<<

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B4, PAGES 6283-6297, APRIL 10, 1993

The Genesis of Oceanic : Injection, HydrothermalCirculation, and CrustalFlow

JASON PHIPPS MOROnN

Instituteof Geophysicsand PlanetaryPhysics, Scripps Institution of ,La Jolla, California

Y. JOHN (2HEN

Collegeof Oceanography,Oregon State University,Corvallis, Oregon

In this studywe constructa thermaland mechanicalmodel for the genesisof oceaniccrust. Magma is halted in its ascentwithin the oceaniccrust when it reachesa freezing horizon, where the dilational volumechange associated with magmafreezing leads to viscousstresses that favor magmaponding near the freezinghorizon. To modelthe steadystate thermal impact of crustalaccretion via injectionand pillow flows, we treat all crustalaccretion in rockscooler than a magma"solidus" to occurin a narrow 250-m-wide dike-like region centeredabout the ridge axis. The rest of the oceaniccrust is modeled to be emplacedas a steadystate magma lens directlybeneath the "solidus"freezing horizon where the steadystate emplacement rate is determinedby the constraintthat this lens supplyall crust that is not emplacedthrough diking/extrusion above the magmalens. If hydrothermalheat transportwithin crustal rocks cooler than 600øC removesheat 8 times as efficiently as heat conduction,then we find that a steadystate magma lens will only exist within the crustfor ridgesspreading faster than a 25 mm/yr half rate. The depthdependence of the magmalens with spreadingrate is in good agreementwith seismic observations.These results suggest that a fairly delicatebalance between magmatic heat injection during crustalaccretion and hydrothermalheat removalleads to a stronglydifferent crustalthermal structureat fast and slow spreadingridge axes. Our resultssupport the hypothesisthat medianvalley topographyis due to extensionof strongridge axis ;it is the differencein thermalregime that is directly responsiblefor the strikingdifference between the typical medianvalley seenat slow spreadingridges (e.g., Mid-AtlanticRidge) and the axial high seenat fast spreadingridges (e.g., EastPacific Rise). This paradigmfor the origin of a medianvalley at a slow spreadingridge predictsthat along-axisvariations in medianvalley topographyof a slow spreadingcenter reflect variations in recentmagmatic heat input alonga segment,that is, that the axial topographyis a goodtime-averaged indicator of the relative importanceof hydrothermalcooling and magmaticinjection along a given sectionof a ridge segment. We determinethe accumulatedcrustal strain associatedwith lower crustal flow which supportsthe hypothesisthat the Oman Ophiolitecrust was createdat a paleo-analogueto a fast spreadingridge and alsosuggests that crustalstrain, and not cumulatelayering, may be the dominantphysical process that generates"layered " within the Oman .

