The effective elastic lithosphere under the Cook-Austral and Society islands

Earth and P1aneta(y 5c1ence Letter5, 77 (1986) 187-202 E15ev1er 5c1ence Pu6115her5 8.V., Am5terdam - Pr1nted 1n 7he Nether1and5

187

[5]

7he effect1ve e1a5t1c 11th05phere under the C00k-Au5tra1 and 50c1ety 151and5 5tephane Ca1mant and Anny Ca2enave 6r0upe de Recherche de 6~0d651e 5pat1a1e, C.N.E.5., 18 Avenue E. 8e11n, 31055 70u10u5e Cedex (France) Rece1ved Ju1y 8, 1985; rev15ed ver510n accepted N0vem6er 30, 1985 We have determ1ned the e1a5t1c th1ckne55 7¢ 0f the 0cean1c 11th05phere a10n9 tw0 v01can1c cha1n5 0f the 50uth Centra1 Pac1f1c: C00k-Au5tra1 and 50c1ety 151and5. We u5ed a three-d1men510na1 5pat1a1 meth0d t0 m0de1 the 11th05pher1c f1exure a55um1n9 a c0nt1nu0u5 e1a5t1c p1ate. 7he m0de1 wa5 c0n5tra1ned 6y 9e01d he19ht data fr0m the 5EA5A7 5ate111te. A10n9 the C00k-Au5tra1 cha1n the e1a5t1c th1ckne55 1ncrea5e5 we5tward, fr0m 2-4 km at McD0na1d h0t 5p0t t0 - 14 km at Rar0t0n9a. At McD0na1d 5eam0unt, h0wever, the data are 6etter exp1a1ned 6y a 10ca1 c0mpen5at10n m0de1. 7he 065erved trend 5h0w5 an 1ncrea5e 0f 7e w1th a9e 0f p1ate at 10ad1n9 t1me. H0wever, the e1a5t1c 1ayer under the C00k-Au5tra1 appear5 5y5temat1ca11y th1nner 6y 5evera1 k110meter5 than expected f0r ••n0rma1•• 5eaf100r, 5u99e5t1n9 that 5u65tant1a1 therma1 th1nn1n9 ha5 taken p1ace 1n th15 re910n. C0n51der1n9 the apparent therma1 a9e 0f the p1ate 1n5tead 0f cru5ta1 a9e 1mpr0ve5 n0t1cea61y the re5u1t5. A10n9 the 50c1ety cha1n 7~ var1e5 fr0m 20 km under 7ah1t1 t0 13 km under Maup1t1 wh1ch 15 10cated - 500 km we5tward. When p10tt1n9 t09ether the 50c1ety and C00k-Au5tra1 7~ re5u1t5 ver5u5 a9e 0f 10ad, we n0t1ce that w1th1n the f1r5t f1ve m11110n year5 after 10ad1n9, 7~ decrea5e5 519n1f1cant1y wh11e tend1n9 rap1d1y t0 an e4u1116r1um va1ue. 7h15 may 6e 1nterpreted a5 the effect 0f 1n1t1a1 5tre55 re1axat10n wh1ch 0ccur5 ju5t after 10ad1n9 1n51de the 10wer 11th05phere and 5u99e5t5 that the pre5ent1y mea5ured e1a5t1c th1ckne55 under the very y0un9 7ah1t1 10ad ( - 0.8 Ma) 15 n0t yet the e4u1116r1um th1ckne55.

1. 1ntr0duct10n

Much 1n519ht ha5 6een 9a1ned 1n the 1a5t decade 0n the rhe0109y 0f the Earth 11th05phere fr0m f1exure 5tud1e5. 7he m05t w1de1y u5ed m0de1 0f f1exure a55ume5 that the 11th05phere re5p0nd5 a5 an e1a5t1c p1ate t0 5urface 10ad1n9 0ver 9e01091ca1 t1me 5ca1e5 a1th0u9h the v15c0e1a5t1c m0de1 ha5 a150 6een c0n51dered. 7he e1a5t1c m0de1 ha5 6een app11ed t0 60th c0nt1nenta1 and 0cean1c 11th05phere 6ut 1t 15 1n the 0cean5 that 1t ha5 pr0ved t0 6e the m05t 5ucce55fu1 1n 5h0w1n9 up a 51mp1e re1at10n5h1p 6etween the th1ckne55 7e 0f the e1a5t1c 11th05phere w1th a9e 0f the p1ate at the t1me 0f 10ad1n9:Watt5 [1] and Watt5 et a1. [2] 5h0wed that t0 f1r5t 0rder the e1a5t1c th1ckne55 1ncrea5e5 11near1y w1th the 54uare r00t 0f p1ate a9e at 10ad1n9 t1me and 6y ana109y w1th the therma1 c0011n9 6ehav10ur 0f the 0cean1c 11th05phere, 5u99e5ted that the 6a5e 0f the e1a5t1c 1ayer c01nc1de5 r0u9h1y w1th the 450°C 150therm. C011ect1n9 a11 ava11a61e e5t1mate5 0f e1a5t1c th1ckne55 made 6y 5evera1 auth0r5 1n var10u5 0cean1c area5, Watt5 et a1. [3] and further Watt5 and R16e [4] n0t1ced that th15 51mp1e 5cheme h01d5 900d f0r a w1de var1ety 0f tect0n1c 0012-821X/86/$03.50

~ 1986 E15ev1er 5c1ence Pu6115her5 8.V.

area5 and a w1de ran9e 0f a9e5 (5ee F19. 1). When 100k1n9 at F19. 1, h0wever, 1t appear5 that the 5catter 15 re1at1ve1y 1ar9e. At 1ea5t three rea50n5 may 6e 1nv0ked: (1) the 5catter revea15 rea1 d1fference 0f the 11th05phere re5p0n5e t0 10ad1n9 due t0 d1fferent tect0n1c 5tate5, (2) the 5catter re5u1t5 fr0m putt1n9 t09ether re5u1t5 06ta1ned 6y d1fferent auth0r5, 5evera1 meth0d5 6e1n9 current1y deve10ped t0 m0de1 e1a5t1c f1exture, (3) the 5catter 15 due t0 uncerta1nty 1n e1ther a9e 0f 10ad5 0r a9e 0f p1ate. Rea50n 0ne ha5 6een d15cu55ed 6y McNutt [5] wh0 n0t1ced that the e1a5t1c th1ckne55 15 5ma11er 6eneath 151and5 and 5eam0unt5 c0mpared t0 11th05phere 0f 51m11ar a9e f1exed at 5u6duct10n 20ne5: trench data tend t0 f0110w the 550-600°C 150therm wherea5 7~ va1ue5 e5t1mated fr0m 5eam0unt 10ad5 f0110w rather the 300°C 150therm. Rea50n tw0 may have a150 50me 1nf1uence: 11th05pher1c f1exure ha5 6een m0de1ed e1ther w1th 2-D 0r 3-D appr0ache5, e1ther 1n the 5pectra1 d0ma1n (adm1ttance) 0r 1n the 5pat1a1 d0ma1n; 1n the 1atter ca5e, e1ther w1th ana1yt1ca1 m0de15 a55um1n9 10ad5 0f 51mp1e 9e0metry 0r numer1ca1 m0de15 c0nven1ent f0r 10ad5 0f ar61trary 5hape. F1na11y, the e1a5t1c p1ate ha5 6een c0n51dered e1ther c0nt1nu0u5 0r

188 A 6 E 0 F P L A 7 E A 7 71ME 0 F L 0 A D 1 N 6 (Ma) 0 1a 10

~

20 J

40 ,

60 ,

80 ,

100 ,

120 1

140 ,

160 ,

180 ,

2 6

15

20 300"C

¢J 30

1507HERM

u~ 40-

50-

600••C 1507HERM 60-

3-D numer1ca1 appr0ach 1n the 5pat1a1 d0ma1n, a55um1n9 a c0nt1nu0u5 e1a5t1c p1ate. 7heref0re, c0mpar1n9 re5u1t5 f0r d1fferent 10ad5 5h0u1d 6e free fr0m m0de1 effect5. A5 far a5 a9e 0f p1ate and a9e 0f 10ad5 are kn0wn, the u5e 0f 5 E A 5 A 7 9e01d data a5 c0n5tra1nt5 0n the m0de1 a110w5 5uch an ana1y515 t0 6e c0nducted 5y5temat1ca11y 0ver 0cean1c area5. Here, we pre5ent re5u1t5 0f 7~ a10n9 tw0 v01can1c cha1n5 0f the 50uth Centra1 Pac1f1c (C00k-Au5tra1 and 50c1ety cha1n5) wh1ch are emp1aced 0n 6r0ad t0p09raph1c 5we115.

