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and Planetary Science Letters 181 (2000) 539^554 www.elsevier.com/locate/epsl

Non-hotspot formation of volcanic chains: control of tectonic and £exural stresses on transport

Christoph F. Hieronymus a;*, David Bercovici b

a Danish Centre, Copenhagen, Denmark b Department of and , University of , Hawaii, USA Received 16 March 2000; received in revised form 13 July 2000; accepted 13 July 2000

Abstract

The South Pacific, in the vicinity of both the superswell and the , is repleat with volcanic chains that, unlike the Emperor-Hawaiian Chain, defy the hypothesis of formation via the relative motion of plates and hotspots. We propose two nearly identical models for the origin of near-axis and superswell chains, assuming that both regions are underlain by significant quantities of more or less uniformly distributed partial melt. Given an initial volcanic load or a local anomaly in the melt source region, volcanic chains form by magmatic hydrofracture at local tensile maxima of flexural and membrane stresses. Fracture wall by magma flow provides a feedback which results in discrete edifices within the chains. The model predicts chains aligned with a deviatorically tensile tectonic stress. Near the ridge, the elastic lithosphere is thin, and observations and theoretical considerations indicate a strong deviatorically tensile stress field perpendicular to the ridge axis. Under such conditions, the model results in parallel lines of volcanoes perpendicular to the spreading ridge. Later, interstitial within the individual chains reduces the average spacing and results in nearly continuous ridges. On the thicker lithosphere of the superswell, membrane stresses are negligible and the model produces chains of much more widely spaced volcanoes. A more isotropic stress field may result in broader chain-like patterns of volcanoes. In both cases, the chains represent self-propagating disturbances; the resulting age progressions are thus independent of plate velocity, but depend only on the dynamics of formation and evolution. ß 2000 Elsevier Science B.V. All rights reserved.

Keywords: magma transport; volcanism; intraplate processes; hot spots; lithosphere

1. Introduction The superswell overlies upper with anom- alously slow surface waves [4] and displays a high The South Paci¢c Superswell is de¢ned as the concentration of volcanic [2]. Both the region surrounding French and is about superswell and its eastward extension towards 250^750 m shallower than `normal' sea-£oor the East Paci¢c Rise (EPR) (Figs. 1 and 2) are based on empirical depth^age relations [1^3]. characterized by abundances of three times higher than on equivalent North Paci¢c lithosphere [5]. The origin of the seamounts as well as the `' island chains has been the * Corresponding author. Tel.: +1-979-845-1309; subject of much debate recently. While island Fax: +1-979-845-6162; E-mail: [email protected] chains elsewhere ^ such as Hawaii ^ are well ex-

0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved. PII: S0012-821X(00)00227-2

EPSL 5582 5-9-00 540 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554

Fig. 1. Map of South Paci¢c Superswell and southern EPR. Contours are residual bathymetry after subtracting tenth order poly- nomial trend to show islands and seamounts while neglecting the elevation due to the spreading ridge and other large scale fea- tures. Contours are at an arbitrary reference depth and at 2000 m above that depth. Data from [52].

plained by the steady motion of lithospheric noes often coalescing to form continuous ridges plates over stationary hotspots or plumes [6,7], [9,10]. Their formation may be enhanced in, or on the superswell even the major island chains even limited to, the near-spreading ridge environ- do not appear to ¢t this model [2]. The alignment ment [5]. Radiometric ages of the Puka Puka of the island chains typically deviates from the ridge [11] do not support a plume or `mini-plume' inferred motion of the Paci¢c plate [2,8], and origin [12^14] of the near-spreading ridge sea- the radiometrically determined age progressions mount chains. For these seamounts, seismic re- are inconsistent with the Paci¢c plate velocity. £ectivity indicates recent volcanism from about The age progressions are in some instances too 30 km to at least 400^500 km away from the slow, in others too fast, in the opposite direction, EPR [10]. decreasing in age outward in both directions from Alternative explanations for the formation of a central volcano, or they display discrete periods and island chains focus on observations of superimposed volcanism [2]. of gravity lineations of various wavelengths; there Smaller seamounts are also typically aligned in is some evidence that volcanic activity correlates chains [9] with the individual cone-shaped volca- with such lineations. Seamount activity appears

EPSL 5582 5-9-00 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 541 enhanced in the troughs of small wavelength lines' of convective upwelling [15^17]. The same (W150 km) lineations [11], although this correla- mechanism has been postulated for the formation tion is not perfect and some chains cross from of the near-axis seamounts [14,20]. Lithospheric troughs onto crests [11], while in other places, stretching or boudinage due to ridge-parallel ten- volcanic activity in an active ¢eld covers several sile stress and subsequent volcanism on the troughs and crests [10]. The Polynesian island thinned portions of the lithosphere also produce chains instead typically fall on the crests of me- a correlation between gravity lineations and sea- dium wavelength (W1000 km) gravity lineations mount chains (but of opposite sign) [11,21], but [15^17]. If the gravity lineations are the surface there is no evidence of signi¢cant extension of the expression of convection rolls aligned with abso- Paci¢c plate [11,22]. lute plate motion [18,19], then the Polynesian is- Another type of model explains the origin of land chains may be explained in terms of `hot- near-axis seamounts by preferential, early melting

Fig. 2. Map of Rano Rahi volcanic ¢eld. Shading shows bathymetry with trend removed as in Fig. 1. Data from [9].

