "! @! " / ( $ $". : 2 ! " / "" $". 0 & F ",! D! ! " / & F ",! ) ( $! ! !9 ! 0 " ( )(" "! 9", . $ / ! "!! (/ D & " ( ! $!"! " ' " ) ' " .' !!!" "! !2 T & 2' 0/"" "0! !' & ? # , "! . $ & " /! /$" l & ? 2' F!", . $ & " /! /$" & ? 2' ) "! / !!!" 10. " !! !, ( T & "!2", & !'! !2 & >< ! "! ) .9"" / / !(" ! ,+' 2 D( , . ! / & ' '! " '2 . ! "! ! '"", !$ F 0'" " "/ & ", ,""! "!$! ! !$ + 5 A . - (, n m e_ ~A(pIk) (bId) exp [{(EzPV )IRT] , (?) / A ! *0!" & s ! b ! " & . $ d ! ! !> n ! 0 m ! !*!> 0 E ! !$! , P ! '(! . V ! !$! $".' R ! .!$ " T ! ' . ) ! eÇ ! '! (, $!!, g s ! &""/ & ' 3 +?- p g~ ~gref exp [(EzPV )IRT] , e_ (#) / gref ~ k (pIk){n (bId){m : A 5 A . +- "". $ ! . "!" ' & "!$! $ , /! ", & !&& & '! '!' $"!" F 0'" ! !&&.! 0 ! (. ! ',( ! ? & !"! !'!" ", !$! , $ ! & ' ? 26 '"x & 7 ,8 '" 26 '"x & 7/8 '" # GJI &'( <??<? Flexure and rheology of oceanic lithosphere # '+ ,!" ' . ! '."!", $!"! ' " "."! . & . !! ! ." & '! '!' !> "! / &""/ 2 (, @. , A .' +<- .' "! ", +! 0 ! - "! ", ! * ! /! ." & 5 A . +- / ! . !"! ', ", ( !' "!$", ! ' . + '! *! ! - /!" !&&.! ! !' "/ ' . ! " & '. ! !" "!$", " +> - ! ! "! . ! "0! !$"$ !!9 ! & ! ""/ / '* . "!$", "/ +!(", # u@- ) & !&&.! ! ((", (" .'! & " ! 4& / .' "! ", + 3 #- $!!, ( 0 ! ' & & $!!, g & E P V R T ) ' P V R T "" ( !( & ! "! + )(" - P ! . ' /! ! !$ (, rgz / r ! $ !, & "! g ! $!!" " ! z ! % V ! !$! $".'% R ! N!$ " = @ T ! ' . ! 2"$! .' T ! !$ (, "! " ' " + A " - ! ! ' " $! !! & $ !! ! & 1 1/ /, & ' '! *! ! F! # !"". $!!, .. & ! "! ." ! $ , !!$ ' . ! (, >? & '!. /! ) '0!* '.' & ! ! . ' ?? 2' & "! /! ,. 1 /! ' ! ""/ " 1 " ! ' G". @ . '" ' .". )!2 & '" !8 ! :!, & . :!, & '" @ !$! $".' = $!!" " ! N!$ " = @ (b) Log10 Viscosity Age of Seafloor (Ma) 50 100 150 200 0 20 Pa s 30 35 a M 10 300 25 18 0 450 Depth ( km) 25 0 150 25 ? = 2' ? < 2 'x 2 'x ?rx# mx molx < ' x < 6 '"x uKx P V R T !( ", .2/ * ' g & E & . 3 +#- . $!!, 9" & "! ( $ !. $". & g & E 4 "."! $!!, 9" /! / 0!' .'( & ", +! ' #- & $!!, ) ", / !$! . $!!, ! (/ / E ", / "/, '"" ? F. ' '0!'.' $!!, / "!'! < ! ! $!!! !1. "."! "." & '."!* ", $!"! ' " " & $ !. !'* !"!, +! *: *:- . ! '" & "! !' & " ! (a) 0 <#? 50 600 50 75 900 75 100 100 E = 120 KJ/mol 1330 o C 125 125 η = reference ref viscosity * 5+ " & ' . .. $!!, & ! "! &.! & +- : $ . ' . ( "*"! ' " + A " - F!"" !" ! ! /! $!!, .. ( '. ! +(- +(- : $ . " & $!!, ( ' " ! /! ! '" ! '"", !$ ) "."! .' !$! , E & 56 '"x & $!!, g & . $!!, ! . '" + & ? 2'- ! # GJI &'( <??