70-

2. 7he C00k-Au5tra1 cha1n 80-

90-

100 110

~ r~;~,0 ~

12C

F19. 1. E1a5t1c th1ckne55 7¢ (km) 0f the 0cean1c p1ate ver5u5 a9e 0f p1ate at the t1me 0f 10ad1n9 (Ma). R e d r a w n f r 0 m W a t t 5 a n d R16e [4]. 5ym6015: 1a = Ea5t Pac1f1c R15e cre5t, 16 = M1dAt1ant1c R1d9e cre5t, 2 = J u a n de F u c a R1d9e cre5t, 3 = M1dAt1ant1c R1d9e cre5t, 4a = N a n k a 1 7 r 0 u 9 h , 46 = M1dd1e A m e r 1 c a 7 r e n c h , 4c = Kur11 7 r e n c h , 4 d = M a r 1 a n a 7 r e n c h , 4e = A1eut1an 7 r e n c h , 5a ~ E m p e r 0 r 5 e a m 0 u n t 5 n 0 r t h 0f 4 0 ° N , 56 ~ Hawa11an R1d9e 50uth 0f 4 0 ° N , 6 = Pac1f1c 0 c e a n at0115, 7 = 6 r e a t M e t e 0 r 5 e a m 0 u n t , 8 = Kur11 7 r e n c h , 9a = A1eut1an 7 r e n c h , 96 = Kur11 7 r e n c h , 9c = 8 0 n 1 n 7 r e n c h , 9 d = M a r 1 a n a 7 r e n c h , 10 = Hawa11an R1d9e, 11 = Hawa11 151and, 12 = we5tern Wa1v15 R1d9e, 13a = M a r 4 u e 5 a 5 151and, 136 = 50c1ety 151and5, 13e = Cr02et 151and, 14 = A m a 2 0 n c0ne, 15 R a r 0 t 0 n 9 a , 16 = 50c1ety 151and. 7 h e 6 r 0 k e n cr055e5 1nd1cate e5t1mate5 t h a t e1ther repre5ent 6 r 0 a d re910n5 r a t h e r t h a n a n 1nd1v1dua1 9e01091ca1 f e a t u r e (5, 6) 0r a r e c0n51dered unre11a61e ( 4 c ) . 5011d 54uare5 are f0r t 0 p 0 9 r a p h 1 c re11ef 0f 0cean1c 1ayer 2, 0 p e n c1rc1e5 f0r r1ver de1ta5, 5011d c1rc1e5 f0r 5 e a m 0 u n t 5 a n d 0cean1c 151and5, 5011d tr1an91e5 f0r deep-5ea t r e n c h - 0 u t e r r15e 5y5tem5. 7 h e 5011d curve5 repre5ent the 3 0 0 ° C a n d 6 0 0 ° C 150therm5.

fractured under the 10ad. Rea50n three n0 d0u6t take5 a150 part 1n the 5catter. 7he pre5ent paper 15 part 0f a m0re 9enera1 5tudy 0n the e1a5t1c th1ckne55 determ1nat10n 1n the 0cean5 u51n9 9e01d data der1ved fr0m the 5 E A 5 A 7 a1t1meter 5ate111te. 7he 06ject1ve 15 t0 determ1ne 1f 5ec0nd-0rder var1at10n5 0f 7~ can 6e detected f0r d1fferent tect0n1c c0nd1t10n5 0f 10ad1n9 (10ad5 f0rm1n9 near r1d9e5, 1n 5we11 area5, 1n 01d 6a51n5, etc.). We u5e a un14ue m0de1 0f f1exure 6a5ed 0n a

7he C00k-Au5tra1 cha1n 15 a v01can1c cha1n 0f 5eam0unt5 and 151and5 0f the 50uth Centra1 Pac1f1c extend1n9 n0rthwe5t 0ver a d15tance 0f a60ut 2000 km fr0m McD0na1d 5eam0unt wh1ch 15 v01can1ca11y act1ve [6]. 7he cha1n 15 made 0f tw0 9r0up5: (1) the Au5tra1 151and5 1nc1ud1n9 McD0na1d and the 151and5 0f Rapa, Ra1vavae, 7u6ua1, Rurutu and Mar1a, and (2) the 50uthern C00k 151and5, w1th Mauke, At1u, Manuae, A1tutak1 and Pa1mer5t0n At011. 50uth 0f the C00k 151and5 9r0up 11e Rar0t0n9a and Man9a1a 151and5. 7he 6athymetry 0f the C00k-Au5tra1 cha1n 15 5h0wn 1n F19. 2. P0ta551um-ar90n a9e5 are ava11a61e f0r a num6er 0f 151and5 [7-10]. 7a61e 1 9ather5 ava11a61e a9e e5t1mate5 a10n9 the cha1n a5 5ummar12ed 6y McD0u9a11 and Duncan [11] and Jarrard and C1a9ue [12]. C0nc0rdant a9e5 are rep0rted f0r A1tutak1 and Rar0t0n9a 151and5 wh1ch appear P1e15t0cene 1n a9e. F0r Rurutu, tw0 e5t1mate5 91ve P1e15t0cene a9e, wherea5 an a9e 0f - 12 Ma 15 mea5ured 6y Duncan and McD0u9a11 [10]. F0r Ra1vavae and 7u6ua1, e5t1mate5 0f K / A r [7] are th0u9ht unre11a61e [12]. 1n 0ur ana1y515, we w111prefer the Duncan and McD0u9a11 [10] e5t1mate5.7he 01de5t rec0rded a9e 15 that 0f Man9a1a 151and wh1ch 15 5u99e5ted t0 6e f0rmed 6y McD0na1d h0t5p0t 51nce 1t f1t5 we11 the 11near a9e 1ncrea5e a10n9 the Au5tra1 cha1n [11]. 7he 50uthern C00k 151and5 m0re t0 the we5t are much y0un9er and c0ntrad1ct the pr09re551ve a9e 1ncrea5e 065erved f0r many v01can1c cha1n5 0f the Pac1f1c, ref1ect1n9 a c0mp11cated 51tuat10n and 1eav1n9 the 0r191n 0f the5e 151and5 a5 yet n0t under5t00d. A9e5 0f the 50uthern C00k 151and5 are d15cu55ed 1n Lam6eck [13]. He fav0ur5 an a9e 0f - 7 Ma f0r A1tutak1. N0 p0ta551um-ar90n a9e 15 ava11a61e f0r At1u wh11e an 01d e5t1mate 0f f0ram1n1fera

189

-26 00

-25

-301 40

0 F19. 2. 8athymetry 0f the C00k-Au5tra1 cha1n w1th the 11m1t5 0f the 5tud1ed 10ca1 map5 and 5e1ected 5 E A 5 A 7 track5. 7he 5tud1ed 1en9th 0f the track5 15 1nd1cated 6y the th1ck 5011d f1ne.

a9e 0f - 5 Ma 15 rep0rted 6y Jarrard and C1a9ue [12]. 7he 151and5 0f R1mat0ra and Mar1a pre5uma61y 6e10n91n9 t0 the Au5tra1 9r0up have n0t 6een dated. 51nce we e5t1mate the f1exura1 r191d1ty 0f the 11th05phere at the5e tw0 151and5, tentat1ve a9e5 are pr0p05ed 6y 1nterp01at1n9 the 4ua51-11near a9e 1n-

crea5e trend 065erved 6y Duncan and McD0u9a11 [11] a10n9 the Au5tra1 cha1n, a55um1n9 an avera9e rate 0f m19rat10n 0f 10.7 c m / y r a5 rep0rted 6y the5e auth0r5. 7 h e a9e 0f the cru5t a10n9 the cha1n 15 n0t we11 kn0wn 51nce ma9net1c an0ma11e5 are a65ent 6e-

7A8LE 1 A9e 0f v01can1c 10ad5 1mp1aced a10n9 the C00k-Au5tra1 cha1n 5eam0unt 0r 151and