INTRODUCTION Rise (EPR) have yielded intriguingclues to the depth, thick- Recentseismic studies of fast and slow spreadingridges ness,and along-strikecontinuity of the axial magmachamber suggestthat a quasisteady state magma chamber exists at shal- at a fast spreadingridge [Detrick et al., 1987; Mutter et al., low • 1.5 km depthsbeneath the axis of a fast spreadingridge 1988; Harding et al., 1989; Vera et al., 1990; Kent et al., 1990; Detrick, 1991]. MCS data collected on the northem EPR [De- but is not presentwithin the crustat a slow spreadingcenter. This observationmay be a fundamentalclue to the physical trick et al., 1987; Mutter et al., 1988] show a bright reflector origin for the characteristicdifference in axial topographybe- interpretedas the top of an axial magmachamber along much tweenthe medianvalley topographyof a slow spreadingridge of the spreadingcenter. Figure 1 showsa typical across-strike andthe axial high topographyof a fast spreadingridge. Obser- MCS profile. The reflectoris continuouswhere the axial depth vationsof crustallayering in the Oman Ophiolitecan alsobe and morphologypoint to strongmagmatic activity, and it dis- used to constrainthe patternof magma injection and crustal appearsas the axis deepensand narrows. The magmachamber flow at a spreadingcenter. After reviewing these observa- reflectoris found along roughly60% of the rise axis between tionalconstraints we presenta simplemodel for heatand mass the Siqueirostransform and 13ø30'N. After correctionfor the transportwithin oceaniccrust that suggeststhat a fairly del- diffractioneffects associated with the magmachamber reflec- icate balancebetween magmatic heat injectionduring crustal tor, the inferred across-strikewidth of the magma chamber accretionand hydrothermalheat removalleads to a strongly reflector is 1-1.5 km [Kent et al., 1990]. differentcrustal thermal structure at fast and slow spreading Analysisof expandingspre. ad profile data confirmsthat the ridgeaxes, that is thata differencein thermalregime is directly reflectorcoincides with a sharpinterface between high veloc- responsiblefor the observeddifferences in axial morphology. ities above and low velocities below [Harding et al., 1989; Vera et al., 1990]. Analysisof the expandingspread profiles SEISMIC OBSERVATIONS [Harding et al., 1989; Vera et al., 1990] and tomographicin- version of seismictravel time data [Burnett et al., 1989; Caress Multichannelseismic (MCS) studiesalong the East Pacific et al., 1990; Toomey et al., 1990] reveal a broader, lower- Copyright1993 by the AmericanGeophysical Union amplitude,low-velocity zone underlyingthe thin (<100-500 m) axial magma chamberreflector (see Figure 1). This axial Paper number92JB02650. low-velocityzone is roughly6 km wide, extendsfrom a depth 0148-0227/93/92JB-02650505.00 of 1.5-2.0 km down to Moho, and consists of velocities de-