<? <## A. B. Watts and S. Zhong (a) (b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less & . ", ! ( " "0 " ! from the base upwards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lexure and rheology of oceanic lithosphere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t=- "! ! " " ) T !$", '"" /! !' .'." ! '" "0 !2 & "! . " & ' ! * ' !'! !2* ! "* ' !2 .! /$ "." T & &/ &/ . ', ."", !'! !2 )! ! (. / $ $ *!'"!9 "! ! & '" ) !'"!9! ." /$ && "* ' ($!. & "! F! ' ( $ ! !' & 10. " !! !, '. ! !" ) ( * $! ( ' . ! F! ? '. ! !" / " >< ! "! . " & / F! !'! !2 !!!" "! !2 & " ! "! ! ."!2", $ , !!9", ! ! !2 & " ! " ! && " *! . "0! /!"" " ( '"" ) ( $! $ ( ". * ! & "! !' & " ! /! '. ! !" & ' ,. "! & ' " "!* (". ) "." 10. " !! !, +"! "!- ! ( !! & '."!", $!"! ' " /! E= 56 '"x g &= & "!* !' & " ! & ? )! ' ( $! + ! ! F! - / !! 2 ! & ! "! !' & " ! & F! / ! 10. " !! !, & & "! !' & " ! & 0"! " 0!* '", . '! *! & ( $ 4& / 2 <#< A. B. Watts and S. Zhong Number 15 1e+26 10 5 0 0 30 60 90 120 150 180 Age of lithosphere at time of loading 1e+25 Flexural Rigidity De (N m) (a) To = 110 km Age of lithosphere at time of loading (Ma) To = 70 150 1e+24 100 90 80 150 110 Ma A 70 of lith ge at timosphere load e of 30 ing 1e+23 1e+22 (b) 1e+21 0.001 N = 51 Multilayered Viscoelastic Model E = 120 KJ/mol 20 ref = 10 Pa s 0.010 0.100 70 60 50 40 30 20 1.000 10.0 100.0 1000.0 10000.0 Age of Load (Ma) (c) * 9+ " & 2 ! ! (" !. & < '. ! !" / !' & . " T $!"(" ) ! (" !. !' ( =C@ ' !( (,' , 9" ) !' $ ( ". * ! +- & ! . +(- " +- T ! . & & "! !' & " ! ' & ( $ !' & 10. " !! !, &"" /!! /! / & "." $". $ ! ! & "!' & ( $! $ !'!" & "! !' & " ! " ! . $ !" ' ! & E= 56 '"x g &= & "", 0"! ( $ 10. " !! !, + T- !' *&& F! / & 0'" 10. " !! !, !' ! F! ." ( 3."", /"" 0"! (, ! ! & $!!, "/ !$! , "/ $!!, ! !$! , ) ! !! E g & ', $ , !"", F 0'" ' & !' & 10. " !! !, &"" .! & ! . $ (" / !' & ' L/!! ! +! /, .- / & ' C' '. +52.- / & ' '. /! ! /! ! 10. " !! !, 0 !' & ' F ",! + !- & ' * :+ @' ! & ( $ ! 10. " !! !, D '. ! !" & ' >< ! "! @! " / ( $ $". /! $ ( ". * ! & "! !' & " ! "! . $ / ! "!! (/ D & " ( '."!", $!"! " ' " ) ' " .' !$! , E & 26 '"x & $!!, & & ! "! at the time of loading & +$, "! "!- ? ) ! ! ' / 2 ! & "! !' & " ! ! ( $ "! +@ - /! ! /! "/ $". ) '". $". ', ! ! !" $ !! ! ! !$! , (" $!!, & "! ( & ' " !$", , ', !" $ !! ! ' . .. & "! ) & $!!, & g &= ! .' ! F! ( ! (" $!!, "! 3.!$"", !' & $!!, & . ' '" "!" (. . ! + . A "! <% G ' et al <- . ! * (" !' & $!!, & . ' '" ( !"", 3.! !" ! 