L0cat10n

A9e ran9e (Ma)

50urce

Qua11ty

McD0na1d Rapa Ra1vavae

29.0°5, 140.2°W 27.6°5, 144.3°W 23.9°5, 147.7°W

7u6ua1

23.3°5, 149.5°W

Rurutu

22.4°5, 151.3°W

Man9a1a At1u Rar0t0n9a A1tutak1

21.9°5, 20.0°5, 21.2°5, 18.7°5,

0 5.0-5.2 3.3-14.1 5.52-7.41 10.8-24.9 8.6-10.4 0.5 1.05-1.09 11.97-12.04 16.6-18.9 3.5-5 1.19-1.83 0.7 0.66-0.77 > 7

cf. [6] cf. [7] cf. [7] cf. [10] cf. [7] cf. [10] cf. [7] cf. [8] cf. [10] cf. [8] cf. [12] cf. [8] cf. [7] cf. [8] cf. [9]

900d 900d p00r 900d p00r 900d 900d 900d 900d 900d p00r 900d 900d 900d 900d

157.9°W 158.2°W 159.8°W 159.8°W

L0cat10n

-

-

29.0 ° • 1 4 0 . 2 ° W 27.5 ° • 144.5°W 24.0 ° , 1 4 7 . 5 ° W 23.3 °, 1 4 9 . 5 ° W 22.7 °. 1 5 2 . 7 5 ° W 22.0 ° 1 5 4 . 7 ° W 21.9 ° 157.9°W 20.0 ° 1 5 8 . 2 ° W 20.1° 157.3°W 18.7 ° 1 5 9 . 8 ° W 21.2 ° 1 5 9 . 8 ° W

7ah1t1 80ra-80ra Maup1t1

-17.6 °,149.5°W -16.6°,151.3°W -16.4°,152.3°W

50c1e0, 151and5 cha1n

McD0na1d Rapa Ra1vavae 7u6ua1 R1mat0ra Mar1a Man9a1a At1u Mauke A1tutak1 Rar0t0n9a

C00k-A u5tra1 cha1n

L0ca1 map

Mehet1a 150 480 480

McD0na1d 0 430 950 1130 1420 1610 1890 2230 2140 2450 2380

D15tance f r 0 m h0t 5p0t (km)

0.8+(1.2 3.2+•0.1 4.2-+0.2

0 5.1-+0.1 6.4-+0.75 9.3+0.75 (13.5) (15.0) 17.7+0.8 -4(~) -5(~) - 7(•) 1.5-+0.3

5eam0unt a9e (Ma)

70 + 5 75 + 5 76.5-+5

43 -+2 52 -+5 65 -+5 70 + 5 78 -+5 80 -+5 85 + 5 87 + 5 85 -+5 87 + 5 87 -+5

Cru5ta1 a9e ( M a )

69 + 5 72 •+5 72.5-+5

43 -+2 47 + 5 58.5-+5 60.5-+5 64.5+5 65 + 5 67.5-+5 82.5+5 80 -+5 80 -+5 85.5+5

P1ate a9e at 10ad1n9 t1me ( M a )

3600+10(1 3800+100 4000-+100

3700+100 3750+100 4150+100 4300+100 4400-+100 4400-+100 4500•+100 4450+100 4450_+100 4500+100 4450-+100

D e p t h 0f 5eam0unt 6a5ement (m)

5.4(4.6) 9 (5.81 13.5(9.31

7 (7) 8 (3.) 17.3(10.81 21.8(12.3) 25 (11.51 25 (10) 28.5(10.8) 27.6(20.61 26.7(22.71 28.5 (24.51 26.7(25.)

7herma1 a9e ( M a ) t~.rr (7)

7 3 2

~ - 2 × 1 0 22 +•1X1022 - + 0 . 5 x 1 0 ~2

~1x102° ~<1×102° 0 . 7 + 0 . 2 × 1 0 "-2 0 . 5 - + 0 . 1 × 1 0 22 0.9-+0.3x1022 0.9+0.1×1022 0 . 3 • + 0 . 1 × 1 0 22 0.8+0.3×1022 1 . 5 + 0 . 6 × 1 0 2: 0.9+0.3x102: 2 -+0.5×10:2

D (N m)

20 15 13

-+2 +1.5 -+1

~<4 ~<4 9 -+1 8 +0.5 10 + 1 10 -+0.5 7 +0.5 9.5_+1 11 -+1.5 10 -+1 14 + 1

7~ (km)

3 3 1

2 13 1 2 1 2 2 2 1 1 1

Num6er 0f p r 0 f11e5

C00rd1nate5 0f 10ad5 5tud1ed, d15tance f r 0 m h0t 5p0t, 10ad a9e, cru5ta1 a9e, t 1, d e p t h 0f 5 e a m 0 u n t 6 a 5 e m e n t . tef f a n d [, re5u1t5 f0r D, e4u1va1ent 7~, n u m 6 e r 0f pr0f11e5

7A8LE 2

6

,%

191

y0nd the Au5tra1 151and5 9r0up (Cretace0u5 4u1et 20ne [14]). Ma9net1c an0ma1y 18 15 c1ear1y 1dent1f1ed near McD0na1d 5eam0unt ( - 4 3 Ma). 7he we5tward p0rt10n 0f the cru5t 50uth 0f the Au5tra1 151and5 1ncrea5e5 1n a9e up t0 - 70 Ma (ma9net1c an0ma1y 30 15 1dent1f1ed near - 1 4 8 ° W ) . 70 e5t1mate the a9e 0f the cru5t a10n9 the Au5tra1 and C00k 151and5, we u5e the 150chr0n5 map e5ta6115hed 6y 5c1ater et a1. [15]. 7he5e auth0r5 ca1cu1ated the p051t10n 0f 150chr0n5 u51n9 (1) ma9net1c an0ma1y 1dent1f1cat10n, (2) deep-5ea dr1111n9 re5u1t5, and (3) r0tat10n 0f pre5ent r1d9e axe5 (deta115 0f the meth0d can 6e f0und 1n the1r paper). 7hen we 1nterp01ate 11near1y 6etween the 150chr0n5 p051t10n5. 7he a9e5 0f cru5t 5urr0und1n9 the v01can0e5 c0n51dered 1n th15 5tudy are 91ven 1n 7a61e 2. 3. E1a5t1c th1ckne55 Au5tra1 cha1n

e5t1mate5

a10n9

the

C00k-

3.1. M0de1 7he e4u1116r1um e4uat10n expre551n9 the def0rmat10n w(x, y) 0f a c0nt1nu0u5 e1a5t1c p1ate 0ver1y1n9 a f1u1d med1um 15: D V 4 W -]- ( P m

-- 10c)9 W =

P

(1)

where w 15 p051t1ve d0wnward5; Pm, Pc = den51ty 0f a5then05pher1c and cru5ta1 r0ck5; 9 = mean 5urface 9rav1ty; P = the 10ad e4ua1 t0 (P1 - P,,)9h1 (h 1= he19ht 0f 10ad a60ve 5eaf100r, Pw = 5eawater den51ty, Pt = 10ad den51ty); D = f1exura1 r191d1ty e4ua1 t0 E7¢3/12(1 - u2) w1th E, u = Y0un9 m0du1u5 and P01550n rat10, re5pect1ve1y. 7he parameter t0 determ1ne 15 D thu5 7¢. 7he 501ut10n w(x, y) 0f e4uat10n (1) 15 06ta1ned 0ver a re9u1ar 9r1d 6y 1nte9rat1n9 numer1ca11y 0ver the v01ume 0f the 10ad 0nce the 6athymetry h~ 15 kn0wn 0ver the 9r1d: the meth0d we u5e 15 that deve10ped 6y Watt5 [16] and further app11ed 6y Ca2enave et a1. [17] and Ca2enave and D0m1nh [18]. 0 n c e the def1ect10n w(x, y) 15 kn0wn, we c0mpute the 9e01d an0ma1y 0ver the 9r1d due t0 (1) the c0ntra5t den51ty 0f the def0rmed M0h0 and 0f eventua11y the f111-1n 0f the def1ect10n, (2) the den51ty c0ntra5t 0f the 10ad. 7h15 15 a150 d0ne numer1ca11y u51n9 a three-d1men510na1 appr0ach (5ee [18]). 7he cru5ta1 th1ckne55 7~ 15 1eft a5 an unkn0wn 4uant1ty adju5ted 51mu1tane0u51y w1th D. 7he c0mputed 9e01d 15 c0mpared t0 the 065erved 0ne f0r 5evera1 va1ue5 0f D and 7c.