EPSL 5582 5-9-00 542 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 of fertile mantle heterogeneities in the upwelling row region subject to normal faulting near the zone beneath a passive spreading center [23,24]. spreading ridges [31]. While simple force balances Such heterogeneities would need to be very elon- indicate that a compressive stress ¢eld may be gated or clustered approximately along mantle produced by a dominant balance of ridge-push £ow-lines to produce chains 60 km or more in force versus friction at the trench [32,34], the state length [10]. Additionally, while small-scale hetero- of stress parallel to the spreading ridge is even geneities are believed to exist in the mantle more poorly understood; in the south eastern Pa- [25,26], they are unlikely to be the cause of vol- ci¢c, the plate is bounded mostly by transform canism far from the ridge since, in that region, faults to the south, and a retreating trench to mantle £ow due to passive spreading does not the north [35]. While Sandwell et al. [11] argue have a signi¢cant vertical component [10]. for a net tensile stress perpendicular to the ridge The model introduced in this paper explains the axis of the EPR, (resulting in boudinage and for- distribution of non-hotspot island and seamount mation of volcanic chains on the thinned parts of chains in terms of the vulnerability of the litho- the lithosphere), we propose an alternative origin sphere to magma penetration due to lithospheric of the volcanic chains which predicts a deviatoric stresses and the e¡ects of melting of the conduit tensile stress in the direction of relative plate mo- walls [27]. The availability of melt is assumed to tion. be controlled by large scale mantle processes such as convection under the superswell [28] or return mantle £ow toward the EPR from the superswell 2. Theory bringing in anomalously hot mate- rial [28,29], resulting in an abundant melt supply Transport of magma through the brittle part of throughout much of the superswell region and the lithosphere is assumed to occur via fractures. near the EPR. Volcanism is activated or sup- As the purpose of the model is not to predict the pressed by tensile and compressive stresses, re- orientation or evolution of individual dikes, but spectively, which are made up of a combination only their time- and space-integrated ability to of tectonic and £exural stresses. Strong evidence transport magma, we assume that dikes form as for tectonic stress control on alignment of sea- soon as the local magma pressure is greater than mount chains comes from the EPR at 5³N to the sum of the tensile strength of the lithosphere 15³N, where absolute and relative plate motion and the least compressive horizontal stress in the di¡er signi¢cantly. In this region, two distinct lithosphere. The e¡ect of the dikes on magma groups of seamount chains are found, one in transport is modeled by the permeability of the which the chains are aligned with absolute plate lithosphere, which depends on the magma pres- motion, and another one with the chains paral- sure and the local stress ¢eld, as well as erosion leling the relative plate motion of the Paci¢c and of the conduit walls [27]. the [30]. While the chains aligned Melt is assumed to be distributed uniformly at with absolute motion indicate an origin due to a the base of the lithosphere. While this assumption stationary melting anomaly in the mantle, it is may not hold perfectly either on the superswell or di¤cult to envision a mechanism for the forma- near the EPR, it does show most clearly what tion of the chains parallel to relative plate motion type of ¢lter the lithosphere provides in determin- that does not incorporate the tectonic stress ¢eld. ing the location of volcanism with regard to the The state of stress in the lithosphere of a vast melting anomalies within the mantle. part of the world's oceans remains unknown due The stress ¢eld is composed of a regional tec- to both a scarcity of observations [31] and an tonic stress ¢eld, £exural stresses, and ^ on thin incomplete understanding of the plate tectonic lithosphere ^ membrane stresses. The total £exure driving forces [32,33]. The most important obser- (including £exural and membrane stresses, but ne- vational constraint is that the tectonic stress ¢eld glecting tectonic stresses) is described by two is mostly compressive throughout, but with a nar- coupled, non-linear di¡erential equations [36,37]