6283 6284 PHIPPSMORGAN AND CHEN: GENESISOF OCEANICCRUST

EPR CROSS-AXIS LINE ot 9ø57' N 3.0 MAGMA CHAMBER WIDTH: 700 M --

,-, 2550 M

~ 4150 M _-

_

5.0 W <--- approx. 5km

2.2

ES--

BRECCIATED DIKI

SHEETED DIKES 5 5.0 7.0

5.5 LV Z I GABBROS / 6.0

10 ULTRAMAFICS ' -•: -I 0 I 2: :5 4 5 6 7 8 9 10 W DISTANCE{kin) E Fig. 1. (Top)East Pacific Risc (EPR) Multichannel seismic (MCS) reflection structure [figure courtesy of G. Kent]. Depthsshown on the right hand side are relative to sealevel. Most of theapparent "width" of theaxial magma chamber (AMC) reflector(shown by centralline pointer) is dueto diffractioneffects (shown by sideline pointers). The actual magmachamber width here is roughly700 m. (Bottom)Correlation of MCS and expanding spread profile (ESP) seismic datawith inferred geological description of . Velocity contours are in kilometersper second. AMC is shaded. Axial low-velocityzone (LVZ) showsregion of "hotrock" (modified from Vera et al. [1990]). pressedby 0.5 to 1.0 km/s. This smallreduction in velocityis that even the smallest discontinuities form boundaries between consistentwith marie or ultramarierocks containingless than differentmagma sources. However, the combinationof a sur- a 3% melt fraction [Caress et al., 1992]. prisinglysmall volumeof subaxialmelt and the along-axis The pictureof axialstructure that emerges from the northern continuityof the magmachamber for tensof kilometerssug- EPR seismicwork includesa 6-km-wide zone of hot plutonic geststhat melt productionmust be quitesteady and that the rockswith a smallor negligibleamount of melt cappedby a magmamust generally cycle through the axialsystem rapidly. thin (<100-500 m thick), narrow(0-2 km wide) lensof high This is a radicallydifferent magma chamber structure than melt fraction. The narrownessof the actual magma cham- that proposedin manyprevious ideas of a crustal-thickness- ber and its further constrictionor interruptionat small axial size chamber,although it is essentiallythe magmachamber discontinuitiesare consistentwith the petrologicalobservation structureenvisioned by Sleep [1975; 1978]. It is consistent PHIPPS MORGAN AND CHEN.' GENESIS OF OCEANIC CRUST 6285 with ophioliteevidence for 100 m scalecryptic geochemical magma lens constraints. variationwithin the crustalgabbros of the Oman Ophiolite [Browning, 1984], and a magma lens of the size seen at the OPHIOLITE OBSERVATIONS EPR is large enoughto easily generatethe major extrusives As noted above, the Oman ophiolite, thought to be cre- recentlymapped along the Cocos-NazcaRidge [Macdonaldet ated at a fast spreadingcenter [cf. Nicolas, 1989], shows al., 1989]. Gravity dataalong the EPR are alsoconsistent with cryptic chemicalvariation which suggeststhat only a small a smallmagma chamber [Madsen et al., 1990],as is along-axis magma body was presentat any time during crustalaccre- petrologic segmentation[Sinton and Detrick, 1992]. Sinton tion [Browning, 1984]. In additionthis ophiolite showsa and Detrick [ 1992] presentan excellentrecent overview of this structuralsequence through the gabbrosection from isotropic emergingparadigm about the axial structureof a fast spread- gabbrosdirectly beneath the sheeteddike/ contact grad- ing ridge axis, and Phipps Morgan [1991] also summarizes ing downwardsto more strongly"layered" gabbros near the recentwork on this subject. J.E. Quick and R.P. Denlinger gabbro/mantleperidotite interface [e.g. Pallisterand Hopson, (Ductiledeformation and the originof layeredgabbro in ophi- 1981; Nicolas et al., 1988]. Changinglayer dips within the olites, submittedto Journalof GeophysicalResearch, 1992) gabbrosection have been usedto infer the shapeof a near- (hereinafterreferred to as Quickand Denlinger, 1992) present ridge magmachamber in which these"cumulate layers" are a petrologicalinvestigation and Henstock et al. [1992] present deposited[Smewing, 1981]. In particular,this fabric devel- a geophysicalinvestigation of this type of magmachamber opmentshown in Figure 2 was cited by Smewing[1981] and structurethat stronglycomplement the resultsof the present Pallisterand Hopson[1981] as evidencefor a broad,gently study. dippingmagma chamber that depositedtilted cumulate layers To date, seismicreflection work on the Mid-AtlanticRidge on its floor. (MAR) showsno evidencefor magmachamber reflectors, sug- Ophiolitecrustal rocks also recordevidence of near-ridge gestingthat magma chambersare transientfeatures on slow hydrothermalalteration [Harper et al., 1988; Nehlig