3.2. Ana1y515 0f 6athymetry and 9e01d data; re5u1t5 7he 6athymetry data 50urce 15 the 5 Y N 8 A P 5 data 6a5e ava11a61e fr0m the N 0 A A 91v1n9 depth 0n a 5• × 5• re9u1ar 9r1d 0ver the 0cean5. Numer0u5 5EA5A7 a1t1meter pr0f11e5 cr055 the C00kAu5tra1 cha1n. 7he5e pr0f11e5 have 6een u5ed t0 c0mpute the 3-D 9e01d 0ver a 0.25 ° × 0.25 ° re9u1ar 9r1d 5h0wn 1n F19. 3. 1n 0rder t0 detect any var1at10n 0f 7~ a10n9 the cha1n, we have c0mputed the def1ect10n 5eparate1y f0r 13 5eam0unt5 0f the cha1n. 70 d0 th15, we have c0n51dered the 6athymetry 0ver 5ma11 area5 0f a60ut 10 54uare de9ree5 c0ver1n9 each 5e1ected 5eam0unt (5ee F19. 2) and have c0mputed f0r each 10ca1 map the def1ect10n f0r 5evera1 va1ue5 0f D ran91n9 fr0m 5 × 10 ~ t0 10 2~ N m. 7hen we have deduced the 6e5t f1tt1n9 va1ue 0f D 6y c0mpar1n9 065erved and c0mputed 9e01d an0ma11e5. 7he cru5ta1 th1ckne55 ha5 a150 6een var1ed fr0m 6 t0 12 km at 2-km 1nterva15. We have a55umed p~ = Pc = 2.8 M9 m -~ and 0,,, = 3.4 M9 m ~. 7he a1t1metry mea5urement 91ve5 the 9e01d he19ht a10n9 the 5u65ate111te track5. Am0n9 a11 5EA5A7 track5 pa551n9 thr0u9h the d191t12ed map5, we have 5e1ected th05e wh1ch are c105e t0 the 5umm1t5 w1th0ut cr0551n9 an emer9ed part 0f the 151and5 t0 1n5ure the 519na1 ha5 n0t 6een d15tur6ed. 70 c0mpare the 9e01d he19ht5 pred1cted 6y the m0de1 w1th th05e fr0m 5EA5A7, tw0 meth0d5 are p055161e: - - E1ther we extrap01ate 0n a re9u1ar 9r1d the 065erved va1ue5 and c0mpare the tw0 map5. - - 0 r we 1nterp01ate the the0ret1ca1 10ca1 map5 a10n9 the 5ate111te track5 and c0mpare the pr0f11e5. We prefer the 5ec0nd 501ut10n wh1ch d0e5 n0t m0d1fy 1n any way the data them5e1ve5 and a110w5 5evera1 1ndependent determ1nat10n5. 7he 0n1y m0d1f1cat10n we have made t0 the 5EA5A7 9e01d data ha5 c0n515ted 1n m0v1n9 0ut the 10n9 wave1en9th5 ( > 1000 km) 1n 5u6tract1n9 the 9106a1 9e0p0tent1a1 m0de1 6 R 1 M 3L1 c0mp1ete t0 de9ree 36 (8a1m1n0, 1n preparat10n). 7he 1nterp01at10n wa5 made w1th the La9ran91an p01yn0m1a1 meth0d:

h(x,,)= 1=1

=

j4:1 H

x 2••• k=1

=

1~k

h(x,,

(2)

192

~N

• 7"

/

--~¢=405

// F19. 3. 7hree-d1men510na1 map 0f the 5EA5A7 9e01d he19ht5 0ver the 50uth Centra1 151and5, 3 = 5 0 u t h e r n C 0 0 k 151and5, 4 = Au5tra1 151and5, 5 = L0u15v111e R1d9e, 6 = 7 0 n 9 a

h ( ~ , ~) 15 the 9e01d he19ht 1nterp01ated at 1at1tude and 10n91tude ~ (~1 ~< ~ ~< ~N and ~1 ~< ~ ~< ~M)1ndexed c00rd1nate5 refer t0 the the0ret1ca1 9r1d. 7 0 c0mpare an 065erved pr0f11e w1th the 5et 0f the0ret1ca1 pr0f11e5 c0mputed f0r 5evera1 D va1ue5 we pr0ceed 1n tw0 5tep5. F1r5t we app1y the u5ua1

Pac1f1c. 1 = M a r 4 u e 5 a 5 151and5, and Kermadec trenche5.

2 ~

50c1ety

cr1ter10n 0f m1n1m12at10n 0f the 5um 0f 54uared re51dua15:

E 1=1

(3)

193

where H(x) and 5(x) are c0mputed a n d 065erved 9e01d he19ht a10n9 the curv111near c00rd1nate x. Np 15 the num6er 0f x p01nt5 a10n9 the pr0f11e and c 15 91ven 6y: ]

1021 •

1022 ,

1023 1

0~Nm~

Np

c=~~, [H(x1)-5(x,) ] "v

(4)

t=1

7he 6e5t f1tt1n9 D va1ue 15 deduced fr0m the m1n1mum 0f the r00t mean 54uare (r.m.5.) curve 6etween 065erved and c0mputed 9e01d he19ht5. 1n 50me 1n5tance5 th15 curve 15 rather f1at 50 that the 6e5t f1tt1n9 D 15 d1ff1cu1t t0 e5t1mate. F0r th15 rea50n, we app1y 5y5temat1ca11y an0ther cr1ter10n 0f m1n1m12at10n 6a5ed up0n 9enera1 11near 1ea5t 54uare5 and expre55ed 6y: up

,•= E [ m x , ) - a 5 ( x , ) - 6 ] 2

(5)

1=1

where a and 6 are c0n5tant5 t0 6e adju5ted. 7he c105er a 15 t0 1, the c105er 15 ~ t0 1t5 m1n1mum va1ue (5ee F19. 4). 1n the part1cu1ar ca5e 0fa=1, 6=c. 7he meth0d de5cr16ed a60ve add5 5u65tant1a1 1mpr0vement 1n the adju5tment 0f the0ret1ca1 pr0f11e5. 1ndeed, 1f r.m.5, rema1n5 a 519n1f1cant cr1ter10n, c0eff1c1ent a 0ffer5 an e5t1mate 0f 4ua11ty 0f the f1tt1n9 and a150 he1p5 1n d15cr1m1nat1n9 6etween the m0de15 (f1exure m0de1 0r 10ca1 c0mpen5at10n m0de15). At McD0na1d 5eam0unt, f0r 1n5tance, even w1th the 5ma11e5t r.m.5., a rema1n5 d1fferent fr0m 1, 1nd1cat1n9 a 6ad a9reement 60th 1n amp11tude and wave1en9th and 5u99e5t1n9 theref0re that the e1a5t1c p1ate m0de1 15 n0t appr0pr1ate 1n th15 part1cu1ar ca5e. We have 06ta1ned re5u1t5 f0r 11 10ca1 map5 and 27 a1t1metr1c pr0f11e5. F19. 5 pre5ent5 1n pr0f11e f0rm 065erved 9e01d he19ht5 acr055 the C00kAu5tra1 v01can0e5 c0n51dered 1n th15 5tudy. 7he 6e5t f1tt1n9 va1ue 0f D a10n9 each 5 E A 5 A 7 pr0f11e ha5 6een e5t1mated and c0nverted 1nt0 e1a5t1c th1ckne55 a55um1n9 E = 10 ]t N m -2 and v = 0.25. Re5u1t5 are 9athered 1n 7a61e 2. F0r each 5eam0unt 15 1nd1cated the num6er 0f 1ndependent determ1nat10n5 6a5ed 0n a11 ava11a61e 065erved 9e01d pr0f11e5: 1n a11 ca5e5 c0n51dered here, D e5t1mate5 f0r a 91ven 5eam0unt fr0m 5evera1 pr0f11e5 are c0n515tent t0 6etter than 5%. 7heref0re, a 51n91e va1ue 15 rep0rted 1n 7a61e 2 wh1ch c0rre5p0nd5 t0 the mean 0f a11 e5t1mate5. Err0r 6ar5 0n D are de-