EPSL 5582 5-9-00 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 543 "# D2w 2 D2w D2w Only the stresses near the surface will be con- P4F ˆ E 3 1† DxDy Dx2 Dy2 sidered as this is where fracturing is most likely to occur [40]. At depth, a transport mechanism dif-  ferent from £ow through brittle fractures is likely 12 13X 2† b 3b †gh D2F D2w P4w ˆ m w ‡ ‡ to be operating. Evidence of this is seen in volcan- EH2 H Dy2 Dx2 ism near the £exural bulges north and south of Hawaii [41] where the £exural stresses at depth  D2F D2w D2F D2w are compressive. 32 3vbgw 2† Dx2 Dy2 DxDy DxDy The £exural stresses associated with plate de- formation are given by  where x and y are the horizontal coordinates, w is EH D2w D2w the vertical de£ection of the lithospheric plate, F c flex ˆ 3 ‡ X 3† xx 2 13X † Dx2 Dy2 is a stress function, bm, bl, ba, and bw are the densities of the magma, the lithosphere, the asthe-  EH D2w D2w nosphere, and of water, respectively, h(x,y) is the c flex ˆ 3 ‡ X 4† yy 2 13X † Dy2 Dx2 height of the surface load of density bm, E is Young's modulus, H is the e¡ective elastic thick- ness of the lithosphere, X is Poisson's ratio, and EH D2w c flex ˆ 3 5† P4 =(D4/Dx4+2D4/Dx2Dy2+D4/Dy4) is the horizontal xy 1 ‡ X DxDy biharmonic operator. The density di¡erence vb =(ba 6 bm) in the last term of Eq. 2 assumes and the membrane stresses are that the moat is largely ¢lled with volcanic debris D2F [38] of the same density as the volcanic edi¢ce. c mem ˆ 6† xx Dy2 With F = 0 in Eq. 2, the familiar thin-plate £exu- ral equation is recovered; the stress function F, D2F de¢ned by Eq. 1, and the additional terms in mem c yy ˆ 7† Eq. 2 are derived by considering the force balance Dx2 due to large de£ections on a small element located D2F on the mid-level plane of the plate, which is stress c mem ˆ 8† free in thin [36]. xy DxDy On old, thick lithosphere, even large volcanoes such as in Hawaii cause only small The normal and components of these stress- de£ections of the lithosphere on the order of 3^5 es are added to the corresponding components of km [39] compared with the elastic thickness of the the regional stress ¢eld to yield the three total plate, which is about 30 km [39]. The thin-plate stress components cxx, cyy, and cxy as functions approximation is therefore valid (membrane of x and y. The local maximum eigenvalue of the stresses are negligible) and the de£ection is de- total two-dimensional stress tensor, representing scribed by Eq. 2 with F = 0, yielding a single, lin- the most tensile principal stress, may be found ear £exural equation [36]. For young lithosphere, using [37] the plate thickness may be as low as 500 m or less 1 [38] with de£ections of the same order, and thus 1 1 c ˆ c ‡ c †‡ c 3c †2 ‡ c 2 2 the membrane stresses have to be taken into ac- max 2 xx yy 4 xx yy xy count. Horizontal stresses (such as a tectonic 9† stress) potentially a¡ect the £exural displacement as well [37]; however, it can be shown that, for the stresses (tens of MPa) and plate thicknesses Following Hieronymus and Bercovici [27,42], (v500 m) considered here, their e¡ect is negligible we formulate the complete dynamical model by and hence use of Eqs. 1 and 2 is appropriate. de¢ning the permeability of the lithosphere which

EPSL 5582 5-9-00 544 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 in turn controls the melt transport via a Darcy where W is the dynamic magma viscosity. Magma £ow law. We assume that the porosity f of the is assumed to solidify in place as it reaches the lithosphere due to magma-¢lled cracks and frac- surface; outwardly horizontal spreading of the tures is controlled by the stress ¢eld and erosion volcanic edi¢ce due to gravity is neglected. The of the fracture walls [27,42] growth of the volcano is then described by Dh Cdf ˆ BdO ‡ dc max ‡ dc m 10† ˆ V 13† Dt where dO(x,y) is the net energy input per volume The net energy content O per volume of the bulk of the bulk medium consisting of magma and wall medium changes primarily due to injection of rock. Energy inputs which induce erosion include magmatic net energy, which is proportional to V: heat (for melting and thermal conditioning), grav- DO vQ itational potential energy, internal mechanical en- ˆ V 14† ergy, kinetic energy (for mechanical and thermo- Dt H mechanical erosion), and chemical potential en- where Q is the drop in magmatic energy per vol- ergy (for reactive and hydrating e¡ects). The ume across the lithosphere (from bottom to top). non-lithostatic melt pressure at the base of the The energy variable O may be eliminated from the lithosphere is given by cm, B is a constant, and problem by noting from Eqs. 13 and 14 that O is C is a parameter whose inverse C31 represents the proportional to h up to a constant. Setting responsiveness of crack or volume to stress O(t =0)=h(t = 0) = 0, we can thus write O = vQ and erosion. We assume that parameter C is a h/H. function of f; a simple relation (C = Co/ Eqs. 1^13 and the above relation for O form a (f(fmax3f)) captures the essential physics by pre- complete set when combined with the boundary cluding meaningless values of f 6 0 and f s fmax. conditions that h, w, V, and all stresses except for The parameter fmax is a maximum porosity be- the tectonic stress vanish far from the region of yond which increases in stress or total energy interest; initial conditions will be speci¢ed in the are partitioned less into changing porosity than next section. The equations may be non-dimen- into other responses, such as heating or deforming sionalized using the length, time, and pressure ê 3 2 1=4 ê the magma. The numerical value of fmax need not scales X =[EH /(12(13X )gvb)] , T = HW/ ê be speci¢ed as fmax only appears in products with [gko(bl3bm)], and P = blgH, respectively. The other parameters. length scale is proportional to the £exural param- Eq. 10 may be integrated using the above rela- eter, while the pressure scale is equal to the litho- tion for C. Assuming a linear dependence of per- spheric overburden. The time scale is the time meability on porosity, it follows that required for traversal of the lithosphere at the Darcy velocity with maximum permeability and k f c ‡ c 3c ‡ BO k ˆ o max 1 ‡ tanh max m o with a driving pressure equal to the lithospheric 2 2Co=f max overburden. After non-dimensionalization and 11† some simpli¢cation, the equations are "# where k is a reference permeability and c is an D2w 2 D2w D2w o o P4F ˆ a 3 15† integration constant representing the tensile 1 DxDy Dx2 Dy2 strength of the lithosphere. The Darcy £ow law governing melt transport 4 through fractures (assuming laminar £ow) is P w ˆ a2h3w‡  khig D2F D2w D2F D2w D2F D2w V ˆ b 3b †g3 b 3b †h ‡ b w† 12† a ‡ 32 16† W l m m w a H 3 Dy2 Dx2 Dx2 Dy2 DxDy DxDy