and Ju- spreadingridges [Detrick et al., 1990]. Along-axisvariations teau, 1988]. Below the volcanics,sheeted dikes, and upper in velocitystructure near the TAG hyrdrothermalmounds area gabbrosof the Oman ophiolite,hydrous activity appearsto of the MAR does,however, suggest a recentintrusion of hot be concentratednear faultsor within narrow,apparently tec- in this region [Konget al., 1992]. Petrologicaldata also tonizedzones [Nehlig and Juteau, 1988]. This suggeststhat indicatethat long-lived magma chambersare not a common there may be a link betweenhydrothermal activity and the featureof slow spreadingridges [cf.Natland, 1980]. In fact, style of extensionaldeformation. Toomeyet al. [1988] and Kong et al. [1992] show that mi- croseismicactivity beneaththe MAR axis extendsto depths HEAT AND MASS TRANSPORT WITHIN OCEANIC CRUST of 6-10 km, implyingthat the brittlelayer is present,at least episodically,to thisdepth. Huang and Solomon [1988] present In this section we will construct a thermal and mechani- teleseismicdata which supportsthis conclusion.Their data, cal model for the genesisof oceaniccrust that we feel is a shownin Figure 8, also show that the thicknessof the seismo- goodcandidate model to integratethe aboveobservations into genicridge axis lithospheredecreases with increasingspread- a coherentsynthesis. The basicmechanical model is not par- ing rate. Since the depth to the seismicbrittle-ductile transi- ticularlynew, and its conceptualfoundation has already been tion is thoughtto roughly correspondto the 750øC isotherm presentedby PhippsMorgan et al. [ 1987], Lin and Parmentier [Bergman and Solomon, 1984; Wiens and Stein, 1983], this [1989], and Chenand Morgan [1990]. Its mostimportant con- observationimplies generally cooler crust at slowerspreading ceptualingredient is that it is the interplaybetween magmatic ridges. Purdy et al. [1992] show a complementaryrelation- crustalinjection and hydrothermalcooling that is responsible ship: the depthto the top of the axial low-velocityzone gets for the presenceof a quasisteady state magma lens beneath shallowerwith increasingspreading rate. Similarly, micro- a fast spreadingridge and the dramaticchange in axial mor- earthquakeobservations [Riedesel et al., 1982] suggestthat phologybetween a fast andslow spreadingridge axis (because the brittle layer extendsto a depthof only •2 km depthat a axial morphologydirectly reflectsthe lithospherestrength or fastspreading ridge where large amplitude ridge axis topogra- thicknessacross a ridge axis which is quite sensitiveto this phy is absent. thermalbalance). The resultingmagma injection and crustal The strongcorrelation between an axial seismic"magma flow structurethat we envisionis extremelysimilar to the chamber"and a surficial"fast spreading"axial morphology qualitativecrustal scenario sketched by Sleep[1975; extendsto intermediatespreading ridges. MCS lines across 1978] and also similar to the subsidingmagma chamber floor the Juan de Fuca Ridge [Morton et al., 1987; Rohr et al., model of Dewey and Kidd [1977]. 1988] and the Valu Fa Ridge in the Lau Basin [Morton and What is new in this study is that we considerhere that Sleep, 1985b; Collier and Sinha, 1990] also show an axial crustalaccretion at a fast spreadingridge is stronglyshaped magmachamber reflector where a "fastspreading" axial high by the maximumheight to whichmagma can rise in a steady morphologyexists. There is a slight spreadingrate depen- state mannerbefore freezing. We also extendthis model to denceto the depthof the magmalens with the shallowestlens calculate the strain associatedwith lower crustal flow, so we depthsat the fastestspreading rates [cf. Purdy et al., 1992]. may compare model predictionsof crustal strain associated These data and uncertaintiesare plottedin Figure 7. Unlike with a givenmagma injection geometry with observationsfrom Purdyet al. [1992] we do not mix measurementsof the depth the Oman Ophiolite. to a magma lens with measurementsof the top of the axial low-velocityzone at slower spreadingrates. We feel that the Magma Ascent and Emplacement depthto an axial low-velocityzone is a differentthermal mea- Magma ascent within the oceanic crust is probably con- surementthan the depth to (or existenceof) a magma lens trolled by two complementaryprocesses: (1) magmawill as- and thus shouldnot be directly comparedwith observational cendonly if buoyancyforces (or, if largeenough, viscous pres- 6286 PHIPPS MORGAN AND CHEN: GENESIS OF OCEANIC CRUST