4& ! $!!, ! " ! & .(! '" / 2 & ! $! A F +- . ' ! & ( $ ! 10. " !! !! !"". ! F! . 7(*98 !$! , & '" & 56 '"x )! ! " ? 56 '"x . (, @. , A .' +<- .! ' $!!, (. " T 4 ! " '"" ( . & ' "( , . ! & ", ,""! '" & "!$! 'E '! " !. & '" 5 A . +- & 0'" $ ! . !$! , & 7/8 7 ,8 '" & ' 56 '"x & "! !&&.! ? 56 '"x & *"! !"! L ! , (/ "( , 79" *( 8 ." ! . & & / 2/ . & ! ! (/ 9" *( "( , !' 4& 5 A . +- . !&&.! ! ' "!2", # GJI &'( <??<? Flexure and rheology of oceanic lithosphere Flexural Rigidity De (N m) 1e+26 4 1e+25 E = 300 K J/mol 1e+24 (a) 240 1e+23 120 20 1e+22 ref = 10 Pa s 60 Seafloor age at time of loading = 70 Ma 1e+21 0.001 0.010 0.100 1.000 10.0 100.0 1000.0 Age of Load (Ma) Flexural Rigidity De (N m) 1e+26 1e+25 1e+24 (b) ref = 10 21 Pa s 1e+23 1e+22 10 20 10 19 10 18 E = 120 KJ/mol Seafloor age at time of loading = 70 Ma 1e+21 0.001 0.010 0.100 1.000 10.0 100.0 1000.0 Age of Load (Ma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t= , - 10. ! "! + F! - " ! . ",! "! "0 ! ", . y? & .(3. 10. ! /!! 2 .(3. ! 10. "/ ! !*$!!, . ' ", & "! ) ." ! ! 2 &. , ' '. & 10. . . ! 9 2, & " ! ) ! 10. /! " $ "!" !'"!! " !'" ! "!" ! '"!. /$" & 10. L ! ! 7 '8 ( $! & 10. + $!, ! '"! 1 , 10 . & & ( & .- . , ', ( . /! 9 + et al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x . ! , .! /! ! " '! */, (/ L/!! . $ .(! & '' , x . ! ' ! F. ' ! ! "!" +" A " ##- . L/!! ( .(* ! ! & (. '' , x ! @! @28 " $!! !" ! ? ) ! $! L/!! ( .(! ! $ " !'" + A F ! <% A @'("" <% D. /! et al - :!" (,' ! & 0'" ! ! / & L/!! ! ! & & & ' /! & ' "$" . ! ! & "!$ "! (!"!, '" & ' & ,!" ! ( & ? 2 /!" '" & ?< ' & ,!" & ?? 2 + < A. B. Watts and S. Zhong * '+ ! 10. & '.*, $"! " & ' ! "! ) "* "! / !!!" +! t=- 10. "! "! / 10. 2, 2, , , , ) !! ( 7(*98 ' ! & !$! , & $!!, 0"! 10. " !! !, !' ! F! A @'("" <- ) . .(! & < '' , x & ??? 2 D. /! et al +- / '" $ . ! < '' , x $ ? ) !' ! ( ' /! ." & N !.'*( ! & .( !" (" ! !!9 !"" " ! (. & L!" L/!! ) 1 .(! & !" & L/!! as a whole ! . & ' ' ! & & & / & L/!! /! & !'!" . & D! & .! / " !" / $ " & 2!"' 7. '8 & L/!! ) . ! !$! ." & !" + A @'("" <- / . , ! ! / & L/!! 4" " !" !" & L/!! ( .(! ! " !" 7. '8 $ 0 ! ."!& = ! A 6 +- & 0'" $ . *"$" ! ! . " ( ! /$*. /$* .' '. & ."!& . . D! "2! . ! ? , )! . ,'! !&& ! !'! & ."!& " !" ) ."!& . & 0'" ? 2 .! ! / ((", ! 3.! & '"! & '! .(' ! & !" (.!" ! L/!! 4 D! 0 ! ."!& $ & ?? 2 /! ! /"" ! .( !" L/!! ! . ! &. & ' L/!! , D! ! ."!& . . ! ? 2 10. " (." ', $ '! " & L/!! 4" &&! . 9 D! ' ", $ . '."!", $!"