F19. 4. Determ1nat10n 0f 7~: Examp1e 0f Rar0t0n9a 151and. Upper curve: 5EA5A7 track 61 w1th the 6e5t f1tt1n9 the0ret1ca1 pr0f11e ( D = 2 × 10 22 N m). Curve (7•/: r.m.5.6etween 5EA5A7 track 61 and the d1fferent c0mputed pr0f11e5 ( 7 ~ - 6 km), referred t0 r19ht-hand vert1ca1 5ca1e (un1t: m2). Curve C,: a6501ute d1fference 6etween h0m0thet1c c0eff1c1ent a and 1 f0r the 5ame pr0f11e5, referred t0 1eft-hand vert1ca1 5ca1e (d1men510n1e55 4uant1ty). D0tted 11ne: 6e5t f1tt1n9 va1ue (D = 2 × 10 22 N m, 7~ =14 km).

duced fr0m r.m.5, curve5 1n app1y1n9 a cr1ter10n depend1n9 60th 0n the 5hape 0f the curve and 0n the va1ue 0f 1t5 m1n1mum. A 5tandard va1ue f0r the cru5ta1 th1ckne55 0f 6 km app11e5 we11 t0 m05t re5u1t5 pre5ented 1n 7a61e 2. A th1cker cru5t 15 5u99e5ted, h0wever, under McD0na1d acc0rd1n9 w1th a 10ca1 c0mpen5at10n 5tate 0f A1ry type. 7he e1a5t1c th1ckne55 7~ var1e5 fr0m 1e55 than 4 km at McD0na1d 5eam0unt t0 - 14 km at Rar0t0n9a. 7he very 10w e1a5t1c th1ckne55 va1ue5 f0und at McD0na1d and Rapa 5u99e5t that the5e feature5 are near1y 1n 10ca1-1505tat1c e4u1116r1um. We have app11ed the A1ry and Pratt m0de15 0f 10ca1 c0mpen5at10n t0 McD0na1d 5eam0unt. F19. 6 c0mpare5 the 065erved and c0mputed 9e01d he19ht5 f0r the d1fferent m0de15 a10n9 5ate111te track 40. 7he 6e5t f1t 15 06ta1ned w1th the A1ry m0de1 f0r a cru5ta1 th1ckne55 0f 6 km and the Pratt m0de1 f0r a depth 0f c0mpen5at10n 0f 20 km. 7he e1a5t1c p1ate 6e5t f1t 15 f0r D = 10 2° N m (7~ -- 2-3 km), 6ut the a9reement 60th 1n amp11tude and wave1en9th 15 w0r5e than f0r the 10ca1 c0mpen5at10n m0de15. A 1ar9er cru5ta1 th1ckne55 (7~ = 8-12 km) 1mpr0ve5 the a9reement (5ma11er r.m.5., a c105er t0 1), the 6e5t f1tt1n9 D va1ue rema1n1n9 0f the 0rder 0f 10 2° N m. F0r the A1ry m0de1, the r.m.5, rema1n5 a1way5 very 5ma11 up t0 7~. = 10 km. When 100k1n9 at F19. 6, 1t appear5 that f0r 5uch feature5 wh1ch

194

A[7UfAK1 A71U R1MA[0RA

7U8UA1

165~

•11:

RA1V1VAE

R~PA

1 1 .=L0~ 1

.L-"1

~-~

C00KAN1.AUL7RAL ) 11LANL)5 150 ° -

-

1

1

~440J~~~

1

16u ° ~

-

2A

""

187~

1

.20 ° -

-30 °

1

10n91tude

140 °

F19. 5. 5et 0f 5 E A 5 A 7 track5 cr0551n9 the C00k-Au5tra1 cha1n.

~2,N~:E PRA77:

W 20km

5~'1~'~ ~ 1

~,"

J

A1RY7 c 12km A1RY7c 6 km

5EA~

VER71CAL5CALE ~ 1ME7ER

6E01D HE16H75

D1FFEREN71AL6E01DHE16H75

F19. 6. C0mputed pr0f11e5 a10n9 5 E A 5 A 7 track 40 (McD0na1d 5eam0unt) f0r the d1fferent m0de15 0f c0mpen5at10n.

195

are part1y c0mpen5ated 10ca11y, d15cr1m1nat1n9 6etween the m0de15 15 very d1ff1cu1t. 7he 1mp0rtant p01nt neverthe1e55 15 that u n d e r McD0na1d 5eam0unt the e1a5t1c th1ckne55 0f the 11th05phere 15 very 10w, certa1n1y 1e55 than 5 km, wh11e a pure 10ca1 c0mpen5at10n m0de1 0f A1ry type w0u1d exp1a1n the 9e01d data a5 we11. A 51m11ar c0nc1u510n 15 06ta1ned f0r Rapa 151and. 4. D15cu5510n 0f the re5u1t5 06ta1ned a10n9 the C00k-Au5tra1 cha1n Prev10u5 e5t1mate5 0f D 1n the 50uthern C00k re910n have 6een rep0rted 6y McNutt and Menard [19] and Lam6eck [13]: McNutt and Menard determ1ned D = 1-2 x 10 22 N m at Rar0t0n9a fr0m up11ft 0f near6y 151and5 wh11e Lam6eck 06ta1ned re5u1t5 f0r Rar0t0n9a ( D = 1 - 2 x 10 22 N m), Man9a1a ( D < 1 x 10 22 N m) and A1tutak1 ( D -- 1 X 10 22 N m) fr0m 6 E 0 5 3 9e01d data. 7he5e re5u1t5 6a5ed 0n d1fferent m0de15 and d1fferent data are 4u1te c0n515tent w1th th05e rep0rted a60ve: we f1nd D = 2 + 0 . 5 x 1 0 22 N m at Rar0t0n9a, D = 0 . 3 + • 0 . 1 x 1 0 22 at Man9a1a and D=0.9•+ 0.1 X 10 22 N m f0r A1tutak1, 5u99e5t1n9 that the

ad0pted m0de1 15 n0t 50 5tr0n91y cruc1a1. Lam6eck [13] 5u99e5ted that the v15c0e1a5t1c m0de1 6e5t exp1a1n5 the f1exura1 r191d1ty e5t1mate5 1n the 50uthern C00k re910n. He 6a5ed h15 ar9umentat10n 0n the h19her f1exura1 r191d1ty 065erved at the y0un9er 151and Rar0t0n9a c0mpared t0 the 01der Man9a1a and f0und add1t10na1 5upp0rt f0r the v15c0e1a5t1c m0de1 fr0m the 50c1ety 151and5 f1exura1 r191d1ty e5t1mate5: 1f 1ndeed the 11th05phere 6ehave5 v15c0e1a5t1ca11y, then the apparent f1exure r191d1ty 5h0u1d decrea5e w1th the a9e 0f the 10ad. H0wever, the d1fference 1n D 6etween Rar0t0n9a, Man9a1a and A1tutak1 a5 rep0rted 6y Lam6eck 15 6are1y d15cerna61e. We have p10tted the e1a5t1c th1ckne55 ver5u5 a9e 0f 10ad f0r the 11 5eam0unt5 c0n51dered 1n 0ur ana1y515 (F19. 7). 7he v15c0u5 re1axat10n trend fav0ured 6y Lam6eck 15 n0t 06v10u5 51nce the 01de5t Man9a1a 15 n0t a550c1ated w1th a 5ma11er r191d1ty c0mpared t0 the y0un9er 10ad5. H0wever, a5 we w111 5ee 6e10w when p10tt1n9 a150 the re5u1t5 06ta1ned f0r the 50c1ety 151and5, there 15 50me ev1dence 0f decrea5e 0f 7~ w1th a9e 0f 10ad. P10t 0f 7e ver5u5 t~ (cru5ta1 a9e at the t1me 0f 10ad1n9) a10n9 the C00k-Au5tra1 15 5h0wn 1n F19. 8. We n0te that 7~ 1ncrea5e5 w1th a9e fr0m 2 - 4 km

A6E 0F L 0 A D (Ma} 0

£9 1-

10

15

20

1

1

•

J

RAPAL

2

LU 2 •v U •-r

5

4 6

, ~ , , . . A N6 A 1A A 11U

8

RA1VAVAE

...~U8UA1 1:~1[~1A1URA•

10,

1 12

RAR070N6A

+

14

80RA 80RA 1~

16 18 2U,

f

1AH171

F19. 7. E1a5t1c th1ckne55 7~ (km) ver5u5 a9e 0f 10ad5 (Ma) a10n9 C00k-Au5tra1 and 50c1ety cha1n5.