GabbroLayering & Genesis-- Oman Ophiolite[Smewing, 1981]

I$otroDic gabbro MagmaChamber

Harzburgit© tectonitt

I I 1 km FeederZone

Fig. 2. Schematicstructural cross section of the crustalsection of the OmanOphiolite. Figure is redrawnfrom Sinewing [1981]. The stratigraphicsequence below the pillow and sheeteddike complexesis shownon the right sideof the figure. Isotropicgabbros just beneaththe sheeteddike complexgrade into gabbroswith a (weakly developed)near verticaldip whichbecomes more developed[Nicolas et al., 1988; Nicolas, 1989] and more shallowlydipping as one movesdeeper into the gabbrosection. (The layeringis best developedand parallelto the Moho directly abovethe gabbro-peridotite• "petrologicMoho" contact.)This dip structurein particularwas usedby Sinewing[1981] to infer that gabbrolayering reflectscumulate deposition on the floor of the largemagma chamber sketched here. We proposethat thesestructures are equally explainedas the by-productof crustalstrain shown in Figure 4, that is, that the structuresare the resultof crustalflow from a magmalens intrusive zone much like that imagedseismically along a largefraction of the present-day (see Figure 1). sure gradients)cause it to; thus magmasmay rest their ascent eled to be emplacedwithin this region. Althoughthis correctly for a while at zonesof neutralbuoyancy until they have frac- treatsheat injection within the sheeteddike section,this ap- tionated and reactedto the point where the magma'sdensity proximationdoes somewhat overemphasize the importanceof is less than that of surroundinghost rock (this idea has been magmaheat injectionwithin the pillow section.Since pillow explored in particular by Ryan [1987]) and (2) magma can flows are extruded on the seafloor,burying previousflows, also be haltedin its ascentwhen it reachesa freezinghorizon, they rapidly cool to the ambientseawater temperature and es- where the dilational volume changeassociated with magma sentiallyadvect this cold boundarylayer downwardwith sub- freezing leads to viscousstresses that favor magmaponding sequantpillow burial and subsidence[Sleep, 1991]; C. A. J. within roughly one viscous"compaction length" (term coined Harding et al. (A multichannelseismic investigation of upper by McKenzie [1984]) of the freezing horizon. This idea has crustalstructure at 9øN of the East Pacific Rise: Implications beenrecently proposed in a particularlysimple form by Sparks for crustalaccretion, submitted to Journalof GeophysicalRe- and Parrnentier [1991] to explain melt focusingto a narrow search,1992) (hereinafterreferred to as Harding et al., 1992). neovolcaniczone at a spreadingcenter. In this study we will The maximum amount that we will underestimatethe depth consideronly the effectsof magmafreezing in limiting melt of the magma lens isothermis given by the thicknessof the ascentand ignore densityeffects on lower crustalmelt trans- pillow sectionabove the magma lens. Recent MCS results port, reaction, and segregation;while magmaneutral density constrainthe axial thicknessof the pillow sectionto be •,, 200 effectsin particularmay play an importantrole in shapingthe m alongthe axis of the EPR, thickeningto •,, 600 m within 2 chemicalstratification in oceaniccrust we wish initially to ex- km of the ridge axis (Harding et al., 1992). plore the idea that it is the Sparks-Parmentiermagma freezing The rest of the oceanic crust is modeled to be emplaced effect that leadsto a quasisteady state magma lens beneatha as a steady state magma lens directly beneath the "solidus" fast spreadingridge. freezing horizon. We take the • 1-km-wide • 250-m-thick Since magmafreezing mustoccur (by definition)within the prismaticshape inferred from recentEPR seismicstudies cited sheeted dike and extrusive sections of oceanic crust, these ac- aboveto be a kinematicconstraint on the shapeof this magma cretionprocesses, unlike a magmalens, mustbe fundamentally lens. Once we have this shape,the steadystate emplacement transientin nature. To model the steadystate thermal impact rate is determinedby the constraintthat this lens supply all of crustal accretionvia dike injection and pillow flows we crust which is not emplacedthrough diking/extrusionabove treat all crustal accretionin rocks below a magma "solidus" the magma lens. The depth of this lens is controlledby the to occur in a narrow 250-m-wide dike-like region centered depth of the magma "solidus"(here taken to be 1200øC)de- aboutthe ridge axis. Within this region, magmaemplacement terminedfrom a self-consistentthermal structurefor a spread- ratesare taken to be equalto the spreadingrate dividedby the ing center. Thus the lens will ceaseto exist in this model if width of the diking region, that is, all shallowcrust is