! ' " !$!* / " & .(! ."!& L/!! . ' !" '! ( . (, ' & ' & " *! . "0! N& .", '."!" " ! ! , & !" ". !" ' ! & ' " ( $! L/$ ' !! ! "!$ " & "0! ( (! !& / .' +- .(' ! !9 & L/!! ! !' , " ! "! ! & ' ! ", / !"", '" (, ? % +- /! & .( !" " / .(3. ? / '"" ! ' ! /! & .(' ! " % +- "! . "! L/!! " ! ' !'!" ! /! '."!", $!"! " /." ! /! '" .. ! !( (, < ! "! '!" .. ! '! (, !$! , & 56 '"x (" $!!, & ! .'! / ', . '."!", ' " ! .(! ."!& ! , & *0!! !" &""/ '! & $"! " ! L/!! F! ' ( $ .(! ."!& /! !! ( '."!", $!"! ' " ) 9. / ."!& D! ( 3.! /"" . & (, ' " 4& E= 56 '"x & $!!, < ! " ."!& /!" $!!, > ! '"" & $!!, & 0"! (", /"" ! 7' 8 & (. ? 2 & !" ! ! D! /." $ ( ! L/!!8 10. " ' /." $ ( .(! ! ) & ' ! ! ' /! & ' & /! . .(! D! (. 2 + A @'("" <- ) & ."!& D! ". . t? 2 ! /$ .>>"! ! . '."!", ' " ."!& ." $ ( . $", (/ !' & ' , !(" 0"! ! ."!& ! & .'! !! L/$ = ! A 6 +- ! . ."!& !(. ! !" + "2!- / " $! & !.. ."!& / &$. ! !! & ."!& D! !&9." 0"! (, . ' " ! .(! ! , & L/!! !"& ) ( ("' /$ /! 0"!! " F # GJI &'( <??<? (a) Subsidence (m) Uplift (m) Flexure and rheology of oceanic lithosphere 19 a s 10 P 150 Lanai 100 20 10 Emergence age 50 Tsunami deposit ? 0 21 50 10 E = 120 kJ/mol 100 150 Age (Ma) Molokai Maui Oahu (b) Hawaii Lanai Terraces Bulge Migration Hilo Harbour Uplift (m) 1000 Hawaii 500 Drowning ages 0 (c) Subsidence (m) 500 1021Pa s 20 10 1000 19 10 E = 120 kJ/mol 1500 Terraces - Moore and Fornari ( 1984 ) Terraces - Ludwig et al ( 1991 ) Hilo Harbour Scientific Drilling Project 2000 0.5 0.4 0.3 0.2 0.1 0.0 Age (Ma) * ,+ @' ! & !! & '."!", $!"! ' " /! ( $! & ."!& .(! ! L/!! 4" )!2 "! / !! ( '."!", $!"! ' " /! E= 56 '"x & $!!, & x +- D! 4" "! ! " / ."!& ( = ! A 6 +- ) ! 2 x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x g &= $! ".!(" 0"! & .(* ! !"", / ! ! ! $"! 7 8 & "" " ! F! ." $ !&& A. B. Watts and S. Zhong 1500 Initial Height 1250 1000 750 500 250 Raitea Bora Bora Depth below sea-level (m) Thickness of Fringing Reef (m) Height above sea-level (m) < Sea Level 0 Kosrae Mayotte 250 Moorea 500 1420 m Ponape 750 1125 Mangareva 1000 1250 Truk Mid-Oceanic Ridge 1500 0 2 4 6 8 10 12 14 Depth after viscous relaxation 825 16 Age (Ma) * &+ " & !2 & & !! & "" &.! & $" F!"" ! " / ( $ !2 ( '!"! & +<- ) "! "! / ! .(! ( '."!", $!"! ' " /! E= 56 '"x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et al +- $ . !'! * 4+ ! ! , & 10. " ' 12 '. ! !" ( '."!", $!"! " ' " ) ! , ( '. & !0 !' :. ! ' ' , ( '. .! '."!", $!"! ' " /! E= 56 '"x & $!!, & !' .' 9"" ' . !