EPSL 5582 5-9-00 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 545

Table 1 The non-dimensional parameters a1 to a10 are ex- Non-dimensional parameters plained in Table 1. Aside from a non-linearity in Parameter Description the stress ¢eld, equations for the lithospheric plate of ¢nite thickness, the set of equations contains a a1 E non-linear feedback in Eq. 17 due to erosion of b lgH the conduit walls which causes the formation of a2 bm3bw discrete volcanic edi¢ces instead of spatially con- vb tinuous or widely distributed ones [27,42]. a3  2 1=2 b l 12Hgvb 13X † vb E 3. Results a4  1 12E3vb 13X 2† 1=4 3 3 The equations are solved using a pseudo-spec- 2 13X†b l H g tral code [43] with 128U128 modes, implicit time a5  1 12E3vb 13X 2† 1=4 stepping for the linear parts of the equations and 3 3 13X†b l H g explicit integration for the non-linear parts. For the ¢nite thickness plate, the £exural equation is a6 b lgHf max iterated over until the solution converges. Co The governing equations exhibit perfect trans- a7 1=4 lational symmetry in both horizontal directions; BvQf max E 2 thus, an initial perturbation is required in all cases Co 12gHvb 13X † a8  12gHvb 13X 2† 1=4 E a 9 b m3b w b l3b m a 10 b a b l3b m

Dh 1hi ˆ 1 ‡ tanh a c 3c †‡a h† Dt 2 6 max o 7

U a83a9h ‡ a10w† 17† where cmax is given by (Eq. 9) and  D2w D2w D2F c 3a ‡ X ‡ ‡ c tec 18† xx 4 Dx2 Dy2 Dy2 xx

 D2w D2w D2F Fig. 3. Map view of pattern of volcanoes resulting from c 3a ‡ X ‡ ‡ c tec 19† £exural stress and two point loads (labeled 1) as initial per- yy 4 2 2 2 yy Dy Dx Dx turbations. Subsequent volcanoes form in order indicated by numbers. Non-dimensional parameters used to generate the D2w D2F ¢gure are: a1 = 60.0, a2 = 0.696, a3 = 0.527, a4 = 23.9, tec a = 28.6, a = 7.79U107, a = 3.60U107, a = 0.597, a = 2.00, c xy ˆ 3a5 3 ‡ c xy 20† 5 6 7 8 9 DxDy DxDy a10 = 4.13.

EPSL 5582 5-9-00 546 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 to localize the volcanic activity. Fig. 3 the model results for a thick lithospheric plate (for which the thin-plate approximation holds) without tectonic stress. Two volcanic edi¢ces were used as initial disturbance since a single volcano would cause a radially symmetric £exural stress ¢eld and thus result in formation of concentric, ring-shaped vol- canoes. The results depicted in Fig. 3 indicate an outwardly radiating pattern of volcanoes. The spacing is given by the distance from the volcanic load to the location of maximum tensile stress, which (for a value of X = 0.25) is 0.46 times the distance to the peak of the £exural bulge. Further volcanoes typically form later in the center of any three neighboring volcanoes, thus reducing the average spacing by a factor of about 0.4. In Fig. 4, output is shown from the same model with a tensile tectonic stress and with a single volcanic edi¢ce as initial perturbation. Here it is the external stress ¢eld which breaks the radial symmetry around the point load. A straight line of volcanoes is formed which is aligned with the regional tensile stress direction. The intervolcanic spacing is again determined by the distance from the center of the volcanic load to the posi- tion of maximum tensile stress. Dimensionalizing with H = 5 km, E = 7.0U1010 Pa-s and vb = 700

Fig. 5. Map view of principal stresses due to tectonic stress of non-dimensional magnitude 0.31 (upper panel), £exural stress caused by a point load of non-dimensional weight 0.23 (middle panel), and a combination of both (lower panel). The arrows were scaled such that length = (magnitude)1=4 in order to show weak stresses more clearly. A constant back- ground pressure of magnitude 0.51 was added (lower panel) Fig. 4. Line of volcanoes resulting from interaction of £exu- representing either a compressive non-deviatoric part of the ral stresses and tensile tectonic stress (in direction of volcanic tectonic stress or the tensile lithospheric strength. The pres- line). Volcanoes indicated by arrows formed as second stage sure keeps the unperturbed lithosphere impermeable. Shaded of eruptions after formation of the original line. Non-dimen- regions indicate locations where maximum principal stress is sional parameters used are: a1 = 420, a2 = 0.696, a3 = 0.199, tensile. 5 6 a4 = 103, a5 = 123, a6 = 5.15U10 , a7 = 7.00U10 , a8 = 0.367, a9 = 2.00, a10 = 4.13. The non-dimensionalized tectonic stress- tec tec tec es are: cxx = 0.082, cyy = 0.038, cxy = 30.057.