196

at t] = 43 Ma t0 a60ut 14 km at t 1 = 87 Ma. 1n c0mpar150n w1th F19. 1 we n0t1ce, h0wever, a d15t1nct trend: 7~ appear5 5y5temat1ca11y 5ma11er 6y 5evera1 k110meter5 than expected f0r ••n0rma1••

0f the 0cean1c 11th05phere cau5e5 the 0cean f100r t0 5u651de, depth 1ncrea51n9 away fr0m the r1d9e cre5t 11near1y w1th the 54uare r00t 0f p1ate a9e, at 1ea5t up t0 80 Ma (e.9. [23]). A10n9 v01can1c cha1n5 (e.9. Hawa11-Emper0r cha1n) the 065erved 5u651dence 15 much m0re rap1d than pred1cted 6y the a9e-depth re1at10n5h1p f0r n0rma1 5eaf100r. L1th05pher1c th1nn1n9 ha5 6een advanced a5 a p055161e mechan15m t0 exp1a1n the ex15tence 0f 60th 5we11 and exce55 0f 5u651dence a10n9 1t: 1f a6n0rma1 heat f1ux 15 a550c1ated w1th the pre5ence 0f the h0t 5p0t, 150therm5 are pu5hed upward, the 11th05phere 15 th1nned and a5then05pher1c mater1a1 rep1ace5 den5er 11th05pher1c mater1a1 at 50me depth cau51n9 up11ft 0f the 5urface (5we11 6y 1505tat1c readju5tment. Wh11e m0de15 6a5ed 0n therma1 c0nduct10n a10ne 1ead t0 1nadm155161e t1me 5ca1e 0f th1nn1n9 [24,25], th1nn1n9 6y 5ma11-5ca1e c0nvect1ve 1n5ta6111ty deve10p1n9 1n the upper 5ect10n 0f the h0t 5p0t

5eaf100r.

Am0n9 the mechan15m5 a61e t0 acc0unt f0r a 10wer e1a5t1c p1ate th1ckne55 under 5eam0unt5, McNutt [5] fav0ur5 therma1 rejuvenat10n cau51n9 th1nn1n9 0f the 11th05phere. 7hu5 1f 1n re910n 0f 1nten5e m1d-p1ate v01can15m the 11th05phere ha5 6een reheated, the depth 0f the 450°C 150therm (wh1ch may c0rre5p0nd t0 the 6a5e 0f the e1a5t1c 1ayer 1n the a65ence 0f reheat1n9) 15 dr1ven upward, 0r e4u1va1ent1y the e1a5t1c 1ayer appear5 th1nner. Reheat1n9 0f the 0cean1c 11th05phere had 6een pr0p05ed ear11er t0 exp1a1n the c0mm0n 0ccurrence 0f m1d-p1ate 5we115 a550c1ated w1th v01can1c cha1n5 and the1r 1ar9er 5u651dence c0mpared t0 n0rma1 11th05phere 0f 51m11ar a9e [20-22]. 7herma1 c0011n9

0

10

2U

30

4u

1

1

1

1

A6E 0F PLA7E A7 7HE 71ME 0F L0AD1N6 (Ma) 50 60 70 80 }

1

1

1

90

100

;

1

t£

Mc D0NALD rv1c D0NALD

1

C00K AU57RAL CHA1N

1 1 1 RAPA --1"•--

w 2

~ 1 RAPA

51 MAN6A1A

MAN6A1A

<

~ V A E7U8UA ~1~

7U8UA1

1

,~

RA1VAVAE

A71U R1A

10

1, 1 MAUKE

1 1

RAR070N6A

1 RAR070N6A 15

----1---1 1

3000 C 45U~C

F19.8.E1a5t1c th1ckne55 7e (km)ver5u5 a9e 0f p1ate at t1me 0f 10ad1n9 t 1 (5011d cr055e5) and effect1ve therma1 a9e at t1me 0f 10ad1n9 [ (da5hed cr055e5) f0r the C00k-Au5tra1 cha1n. 5011d curve5 repre5ent the 300°C and 450°C 150therm5 re5pect1ve1y.

197

a5 pr0p05ed recent1y 6y Yuen and F1e1t0ut [26] can 6e acc0mp115hed 0n a rap1d t1me 5ca1e (10 Ma). 7h15 mechan15m 15 a150 a61e t0 pr0duce the r19ht am0unt 0f t0p09raph1c up11ft. 7he new 5eaf100r depth def1ne5 a therma1 a9e wh1ch 15 n0w d1fferent (5ma11er) than the cru5ta1 a9e. After reheat1n9 and th1nn1n9, the 11th05phere w111 5tart t0 c001 a9a1n and 5u651de 6ut at a rate wh1ch depend5 0n 1t5 new th1ckne55, that 15 0n 1t5 therma1 a9e rather than 0n 1t5 cru5ta1 a9e. 51nce y0un9 11th05phere 5u651de5 m0re rap1d1y than 01d 11th05phere, the reheated 11th05phere 5h0u1d 5u651de m0re rap1d1y than expected fr0m 1t5 cru5ta1 a9e 0n1y. 7h15 15 exact1y what 15 065erved. A11 the5e 065ervat10n5 1ed McNutt [5] t0 rec0n51der the (e1a5t1c th1ckne55-p1ate a9e) emp1r1ca1 re1at10n5h1p f0r 5eam0unt5: 5he pr0p05e5 that 1t 15 n0t cru5ta1 a9e 0f the p1ate at the t1me 0f 10ad1n9 that 5h0u1d 6e c0n51dered 6ut rather the therma1 a9e at the t1me 0f 10ad1n9 when 10ad5 are v01can1c cha1n5

2t~ 1

0r 5eam0unt5 5uper1mp05ed 0n 6r0ad 6athymetr1c 5we115. 5he def1ne5 thu5 an ••effect1ve therma1 a9e•• feff f0r each 5eam0unt 10ad a5: teff = [ ( d - 2500)/350] 2

(6)

where d 15 the depth 0f 5urr0und1n9 5eaf100r 1n meter5 1f tefr 15 1n Ma. Re1at10n (6) 15 51mp1y the emp1r1ca1 a 9 e - d e p t h re1at10n pr0p05ed 6y Par50n5 and 5c1ater [23] f0r 5eaf100r 5u651dence 1n the ran9e 0 - 8 0 Ma. McNutt 5h0w5 that p10t 0f e1a5t1c th1ckne55 7 e ver5u5 effect1ve therma1 a9e at the t1me 0f 10ad1n9 1mpr0ve5 c0n51dera61y the 0r191na1 emp1r1ca1 re1at10n5h1p 1n reduc1n9 the 5catter 0f the re5u1t5 and c1u5ter1n9 the 7e e5t1mate5 a10n9 the 550°C 150therm. We have c0n51dered the effect1ve therma1 a9e at the t1me 0f 10ad1n9 ~ 1n5tead 0f tj f0r each 5eam0unt 0r 151and 5tud1ed. We have n0t u5ed re1at10n (6) t0 c0mpute te,, h0wever, 6ut rather that pr0p05ed 6y Cr0u9h [24] and deduced fr0m

0 1

~000

-15

F19. 9. 8athymetry 0f the 50c1ety cha1n w1th the 11m1t5 0f the 5tud1ed 10ca1 map5 and 5e1ected 5EA5A7 track5. 7he 5tud1ed 1en9th 01 the track5 15 1nd1cated 6y the th1ck 5011d 11ne. L0cat10n 0f an uncharted 5eam0unt 15 n0ted 1n hatch1n9.