mod- the steadystate thermal structureplaces this solidusisotherm PHIPPSMORGAN AND CHEN: GENESISOF OCEANICCRUST 6287 beneaththe crust. In addition, the injection rate within the Thus for a lower Tcutoffwe find that we will needa higher lens will diminish as the lens moves deeper into the crust, Nu value to producea magmalens at a given depthfor a fast sincemagma injection into the lensonly suppliesmagma for spreadingnumerical experiment. Figure 3 showsthe strong crustal sectionsbelow the sheeteddike complex. Note that trade-offbetween Tcutoff and Nu in coolingoff the axialup- this "solidus"temperature should be viewed as the effective per crust, illustratinggraphically that once we can determine temperatureat which the magmais sufficientlycrystallized to Tcutofffrom rock and waterchemistry observations, then we behave mechanicallyas a strong, viscousfluid. While the canuse this approachto determinethe effectiveadditional heat freezinginterval of a coolingbasaltic liquid will have impor- transportby hydrothermalcirculation and so estimatethe ef- tant effects on the chemical/petrologicevolution of magma fective permeabilitywithin the hydrothermalsystem. Gregory and rock, it will only have a secondaryeffect on the thermal and Taylor [1981] report that subsolidusoxygen isotopeex- structureand flow away from a magmalens and will therefore changeoccurred mainly within the upper5-6 km of the ophi- be neglectedwithin this initial studyof the physicsof crustal olite, thus giving an estimateof the maximumdepth of water flow and heat transport. For the same reasonwe do not ad- penetration. In these studieswe generally chooseto model dressconvection and magmafractionation processes within the hydrothermalheat transportas Nu = 8. We choosethis value magmalens. See Quick and Denlinger(1992) for an analysis becauseit leads to a solutionwhere a steady state magma of someof the petrologicconsequences of crustalgenesis by lens can exist at 1.2- to 1.5-km depthsbeneath a fast spread- predominantmelt injectionwithin a small magmalens. ing ridge and not exist beneatha slowly spreadingridge (see The thermalstructure at a spreadingcenter is predominantly Figure 7). influencedby two factors in this model: (1) the depth and As noted above, deep hydrothermalalteration within the injectionrate within a potentialsteady state magma lens, and Oman ophiolite seemsto be concentratednear faults. This (2) the efficiencyof hydrothermalcirculation in removingheat observationsuggests that it may be a reasonablehypothesis throughrocks that are cool enoughto permitcracking and hy- that crustalextension through faulting openschannels for hy- drothermalheat transport.To assessthis conceptualmodel we drothermalflow and thesechannels lead to a highereffective haveimplemented it asa finiteelement code based on thecode hydrothermalcooling enhancement in slow spreadingenviron- describedby Chenand Morgan [ 1990]. We havemodified the mentswhere large medianvalley boundingnormal faults and flow solver of this code to solve for a flow problem which 6- to 10-km-deepseismically active faults are present(Figure includesthe effectsof magmainjection or removalinstead of 8a). In this studywe will only briefly explorea spreadingrate purely incompressibleviscous flow. Details of our solution dependenceto the efficiencyof hydorthermalheat transport. algorithmare presentedin the Appendix. If this dependencedoes exist (which we feel is likely), it is likely to be an enhancementfrom Nu =8-10 at fast spreading Hydrothermal Cooling ridgesto Nu =12-15 at medianvalley ridges. We choosenot The primary remaininguncertainty in thesenumerical ex- to include this effect becauseit will only enhancethe already perimentsis how to appropriatelyparameterize the form and strongtrends that are seenin the following suiteof numerical magnitudeof theseeffects of hydrothermalcirculation on shap- experiments. ing heattransport within the crust.We choosethe formulation MODEL RESULTS developedby PhippsMorgan et al. [1987] whouse the results At a fast spreadingridge where hydrothermalcirculation of Combarnous[1978] to treat hydrothermalheat transport as an enhancedthermal conductivity within the temperature • o.o and depthrange where hydrothermalactivity occurs.Where 50 mm/yr hydrothermalcooling occurs,the ordinarythermal conductiv- 0.5 ity is enhancedby a factor Nu, the Nusseltnumber or ratio of hydrothermalheat transportwithin a permeablelayer to •.0 heattransport by heatconduction alone. Rock at temperatures greaterthan 600øCor a depthgreater than 6 km is assumedto •.5 be impermeable.Since water as hot as 400øCdischarges from vents on the seafloor,this is a minimum value of the maximum 2.0 temperaturethrough which water mustcirculate. Phipps Mor- 2.5 