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3 kg/m , the volcanic spacing is about 25 km. With tive magnitudes of co, cm, h, and ctec. A second, 3 3 W = 100 Pa-s, bl = 3400 kg/m , bm = 2600 kg/m , later stage of volcanism results in the formation 311 2 and ko = 3.7U10 m , the time scale of volcano of further edi¢ces mid-way between the volcanoes formation until the edi¢ce reaches 95% of its ¢nal of the ¢rst set. Further volcano formation was not height is 1.0 Ma. The propagation velocity of the observed, although it should be noted that the chain is then 5.4 cm/yr, yielding an average age cut-o¡ time for stopping the numerical calcula- di¡erence of 460 kyr between adjacent volcanoes. tions is somewhat arbitrary; since the lithospheric The relative time scales of volcano formation and permeability is small, but non-zero everywhere, chain propagation depend on the non-dimension- then as tCr, the model will tend to a single al parameters; the absolute value of the time volcanic edi¢ce covering all space with uniform scales is given by the dimensionalization scale Tê . height. As a practical solution, we stopped the Fig. 5 demonstrates how the interaction of tec- computation if no new volcanism was initiated tonic stresses and £exural stresses due to a point over a time scale which is long in comparison load results in localized tensile stress maxima in with the time scale of volcano evolution. As any the lithosphere where the next volcanoes form. later eruptions begin with very low permeability, The volcanic ages become increasingly younger magma solidi¢cation in the conduit is likely to outward from the initial, central volcano. The counteract the e¡ect of the feedback due to con- propagation velocity of volcanic activity depends duit wall erosion and preclude the eruption. For on the rate with which the individual edi¢ces form simplicity, the details of the thermodynamics in- as well as on the size of load su¤cient to initiate cluding solidi¢cation of magma at low £ow rates the next volcano, which is a function of the rela- were neglected in the model.

Fig. 6. Sketch of the stresses in the lithosphere due to a volcanic load, also indicating the possible location of the next eruption. The bending stress, whose sign is indicated by shading, varies linearly with depth and is antisymmetric about the mid-plane of the lithosphere. Membrane stresses, which are independent of depth, are caused by local extension or compression of the mid-lev- el plane of the lithosphere, which is indicated by a thick, dashed line; underneath the volcanic edi¢ce, membrane stresses are mostly tensile. The relative magnitudes of bending and membrane stresses are determined by the ratio of the £exural displace- ment to the plate thickness.

EPSL 5582 5-9-00 548 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554

Fig. 7. Principal stresses due to tectonic stress of non-dimensional magnitude 0.23 (upper left panel), membrane stresses caused by point load of weight 0.226 (upper right panel), £exural (bending) stresses (lower left panel) and a combination of all three plus a constant compressive pressure of magnitude 0.52 (lower right panel). Non-dimensional lithospheric thickness is 0.2. Arrows were scaled as in Fig. 5.

The existence of large de£ections of the litho- dominate, but decay with distance more rapidly sphere in comparison with its thickness requires than the tensile membrane stresses. The location the use of the £exural equations for a plate of of maximum tensile stress (where the next volcano ¢nite thickness, thus introducing membrane forms) is thus moved closer to the center of the stresses into the problem (see Fig. 6). When ini- £exural depression. The degree to which the £exu- tialized with a single point-perturbation, the mod- ral de£ection is governed by either the bending el again produces a line of volcanoes. The vol- stresses or by the membrane stresses (which is canic spacing is smaller than that for the given by the magnitude of the vertical de£ection equivalent thin-plate approximation because, for relative to the plate thickness) determines how the parameters chosen, the mostly tensile mem- close to the ¢rst edi¢ce the next eruption will brane stresses are of the same order of magnitude start. The possible intervolcanic spacing ranges as the bending stresses (see Fig. 7). Close to the from the maximum predicted by thin-plate theory volcanic load, the compressive £exural stresses (described above) to a minimum of zero spacing