195 avera9e rate 0f m19rat10n 0f a60ut 11 c m / y r [11]. Rec0rded ma9net1c an0ma11e5, a60ut 250 km we5t 0f Mehet1a 1nd1cate that the cru5t 15 60-65 Ma there. A5 f0r the C00k-Au5tra1 cha1n, we have deduced the a9e 0f the 5eaf100r 5urr0und1n9 the 5tud1ed v01can0e5 6y 1nterp01at1n9 the 150chr0n5 map 0f 5c1ater et a1. [15]. A9e 0f 151and5 and a9e 0f cru5t are rep0rted 1n 7a61e 2. We have d1v1ded the 50c1ety 151and5 re910n 1nt0 three 5ma11 10ca1 map5 centered 0ver 7ah1t1, 80ra 80ra and Manuae 151and5 (5ee F19. 9 5h0w1n9 re910na1 6athymetry and 10ca1 map5). 1n th15 f19ure are 5h0wn 5e1ected 5EA5A7 track5 cr0551n9 the v01can0e5 n0t t00 far fr0m the1r 5umm1t. We have app11ed the 5ame pr0cedure a5 f0r the C00k-Au5tra1 t0 determ1ne the f1exura1 r191d1ty 0f the 50c1ety 151and5:u51n9 the 5 Y N 8 A P 5 6athymetry, the0ret1ca1 9e01d he19ht5 have 6een c0mputed f0r each 10ca1 map f0r d1fferent va1ue5 0f the f1exura1 r191d1ty and cru5ta1 th1ckne55 0ver the c0rre5p0nd1n9 9r1d; 6e5t f1tt1n9 va1ue5 have 6een deduced 6y c0mpar150n w1th 065erved 9e01d he19ht5 a10n9 the 5e1ected 5EA5A7 track5 (5ee F19. 10). Re5u1t5 are 9athered 1n 7a61e 2 and pre5ented 1n F19. 11. A5 track 174 0n 0ne hand and track5 246, 101 and 24 0n the 0ther hand cr055 d15t1nct 151and5 (5ee F19. 10) and thu5 91ve d1fferent 6e5t f1tt1n9 D va1ue5, the map named

depth data at 1ar9e d15tance5 fr0m h0t 5p0t5 1n the At1ant1c and 1n the Pac1f1c: t~rr =

[(d- 2900)/300] 2

(7)

7he depth 0f the 5we11 5umm1t ha5 6een e5t1mated 6y 5m00th1n9 the re910na1 6athymetry and 0m1tt1n9 data ju5t 6e10w the 5eam0unt at the 5we11 cre5t. Va1ue5 0f d, ter~ and 7 are 91ven 1n 7a61e 2 f0r each v01can0 5tud1ed. F19 8 d15p1ay5 a p10t 0f 7~ ver5u5 7 f0r the C00k-Au5tra1 cha1n. We n0te a much 6etter a9reement than ear11er, the 7~ va1ue5 fa111n9 n0w 6etween the 300 ° and 450°C 150therm5. 5. 7he 50c1ety 151and5 cha1n; re5u1t5 and d15cu5510n We have carr1ed 0ut a 51m11ar ana1y515 u51n9 5EA5A7 9e01d he19ht data a10n9 the 50c1ety 151and5 cha1n 1n 0rder t0 determ1ne the f1exura1 r191d1ty. 7he 50c1ety 151and5 e10n9ate 0ver a60ut 500 km, f0rm1n9 a near1y 11near cha1n 0f v01can0e5. Mehet1a 10cated at the 50uthea5t end 0f the cha1n 15 a very 5ma11 v01can0 wh1ch 15 th0u9ht t0 6e 5t111 f0rm1n9. A few 151and a9e5 are rather we11 kn0wn 51nce 1ndependent e5t1mate5 5h0w 900d a9reement [10,27]. A9e5 1ncrea5e a1m05t 11near1y fr0m Mehet1a t0 Maup1t1 t0ward the n0rthwe5t d1rect10n w1th an 1

80RA 80RA

UNNAMED 5EAM0UN7

1

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155°W

1

L0N617UDE

150°W

F19. 10. 5et 0f 5EA5A7 track5 cr0551n9 the 50c1ety cha1n w1th 6e5t f1tt1n9pr0f11e5.

199 A6E 10

20

30

40

1

1

1

1

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50

60

70

80

90

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MAUP171

50C1E7Y

(Ma) ~(

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MAU1P171 p

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%~

F19. 11. E1a5t1c th1ckne55 7 e (km) ver5u5 a9e 0f p1ate at t1me 0f 10ad1n9 t 1 (5011d cr055e5) and effect1ve therma1 a9e at t1me 0f 10ad1n9 [ (da5hed cr055ed) f0r the 50c1ety cha1n.

80ra 80ra ha5 6een 5eparated 1n tw0 part5: (1•) 80ra 80ra and (2) Maup1t1. At 10cat10n - 18°15 • - 153°W, the 9e01d 519nature 1nd1cate5 the pre5ence 0f an uncharted

MAR1A

5eam0unt: F19. 12 d15p1ay5 the 5 E A 5 A 7 9e01d he19ht pr0f11e5 5h0w1n9 the 9rav1tat10na1 519nature 0f th15 5eam0unt. An e1a5t1c th1ckne55 0f 20 + 2 km 15 f0und f0r

MAUP171

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101

24

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F19. 12. Detect10n 0f an uncharted 5eam0unt 0n 5 E A 5 A 7 track5 246, 101 and 24.

2{)0

7ah1t1, a va1ue 5119ht1y 1ar9er than that rep0rted 6y McNutt and Menard [19] fr0m up11ft 065ervat10n5 and 6y Lam6eck [13] fr0m 6 E 0 5 3 9e01d he19ht data (7~ = 14 km). An avera9e va1ue 0f 20 km had 6een determ1ned, a150 fr0m 6 E 0 5 3 065ervat10n5, 6y Ca2enave et a1. [17] 0ver a 1ar9e re910n 1nc1ud1n9 7ah1t1 and 80ra 80ra. 1n the 1atter 5tudy, n0 attempt wa5 made t0 5h0w up any var1at10n 0f 7~ a10n9 the cha1n. 7he f1exura1 r191d1ty e5t1mate5 a10n9 the 50c1ety 151and5 are reduced t0 0n1y three v01can0e5 6ecau5e 0f three m0t1ve5: (1) n0 track pr0ceed5 c105e en0u9h t0 the new h0t 5p0t 5eam0unt, Mehet1a, (2) c0ra1 reef5 d15tur6 many a1t1metry mea5urement5, and (3) n0 a9e data, e1ther f0r p1ate 0r v01can0e5 are ava11a61e we5t 0f Maup1t1. 7h15 1a5t p01nt 15 very 1nc0nven1ent 51nce a very 10w r191d1ty va1ue ha5 6een f0und f0r an unnamed 5eam0unt (X = 156°W; ~ = - 1 5 ° 4 0 •) c0mpared t0 th05e f0und f0r 7ah1t1 0r ar0und 80ra 80ra. 0 u r re5u1t5 5h0w that 7 e decrea5e5 519n1f1cant1y t0ward the n0rthwe5t fr0m 20 km at 7ah1t1 t0 13 km at Maup1t1. 7he5e re5u1t5 m19ht 5u99e5t a decrea5e 0f the e1a5t1c th1ckne55 w1th a9e 0f 10ad 51nce Maup1t1 15 a60ut 4 Ma 01d wh11e 7ah1t1 15 0n1y 0.8 Ma 01d. We have p10tted 0n the 5ame f19ure va1ue5 0f 7~ ver5u5 a9e 0f 10ad f0r the C00k-Au5tra1 and 50c1ety 151and5 (5ee F19. 7). F19. 7 5h0w5 an 1ntere5t1n9 trend: 1f we except Rapa wh1ch ha5 6een 5h0wn t0 6e 1n 10ca1 1505tat1c c0mpen5at10n (5ect10n 2), we n0t1ce a c1ear decrea5e 0f the e1a5t1c th1ckne55 w1th 10ad1n9 t1me, the decrea5e 6e1n9 very rap1d 1n1t1a11y. 7h15 6ehav10ur had 6een pred1cted 6y 5evera1 the0ret1ca1 5tud1e5 0n the 10n9-term mechan1ca1 re5p0n5e 0f the 0cean1c 11th05phere t0 10ad1n9 [28-31]. Wh11e d1ffer1n9 1n the deta115, the5e 5tud1e5 5h0wed that when a 10ad 15 app11ed, the re5p0n5e 15 pr1mar11y e1a5t1c f0110wed 6y rap1d 5tre55 re1axat10n 1n the 10wer p0rt10n 0f the p1ate up t0 depth5 c0rre5p0nd1n9 appr0x1mat1ve1y t0 the 6a5e 0f the e4u1va1ent e1a5t1c 1ayer; 1n1t1a1 th1nn1n9 0f the e4u1va1ent e1a5t1c 1ayer w1th 10ad1n9 t1me f0110w5 a 109ar1thm1c 6ehav10ur and theref0re 15 rap1d 1n1t1a11y, 6ec0m1n9 510wer and 510wer a5 the p1ate appr0ache5 1t5 e1a5t1c th1ckne55. La90 and Ca2enave [29] 5h0wed that 1f 1n add1t10n therma1 c0011n9 15 taken 1nt0 acc0unt, e1a5t1c th1nn1n9 pr0ceed5 fr0m a 109ar1thm1c t0 an a5ympt0t1c 6ehav10ur t0ward5 a c0n5tant va1ue and that a60ut