gan et al. [1987] and Sleep[1991] use a value of 400ø-450øC for this cutoff temperature,while Morton and Sleep [1985a] and Wilsonet al. [1988] prefer a hotter600øC cutoff for hy- Tcutoff=400oC xx Tcutoff=6000C xx drothermalcirculation. Morton and Sleep [ 1985a] suggestthat 5.5 the limit temperatureshould be at least that obtainedby ex- Tcutoff=800oC xx trapolatingthe surfacehydrothermal venting temperature down 4.0 to 45-MPa pressuresat a shallowmagma lens which yieldsa 4 6 8 10 12 14 465øC cutoff [Bischoffand Rosenbauer,1984]. In addition, Nusselt number (Nu) they suggestthat hydrothermalcooling will rapidly cool the Fig. 3. Plot of the depth to the top of an axial magma lens de- near crack environsso that the averagerock temperaturecan scribed in the text for a half-spreadingrate of 50mm/yr and vari- be ,-•600øCwith fluid presentin locally coolercracks. ous hydrothermalheat transportenhancement factors Nu and cutoff For the purposesof this studywe can sidestepthis question isothermsTcutoff above which hydrothermal flow ceases.The effec- to some degree becausethe hydrothermalheat loss will be tivenessof hydrothermalcooling will determinehow deep a steady statemagma lens will reside.Thus if we candetermine Tcutoff by governedby an approximateproduct of the hydrothermalheat a geochemicalmeans, then the depth of a steadystate magma lens transportenhancement factor Nu timesthe hydrothermalcut- will directly constrainNu. See text for more explanationof this off temperature,e.g., qhudro• (Tc,,.toff-Twater)Nu/zc•,.toff. relationship. 6288 PHIPPSMORGAN AND CHEN: GENESISOF OCEANIC CRUST __ removesheat 8 timesas efficiently as purelyconductive crustal SpreadingRate Dependenceof a Magma Lens coolingwhen the crustis coolerthan 600øC, magmafreezes Figure 7 showsthe depthto a magmainjection lens plot- at 1200øC, and the latent heat of solidificationis 334 kJ/kg, a ted versusspreading rate whereNu and the solidustemper- steadystate magma chamber exists 1.35 km belowthe seafloor ature are fixed and only the spreadingrate is varied. In this 0øC boundingisotherm (see Figure 4). All magmathat forms casethere is a fairly abrupttransition with spreadingrate from the lower crust rises to this level, freezes, and then flows to a shallowsteady state magma lens at a 30mm/yr spreading deepercrustal levels. half rate to no steadystate magma lens within the crustat a 20 mm/yr spreadinghalf rate. There is goodagreement with Strain and the Developmentof GabbroLayering seismicobservations of thedepth to a magmalens as a function Once we have solved for a steadystate flow field, the ac- of spreadingrate which are alsoplotted in Figure7. (Note, cumulated crustal strain associated with crustal flow is found however,that the higher Nu=12 shownin Figure 7 is more using the formulationand techniquesdeveloped by McKen- consistantwith the 30- 35 mm/yr spreadinghalf rate which zie [1979]. Figure 4 showsthat at a fast spreadingridge is roughlyobserved [Macdonald, 1986; Smalland Sandwell, the accumulatedstrain during this flow processis most in- 1989] as the transitionalspreading rate between median valley tenseat deepercrustal levels. Strain becomesprogressively andaxial high relief, but it is lessconsistent with the depthof more intenseand more flat lying as the Moho is approached; the magmalens at fastspreading ridges; these results support a the strain within the lowermost kilometer of the crust is too slighthydrothermal enhancement associated with medianval- strongto effectively show with with the "stretchedellipse" ley extension.)We performeda suiteof numericalexperiments conventionshown in Figure 4. A comparisonof Figure 4 in whichthe magmalens was assumed to be a 2-km-wide,500- with Figure 2 clearly showsthat crustalstrain can produce m-thickbody, that is twice the width and morethan 4 times layeringwith the dip andlayer developmentseen in the Oman the volume of the lens in the above numerical experiments. Ophiolite,thus providing an appealingexplanation for the ori- We foundthat the depthof the lensis moststrongly controlled entationand strengthof lower crustallayering. In contrast, by the balancebetween the rate of magmainjection within for a slow spreadingridge (Figure5), no steadystate magma the lensand hydrothermalcooling; to first ordera biggerlens lens existswithin the crustfor the samehydrothermal cooling doesnot influencethe net rate of magmainjection and hence enhancement,while for an intermediatespreading half rate of doesnot effectthe depthof the lens. To secondorder, a wider 30 mm/yr a steadystate magmalens can exist at a deeper lensis moreefficiently cooled at the axis,resulting in a slightly level within the crust(see Figure 6). (200-300m) deeper2-km-wide lens than a 1-km-widelens for