>" . & +- ' , !$ (, 10. ( & ! . +! - +(- ' , !$ (, & ! . /! !". $"! " +- +(- 0 !' .' .'." & " " 4+, 2 < ) .(! ."!& ! , & ! !" ! '!& ", ! ! *. "!" " & (. " ! ! , & 10. " ' 12 ' ) ! / $! + et al <- & 0'" 12 & ! !" '. .(E " *" " &!". ) ' !" !$"$ ! &!". '$ /" ! 12! ' 4& ' ' , /! !' . '."!", $!* "! " ' " ! + F! - ! ! ! 7 !. 8 ',( 7* 8 & # GJI &'( <??<? Flexure and rheology of oceanic lithosphere 1! 9" !> ! ! . ! L/!! ' ), / *' 9" ' ! !> (, "/ ' .! " 10. " (." '! " &1! .! '! (2 / !" . ' .! ! & ' ), !(. &1 $ !! ! 1.0 & !' , ' !" ! ' . & 0'" & ! !$! ." !" ! ! .(E " *" 12 "" !&& !' et al +- " 0'! "*' 9" ), / & &1 " " ! "*' 9" ), !(. !$ " ! & "! " (, .!$ $" ! ! !" / . /! et al +- &1 " "*' 9" . !$ " ! & / ! !"", "! " / ! /! ! ! ! & &1 *' 9" ) ' " ! F! ? . $ !! ! ' !" 1.0 , & ' (, !" ", ' & 0"!! &1 $" ! 10. " ' ) &1 ." ( 3. & .! ! /! & ' . "0! ! . ",! "! N& .", ! ! !9"" ! 10. " ' ( ! ", &/ ""!! ! ! , !(" .! . ! ,! &."", 5 %"%.!" / &""/! ".! & ' ! . , +- ) "! !2 & ! "! T ! . (, $!. . ! &.! & '" & "! !' & " ! (! /"" !( (, # u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x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aci®c Sci., 20, ?# ! 6L 2" A < ( $! & 10. ", & ! "! J. geophys. Res., 86, #? /! @ A !""! 6 <? B!$ $!, '", $ ! !& $"",; ! *"! ! #uB Tectonophysics, 113, ?# , " 6: < F !! & 2 Pageoph, 116, #?## @" /"" 6= L0(, F 5 ! :C A ). :D # "!(!"!, & .!$ " "! 9" Earth planet. Sci. Lett., 31, # @" /"" 6= A ). :D : & "! !2 & ! "! J. geophys. Res., 84, ??# @"' < ) "! !2 & "! ! !9 Earth planet. Sci. Lett., 85, << @"' A @>$ <# ) &&!$ "! "! . @2*. " !, !" Earth planet. Sci. Lett., 77, < @"' F . 6 A @>$ C"! ", !2! /! & ! "! Geophys. J., 100, ?# < A. B. Watts and S. Zhong @" D ? The Viscosity of the Earth's Mantle, ! N!$ !, ! @>$ A :'! 5 < =! ! $ D.!$!"" ! +. !9- J. geophys. Res., 89, @>$ D :'! 5 A D'(2 5 < & "! '. " & ' = ""! "!' ( $! Geophys. J. R. astr. Soc., 63, ? @". : A 6 : ) ! , !9 " '! . & ' L/!!C' @! Geol. Soc. Am. Bull., 84, ?? @"! A . $ C # ) ''!" .. & C. !" "! ; ! & ' "!" 9" CC) !' Geophys. J. Int., 124, #? @ 6 = $!, '! !$!! ! =.! ! C3. !" "! Geol. Soc. Am. Bull., 84, #< @ 6 ",! & !, ! / " 8 ! ! J. geophys. Res., 84, @. , @ A .' @ < ) '"",*!$ 10. & ! "! Nature, 305, :K(!! 66 A @" 6 !'! & "! !2 & "! ! @ , !" .! '! &.! Geophys. Res. Lett., 21, ##? :K(!! 66 @" 6 A :! = !'! & "! !2 & "! ! @ , !" .! '! &.! Geophys. Res. Lett., 21, ##? : !2 A @ . ) < 4" .(! "! ! !! J. geophys. Res., 83, # : !2 A ",! & !, ! / " 8 !'