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(i.e. a continuous ridge) for a system dominated entirely by the membrane stresses. Even if bending and membrane stresses are of the same order and there is thus a signi¢cant dis- tance between adjacent volcanoes, a series of later eruptions ¢lls in the space between the edi¢ces, eventually creating a nearly continuous ridge. Due to the tensile membrane stresses, several vol- canoes typically form in the space between any two volcanoes of the initial chain. This is in con- trast with the solution containing only £exural stresses, where over reasonable time spans only one further volcano was observed to form be- tween any two of the older ones. Membrane stresses perpendicular to the axis of the volcanic line or ridge also interact with the £exural stresses to generate volcanism away Fig. 8. Multiple lines of volcanoes resulting from interaction from the axis. This o¡-axis volcanism eventually of £exural, membrane, and tectonic stresses. Non-dimension- 3 forms additional lines of volcanoes parallel to the al parameters used are: a1 = 2.10U10 , a2 = 0.300, a3 = 0.135, a = 279, a = 335, a = 175, a = 5.00U109, a = 0.199, ¢rst one. The spacing between the individual lines 4 5 6 7 8 a9 = 0.375, a10 = 4.13. The non-dimensionalized tectonic tec tec tec is of the same order as the spacing between the stresses are: cxx = 0.225, cyy = 0.675, cxy = 0.390. ¢rst edi¢ces within the initial line. Eventually, fur- ther lines of volcanoes are formed in parallel, with some in-¢ll of additional volcanoes in between. 4.1. Volcanism on the South Paci¢c superswell Fig. 8 shows model results before the output be- came excessively convoluted; as mentioned above, Volcanism on the relatively old lithosphere of slowly developing late stage eruptions are prob- the South Paci¢c superswell is dominated by and ably suppressed thermodynamically by solidi¢ca- perhaps limited to [5] the large volcanic chains of tion of magma in the conduit. Dimensionalizing the Tuamotu Islands, the , the with H = 2000 m, volcanoes within each chain are Cook and Austral chain, and the Marquesas Is- about 5.5 km apart, while the spacing between lands to the north. chains is around 19 km. Strong evidence against a origin for at least the Cook and Austral chains derives from inconsistent age progressions [2]. The Soci- 4. Discussion ety Islands extend hundreds of kilometers south- eastward beyond the point of `zero age' [2]; if Our model assumes that the lithosphere of the both parts of the chain are of the same origin, South Paci¢c superswell and in some near-ridge then the plume theory fails also for the Society environments is underlain by large quantities of Islands. The fact that geometric techniques [8] partial melt. Without perturbations and/or tecton- do not clearly locate any ¢xed hotspots on the ic stresses, the lithosphere forms an impenetrable superswell may indicate that none of these chains lid where the tensile strength of the rock and pos- are the product of hotspots. sibly a generally compressive tectonic stress re- We thus propose that the chains on the super- gime preclude the formation of magma fractures. swell are caused, at least in part, by the stress In our model, approximate alignment of volcanic ¢eld. Volcanic chains whose age progressions are lines with plate motion indicates deviatoric ten- impossible to reconcile with plate motion over sion in that direction. stationary hotspots are likely to be self-propagat-

EPSL 5582 5-9-00 550 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 ing disturbances of volcanic loads and associated mounts may cause deviations from perfectly linear £exure with a more-or-less uniform sublithospher- chains, resulting in the typically observed wider ic melt distribution as illustrated in Fig. 4. Other volcanic patterns within the chains (Fig. 3). Alter- chains are either generated by the same mecha- natively, the availability of melt may be concen- nism, or by plumes that are too weak to penetrate trated along the maxima of the intermediate the lithosphere on their own; above these plumes, wavelength (W1000 km) gravity anomalies. In melt migration may be aided by tectonic and this case, the volcanoes may be mostly radiating £exural stresses, such that the chains are self- outward in a pattern similar to that in Fig. 3, but propagating, but at the same time limited in ex- be constrained to chain-like patterns by a dearth tent to the melting region of the plume. The initial of melt away from the maximum of the gravity perturbation required to start the island chains lineations. Both models are consistent with the may be provided by a change in the tectonic stress observation that mid-plate stresses are typically ¢eld due to a plate motion reorganization (which not strongly deviatoric [31]. is ampli¢ed locally by an inhomogeneity in the lithosphere), the formation of a small sublitho- 4.2. Volcanism near the East Paci¢c Rise spheric melting anomaly, or a change in convec- tion. There is some evidence that mid-plate vol- While the morphology of volcanism near the canism or periods of volcanism initiate at times of East Paci¢c Rise (EPR) is strikingly di¡erent plate motion changes. On or near the superswell, from the mid-plate volcanoes of the superswell, the start of volcanism in the McDonald chain we propose that the mechanism generating both (within the Austral chain) around 4 Ma [44] types of volcanism is largely identical. The di¡er- may correlate with plate motion changes at 5 Ma ences are due to a thinner lithosphere and a more [45] or 3 Ma [8]; volcanism in the coherent stress ¢eld near the EPR. at 25 Ma [2] correlates with a plate motion change As explained in Section 2, a thin lithosphere at that time [46,47]; volcanic events in the Line with respect to the amplitude of the £exural dis- Islands at 89 and 39 Ma (or possibly 43 Ma) [48] placement necessitates the use of the equations for correlate with plate motion changes at 84 Ma [49] a plate of ¢nite thickness, which results in coales- and 43 Ma [46], respectively; and volcanism in the cence of individual volcanoes into a continuous Foundation chain at s 21 Ma [50] possibly cor- ridge over time. Flexural studies indicate that relates with the 25 Ma plate motion change the lithosphere near the EPR has an elastic thick- [46,50]. Once the ¢rst volcanic load has been em- ness of 0^1 km around 500 km from the ridge placed following some local perturbation, the next axis, increasing to 3^4 km at a distance of 2500 volcano forms near the £exural bulge of the ¢rst km from the axis [38]. While the £exure under- edi¢ce where the surface £exural stresses are most neath the volcanic loads has not been observed tensile. Such volcanism located on or near £exural directly, volcanic heights on the order of 200^ arches has been observed both as late stage £ood 2000 m and diameters of several kilometers volcanism in Hawaii [41] and as secondary chains [9,10] suggest that the resulting de£ection must in the [44]; it therefore seems be signi¢cant in comparison with the lithospheric plausible that the volcanoes within the chains thickness. The predicted coalescence of volcanoes form on the £exural bulge of the next older vol- is clearly observed in the Rano Rahi volcanic area cano, as predicted by the model. [9,10]. Signs of active or recent volcanism are ex- The general alignment of volcanoes suggests istent from the near-ridge environment out to at that a deviatoric tensile stress ¢eld interacts with least 500 km from the ridge axis [10]. It thus the £exural stresses to generate local stress max- seems reasonable to interpret the distance from ima which cause the volcanoes to form chains the ridge as a snapshot of a steady-state temporal rather than area-covering patterns as demon- evolution of volcanism. Volcanic activity com- strated in Fig. 1. Additional perturbations in mences some 30 km from the EPR in form of form of tectonic fabric or near-axis generated sea- small, individual cones [10]. The cones increase