90% 0f the e1a5t1c th1ckne55 15 ac4u1red 1e55 than 5 m.y. after 10ad1n9. 5uch a 6ehav10ur 15 c1ear1y 5u99e5ted 1n F19. 6, the tran51t10n fr0m 109ar1thm1c t0 a5ympt0t1c th1nn1n9 0ccurr1n9 ar0und 5 Ma a5 pred1cted 6y th15 m0de1. 1t w0u1d n0t 6e rea50na61e h0wever t0 1nterpret the a5ympt0t1c va1ue 0f 7~ deduced fr0m th15 p10t a5 a mea5ure 0f the e1a5t1c th1ckne55 0f the 11th05phere at the t1me 0f 10ad1n9 51nce a 51n91e cru5ta1 a9e 15 n0t appr0pr1ate f0r the 11 10ad5 c0n51dered here (cru5ta1 a9e vary1n9 fr0m a60ut 50 t0 90 Ma). 6. D15cu5510n Re5u1t5 06ta1ned 1n th15 5tudy f0r the e1a5t1c th1ckne55 0f the 11th05phere 6eneath the C00kAu5tra1 151and5 1nd1cate c1ear1y that th15 re910n 15 an0ma10u5. App1y1n9 the therma1 a9e c0rrect10n reduce5 519n1f1cant1y the d15crepancy w1th the avera9e trend 5h0wn 1n F19. 1, a 5u99e5t10n that 5u65tant1a1 11th05pher1c th1nn1n9 (whatever the re5p0n5161e mechan15m) ha5 0ccurred under the Au5tra1 and C00k 151and5. 7en 8r1nk and Watt5 [32] a150 1nv0ke reheat1n9, e1ther 0n a 10ca1 0r re910na1 5ca1e, t0 exp1a1n 5e15m1c ref1ect10n data acr055 the f1exura1 m0at f1ank1n9 the 0 a h u 151and (Hawa11an cha1n). Yet, the mea5ured e1a5t1c th1ckne55 under Hawa11 d0e5 n0t depart fr0m the avera9e trend 0f F19. 1. 0 "-.t

0 C0

0 C0

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45

1

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x2

F19. ]3. 6e01d an0ma1y map f11tered 0 u t 0 f the very 10n9 wave1en9th

( > 4000

km).

] = Mehet1a

5eam0unt,

2 =

M c D 0 n a 1 d 5eam0unt. D 0 t t e d 11ne5 are f0r 10w5, fu11 11ne5 f0r

h19h5 a n d th1ck 11ne5 are f0r 1eve1 0.

201

0 n e p05516111ty f0r the C00k-Au5tra1 cha1n 15 that 1t extend5 0ver the r151n9 p1ume 0f 5ma11-5ca1e c0nvect10n current5 5u5pected t0 ex15t 1n the upper mant1e: a5 5h0wn the0ret1ca11y 6y McKen21e et a1. [33] and Par50n5 and Da1y [34] 1n ca5e 0f c0n5tant-v15c051ty c0nvect10n, h0t r151n9 re910n5 5h0u1d c0rre1ate w1th 60th t0p09raph1c 5we115 and 9e01d h19h5. 6e01d an0ma1y map5 f11tered 0ut 0f the very 10n9 wave1en9th5 ( > 4000 km) 5h0w 1n the Pac1f1c 0cean a re9u1ar pattern 0f 9e01d h19h5 and 10w5 0f 6-8 m ha1f-amp11tude, 5eparated 6y a character15t1c d15tance 0f - 2000 km (5ee F19. 13). 7he p051t1ve c0rre1at10n w1th re51dua1 depth an0ma11e5 ha5 6een a550c1ated w1th the 5ma11-5ca1e c0nvect10n pattern [35,36]. 51nce the C00k-Au5tra1 cha1n 15 r19ht1y 10cated 0ver 0ne 0f the5e 6r0ad 9e01d h19h5 (5ee F19. 13), h19h heat f1ux a550c1ated w1th the upwe111n9 c0nvect1ve f10w m19ht 6e adv0cated t0 exp1a1n 11th05pher1c th1nn1n9 and theref0re the very th1n e1a5t1c th1ckne55 065erved 1n th15 re910n. Under 7ah1t1, the e1a5t1c th1ckne55 0f the 11th05phere ha5 n0t 6een f0und t00 10w f0r 1t5 a9e (F19. 11); yet, the 50c1ety 151and5 are a150 10cated 0ver a t0p09raph1c 5we11. At f1r5t 100k, 1t c0u1d appear 1nc0n515tent t0 1nv0ke 11th05pher1c th1nn1n9 6eneath the C00k-Au5tra1 151and5 and n0t 6eneath the 50c1ety 151and5. 5evera1 tentat1ve exp1anat10n5 m19ht 6e advanced: (1) 7ah1t1 may 6e 10cated 1n a re910n 1e55 vu1nera61e t0 th1nn1n9. (2) 7he 50c1ety 151and5 are n0t 10cated 0ver a 6r0ad 9e01d h19h (F19. 13) and theref0re may n0t 6e a550c1ated w1th a r151n9 c0nvect1ve f10w. 1f a p1ume ex15t5, th1nn1n9 15 perhap5 1e55 1mp0rtant. (3) A5 we have 5h0wn 1n 5ect10n 4 (5ee a150 F19. 7), the e1a5t1c th1ckne55 5h0w5 a c1ear decrea5e w1th 10ad1n9 t1me 6ut the va1ue5 06ta1ned f0r the 01de5t 10ad5 fav0ur an a5ympt0t1c 6ehav10ur rather than the 109ar1thm1c 6ehav10ur expected f0r v15c0e1a5t1c re1axat10n. 1n1t1a1 5tre55 re1axat10n may 5t111 6e effect1ve under the very y0un9 7ah1t1 10ad (0.8 Ma 01d): 6ecau5e 0f the a550c1ated upward m19rat10n 0f 150therm5, the pre5ent1y mea5ured e1a5t1c th1ckne55 ha5 n0t yet reached 1t5 e4u1116r1um va1ue and 91ve5 an apparent 1ar9er va1ue c0mpared t0 a few m11110n year5 01der 10ad (c0n51der1n9 the 5ame p1ate a9e). 7he 1atter ar9ument c0u1d exp1a1n the d1fference 065erved 1n the 7 e re5u1t5 6etween the C00k-Au5tra1 (exc1ud1n9 McD0na1d and Rapa

wh1ch are 10ca11y c0mpen5ated)and the 50c1ety 151and5. A1th0u9h we cann0t exc1ude hyp0the5e5 (1) and (2), we are 1nc11ned t0 fav0ur hyp0the515 (3) wh1ch can 6e te5ted 6y determ1n1n9 add1t10na1 e1a5t1c th1ckne55 va1ue5 under 5we11 area5 0f e4u1va1ent p1ate a9e and 10ad5 0ffer1n9 a 5uff1c1ent1y 1ar9e a9e ran9e.

Ackn0w1ed9ement5 7h15 5tudy ha5 6een 5upp0rted 6y the Centre Nat10na1 d•Etude5 5pat1a1e5 and the 1n5t1tut Nat10na1 de5 5c1ence5 de 1•Un1ver5 (France).

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