! ! J. geophys. Res., 84, ##? F! A ! D! ! .. '! '!' & =" J. geophys. Res., 99, ## F!"' C A B. 5 < =! '"! $ @ , 4" = . Mar. geophys. Res., 11, < F! 5 B. 5 A . D <# ) '" '!" ! "! ( 3. /"" Nature, 332, # FE" 2 G!!, !2 & & ' F ! ."!& Earth planet. Sci. Lett., 126, => @ < ) '!' & ! "!$! Phil. Trans. R. Soc. Lond., 288, = /!""! A "!' ! (,' ! . , & "! !2 ! " !9 Earth. planet. Sci. Lett., 118, # = ! A 6 ) N"!& . (, "! ! 10. ! L/!! !" $" (, "$ " ! Mar. Geol., 141, ? =. 3.!!$ $".! & !1. & "! '"! & $!, Franklin Inst. J., 236, #? L ! B A @' : ' ! & '!" !2 !' & ' . '. " ! ! . =."& & "2 J. geophys. Res., 99, L! = A 5" :D # ! ! . '"; !'"!! & ", '" 0 ! $".! & "! Earth planet. Sci. Lett., 144, < 4 = B. 5 A =!( D ? @ ." .. & ).'. ". ? !'"!! & ! !! J. geophys. Res., 100, << 4/2! ) A .8. < H.!*! ." & '! . . & " ; "!" .. & C 8 . . '" J. Phys. Earth, 30, #?< 6. G A B. 5 ) "!! (/ " . $. "! " !2; . , & .@!" J. geophys. Res., 96, # #?# # 5 A . ", & N " Science, 260, < 5 =: < " ! & !! ' " BMR J. Aust. Geol. Geophys., 7, ??# 5 =: A !" 65 F ""! "! & ' !" & '! & ! "! ! @ " 4 ! J. geophys. Res., 95, ? < 5 . C D!. 6 B :F A :. C&&!$ "! !2 & "! " C '. @! J. geophys. Res., 102, ? 5. J A '! C <# F"0. !2! & "! C !9 ! Geophys. Res. Lett., 13, #<#< D'(2 5 < F"0. & "! & ' !" ."!& (,' , ! ! ( $!; !, 4" Geophys. J. R. astr. Soc., 67, D'(2 5 <( D! ! $"! " ! ! . @2 4" Earth planet. Sci. Lett., 55, <# D'(2 5 A B2!(". < '. " ! ! "! G!"! "!*$!"! ' " J. geophys. Res., 86, ###< D$! : A /"" :) ? D! ! ( ! .( .! > ( . ! ""! $!, J. geophys. Res., 100, D. /! 5 >( 6 6= A !'' 5 @ ." .(! & L/!! '! & ' NI<N & / " & Geology, 19, :@ A ! @F < ( $! & "! ! 10. / & J. geophys. Res., 89, :@ @" /"" 6= A ). :D < "! &", "! ( ! & "! . "!> " ! /! "!! 5. !" ) Geophys. J. Int., 54, # : ! @F A .". <? ( $! & 10. ; C$! & "! Tectonophysics, 116, @"" 5 #< G!!, & '" & ' "0! !' & !! E.' J. geophys. Res., 73, <? 5>! : A /! @ # ) "!! (/ (,' , $!, ! "! J. geophys. Res., 81, ? B. 5 @'! & ! ,; "!! & &.! !3. . $, J. geophys. Res., 84, ?<?< B. 5 < D! ! 10. '" '"! J. geophys. Res., 89, < B. 5 << ) '" '!" ! & @ G ! J. geophys. Res., 93, < B. 5 A L < D! ! 10. ."!& "" J. geophys. Res., 83, # B. 5 A 2 D < 4, ! . "! $".! & '! '!' Science, 199, ? 6 F , : A : !2 < / !* ! ' " & C !9 ! @ J. geophys. Res., 89, # L < 4." ! !, .(! Science, 220, !."" ) A > 6 = $!, '"! 10. & "! ! 4" Geophys. J. Int., 131, # ! $! 6 A F !" 9" & '" $!!,; ." & ' E! !$ ! & $! *"!" (. ( $(" J. geophys. Res., 102, ?