EPSL 5582 5-9-00 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 551 in height away from the ridge. A transition from terminate some 30 km from the ridge; closer to distinct to overlapping volcanoes occurs at a dis- the ridge, the tensile stress becomes too weak to tance of 75^200 km from the ridge axis, while a allow magma penetration through the lithosphere. further change to continuous ridges occurs at a Alternatively, the mechanism of magma transport distance of about 500 km [10]. The predictions toward the ridge axis may be more e¤cient near of the model of volcanic lines formed initially the axis, thus starving the near ridge environment with fairly large intervolcanic spacing and a sub- of magma available for seamount formation. sequent decrease in spacing by additional erup- As described in Section, Fig. 8 shows the model tions within the individual lines is thus in excellent results after formation of 5 parallel chains of sea- agreement with the observations. The spacing be- mounts, but before further volcanism between the tween the volcanic lines or ridges is on the order lines perturbs the regular pattern. Shen et al. [14] of 15^20 km [10], corresponding to an elastic demonstrated that the individual lines of volca- thickness of the lithosphere of 1^2 km in the mod- noes compete with each other for melt. It is el. thus possible that the region between the volcanic The rather straight and long lines of seamounts lines has largely been drained of magma, thus are indicative of a strong and coherent stress ¢eld allowing only the formation of small seamounts near the ridge which overwhelms most perturba- [10]. The suppression of late volcanism after for- tions. Tensile stresses in the ridge-perpendicular mation of the volcanic lines is ampli¢ed by the direction are expected near the axis as they con- fact that the late eruptions must, by de¢nition, stitute the force required for driving the passive penetrate thicker and colder lithosphere. upwelling of the mantle and for extending and The Rano Rahi volcanic ¢eld and its extension fracturing of the lithosphere at the spreading cen- into the Puka Puka ridge system provide an ideal ter. It is also reasonable to expect a tensile stress regime for application of our simple model be- maximum at some distance from the ridge axis. cause the area is well studied and the EPR is The `ridge-push' force, contrary to its name, does free of major perturbations there. The situation not act on the accretionary plate boundary, but is is more complicated at other parts of the EPR distributed over the entire width of the plate [23]. where transform faults, overlapping spreading p If the thickness^ age relation holds for the litho- centers and microplates, strongly alter the near- sphere and assuming perfect , then the ridge stress ¢eld. While it is not clear if the major force due to `ridge-push' is constant over the plate near-ridge volcanic edi¢ces, such as the Easter and is probably mostly balanced locally by asthe- chain, the Foundation seamounts, and the chain nospheric drag. The forces relevant near the ridge west of the are of hotspot (or are then a plate-driving force due to slab-pull and hotline) origin or due to some other process, the resistive forces due to passive mantle upwelling, morphology of these chains and their arrange- normal faulting near the ridge, and opening of the ment into sets of ridges [51] is likely controlled ridge itself. The force thus transmitted along the by the interaction of £exural stresses with the re- plate is lowest at the ridge and greatest (and con- gional and local tectonic stress ¢eld. stant) outward from the edge of the active ridge system and upwelling region. Stress is de¢ned as force per cross-sectional area; since the plate 5. Summary and conclusions p thickness varies as age away from the ridge, but is more nearly constant in the immediate vi- A simple model of volcano formation based on cinity of the ridge, a tensile stress maximum is hydrofracture of the lithosphere in locations expected at some distance from the ridge axis. where magma pressure exceeds the local near-sur- Such a coherent stress ¢eld would not only ex- face stress ¢eld can explain the formation of vol- plain the persistence of the volcanic lines and their canic chains both on the South Paci¢c Superswell relative invulnerability to minor perturbations, and near the southern EPR; the model comple- but it may also explain why the volcanic lines ments the classical hotspot or plume models of