# ! $! 6 A "! ) !& & '" $!!, & ' !$ ! & F ! "0! .' Geophys. J. Int., 114, ?# 6= "!! (/ .(! $"! " L/!! Bull. Volcanol., 34, ?#?# # GJI &'( <??<? Flexure and rheology of oceanic lithosphere 6= A @'("" 6F < & !" & L/!! J. geophys. Res., 92, ### 6 A F ! :6 < : / & ! ! & & .(! & !" & L/!! J. Geol., 92, ?? 6= @". : L"'( ) D!' B ' 2 A ) C < !. .(' ! " * "! L/!! ! J. geophys. Res., 94, #? < B ! # Theory of Flow and Fracture of Solids G" = /*L!"" B/ J 2 B/' A ! B ", & !" "!* !& & ' !' , (! Nature, 385, ## B!!'. @C A F , : < ) ! ! .. & . '" ! !9 Geophys. J., 96, C A " 6= ",! & $ !! & 1 (,' , 1/ /! J. geophys. Res., 82, << H.!" = A .' @ < "! .! "! ! 10. ">! ! , & 4 ! & B ' ! Can. J. Earth Sci., 21, # : !2 A @2", 6 !'! ! , & L/!! 10. " ' Geol. Soc. Am. Bull., 105, <? F A B. 5 < @ ! '" '!" .. & ! "! '. ! & ' ! ! '"! Earth planet. Sci. Lett., 93, " BL L $"!' '" ".' Ann. Rev. Earth planet. Sci., 20, " BL A "" B # ) '" ! 10. & '! *! "! ' !" (! Geophys. J. R. astr. Soc., 45, ?? '! LF . !" L A !" < ) "" '.; C ", @ . & . !9 !! '" '", J. geophys. Res., 94, ? ? ., C & '! ! . & " !; "!! & '! & L/!! ! PhD thesis, N!$ !, & L/!! L/!! !2 N A <? !'! ! , & 10. " ' 12! L/!! 4" Nature, 317, G ' DD ( !! :$! D. ! G .!"! ! @ A ! = < " $!!, !& & ' E! !$ ! & "! "!!*! . ! !" /! / D ",! " / Geophys. Res. Lett., 25, ## " 4 F"0. " !! !, $!!, & "! J. geophys. Res., 75, ? # GJI &'( <??<? <? " 4 ( F"0. & "! L/!! Tectonophysics, 9, ?# " 4 4! " ! & . ! @ Can. J. Earth Sci., 7, # A @ 6 = $!, '"! !, '" 1/ C !9 ! J. geophys. Res., 98, ?? ? < ",! & !, ! / " 8 ; L/!!C' '. ! J. geophys. Res., 83, ?<# @ ." .. $!, '"! 10. & "! ! @ , 4" Geophys. J. Int., 119, #<### A @ 6 = $!, '"! 10. & "! " L/!!C' '. ! Geophys. J. R. astr. Soc., 38, A !( B < ! ! 10. & "! '. J. geophys Res., 89, ? A !2 N < @ ." .. 10. .(! ! , & L/!! 4" J. geophys. Res., 94, ? @ 6 A "> = ? = $!, '"! 10. & "! ; * !'!" . , & = '. BC "! J. geophys. Res., 80, < ! 6L A !( B < ( $! & 10. "!" $".! & !9 (! Nature, 283, ?? ! @ @""! 6 :"/ @" 6 A L2 )6 !'! . , & "! ! 10. ! $!!!, & ) !& @ , 4" Earth planet. Sci. Lett., 146, " *0'!! & 10. " & '! ( L/!! 4" J. geophys. Res., 98, " A L0(, F ) '" !&& !" .(* ! 10. ! & . > J. geophys. Res., 95, ? " A '! LF F &/ " ' !", EOS, Trans. Am. geophys. Un., 72, # "& : < . (. "! !2 & ' "!!! E.' ! F ! J. Geophys., 61, . A "! < ="!" !! E.' & *! $!, '", ! '" $!!, Geophys. J. R. astr. Soc., 74, :,'! & ." '! ! !1. ." !, J. geophys. Res., 102, ? <?
© Copyright 2026 Paperzz