EPSL 5582 5-9-00 552 C.F. Hieronymus, D. Bercovici / Earth and Planetary Science Letters 181 (2000) 539^554 island chain formation in other locations. The of plate motion reorganizations when the tectonic chains are generally aligned with the direction of stress ¢eld changes.[RV] the most tensile principal tectonic stress. The propagation velocity of the volcanic chains de- pends on how much of a disturbance relative to References the unperturbed state is required to cause an eruption, and how fast the individual volcanoes [1] M.K. McNutt, K.M. Fischer, The South Paci¢c super- form. swell. In: B.H. Keating, P. Fryer, R. Batiza, G.W. Boeh- The persistence and straightness of the near- lert (Eds.), Seamounts, Islands, and Atolls, Geophysical Monograph Vol. 43, AGU, Washington DC, 1987, pp. ridge volcanic lines suggests that the tectonic 25^34. stress ¢eld is coherent over great distances along [2] M.K. McNutt, Superswells, Rev. Geophys. 36 (1998) 211^ the ridge axis and strongly deviatoric with the 244. least compressive stress perpendicular to the [3] M.K. McNutt, L. Sichoix, A. Bonneville, Modal depths axis. Such a stress ¢eld may be due to the force from shipboard bathymetry: there IS a South Paci¢c Superswell, Geophys. Res. Lett. 23 (1996) 3397^3400. driving passive mantle upwelling near the spread- [4] C.E. Nishimura, D.W. Forsyth, Anomalous Love-wave ing axis and is in agreement with observations of phase velocities in the Paci¢c: sequential pure-path and normal faulting near the ridge axis. While not well spherical harmonic inversion, Geophys. J.R. Astron. Soc. constrained observationally, the stress ¢eld on 81 (1985) 389^407. older parts of the Paci¢c plate may be similar in [5] K.G. Bemis, D.K. Smith, Production of small volcanoes in the Superswell region of the South Paci¢c, Earth Plan- direction if the zone to the north does et. Sci. Lett. 118 (1993) 251^262. not exert a signi¢cant stress, perhaps because of [6] J.T. Wilson, A possible origin of the , processes such as trench roll-back. Membrane Can. J. Phys. 41 (1963) 863^868. stresses due to volcanic loads cause the volcanoes [7] W.J. Morgan, Convection plumes in the , within near-ridge chains to coalesce into continu- Nature 230 (1971) 42^43. [8] P. Wessel, L. Kroenke, A geometric technique for relocat- ous ridges over time. ing hotspots and re¢ning absolute plate motions, Nature Local perturbations in the stress ¢eld due to 387 (1997) 365^369. transform faults, overlapping spreading centers, [9] D.S. Scheirer, K.C. Macdonald, D.W. Forsyth, S.P. Mill- microplates, and propagators may result in vol- er, D.J. Wright, M.-H. Cormier, C.M. Weiland, A map canic patterns such as those observed in the series of the southern East Paci¢c Rise and its £anks, 15³S to 19³S, Mar. Geophys. Res. 18 (1996) 1^12. Foundation seamount chain, the Easter chain, [10] D.S. Scheirer, K.C. Macdonald, D.W. Forsyth, Y. Shen, the volcanic ridges west of both the Easter micro- Abundant seamounts of the Rano Rahi seamount ¢eld plate and the ancient Selkirk microplate, as well near the southern East Paci¢c Rise, 15³S to 19³S, Mar. as possibly some of the volcanic ridges associated Geophys. Res. 18 (1996) 13^52. with transform faults (often termed `leaky trans- [11] D.T. Sandwell, E.L. Winterer, J. Mammerickx, R.A. Duncan, M.A. Lynch, D.A. Levitt, C.L. Johnson, Evi- forms'). dence for di¡use extension of the Paci¢c plate from the If the stress ¢eld on older parts of the litho- Pukapuka ridges and crossgrain gravity lineations, sphere is strongly deviatoric as well, island chains J. Geophys. Res. 100 (1995) 15087^15099. on the superswell may simply be a mid-plate ana- [12] A. Barone, W.B.F. Ryan, Single plume model for asyn- log of the near-ridge chains. However, for a chronous formation of the Lamont seamounts and adja- cent East Paci¢c Rise terrain, J. Geophys. Res. 95 (1990) weakly deviatoric stress ¢eld, the model predicts 10801^10827. a pattern of volcanoes spreading radially out- [13] L. Fleitout, C. Moriceau, Short-wavelength geoid, bathy- ward; chains may then be formed if the sublitho- metry and the convective pattern beneath the Paci¢c spheric melt is concentrated along hotlines which Ocean, Geophys. J. Int. 110 (1992) 6^28. also correlate with observed medium wavelength [14] Y. Shen, D.S. Scheirer, D.W. Forsyth, K.C. Macdonald, geoid undulations. Our model based on litho- Trade-o¡ in production between adjacent seamount chains near the East Paci¢c Rise, Nature 373 (1995) spheric stresses is in agreement with the observa- 140^143. tion that volcanism is typically initiated at times [15] A. Cazenave, B. Parsons, P. Calcagno, Geoid lineations of

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