MOR CRUSTAL FLOW & TEMP (50 mm/yr)

ß •: ..•;•.•-:t:••,...... %.•:•;•-:-... ß...... , ...... • --'?-.. ..:--•:•--:.-•:,----• lOOO

...... ':'• .'...... ß :;'" '•':' {•1' .

750

;*.•:•'-'""...... ½ t•:.•'•:::' .... • ...... •i"..... "*• ...... •.'• .... :*•-'a•i ..... ,'ill:'. ":•' '•'•' "•..... •i'•/;.:•'. i...... 600 3 -':-:':":"" g' d ;t ?g?'.,½ :.i.lil.

E;::I i::!':::: ß 5 .....-...... i! :.::?:;:::;;:i ...... ::'.:!:!..:-::.:::;;::-•.: ...... "..:..:.i:t:!:•i;i .:•..;•:•,.---i;;; ...... •!' ...... :-:e'."- ...... '',:::a ...... •-:'";-•.•.:?..'• at" •, i"!i'•"":•:'ii;.j-.- ..---•-•.-:,':,.- .':':-' ";-,.'--•a• ':'"' ...... ' ..'"';",.:x-.-.,-'• :,:'": '.

I I 0 a 4 6 8 10 Distance from ridge axis (km) 100 mrn/yr 1 (undeformed) Fig. 4. Temperature,flow, and crustal strain for a modelspreading center with an openinghalf rate of 50 mm/yr, Nu = 8, andTcutoff = 600øC.Thermal structure is shown by levels of greyshading; crustal flow is shownby arrows. The extentof themagma intrusion zone is shownby theheavy contour; in thiscase intrusion is limitedto the "dike" sectionand a shallowmagma lens directly beneath the dikingzone. Crustalflow linesaway from the intrusionzone areshown by lightlines, and accumulated strain is shownat 15,000-yeartime steps along the crustalflow lines. We suggestthat the gabbro fabric will reflectthe accumulated strain pattern resulting in a fabricdevelopment like thatseen by Smewing[1981] (Figure 2) thatis a consequenceof a crustalflow away from a quasisteady state shallow level intrusion zone.This figure was extracted from a calculationdone in thelarger computational domain shown in FigureA1. Seethe text and Appendixfor detailsof the solutionprocedure. PHIPPS MORGAN AND ellEN.' GENESIS OF OCEANIC CRUST 6289

MOR CRUSTAL FLOW & TEMP (10 mm/yr

200

0 0 2 4 6 8 10 Distance from ridge axis (km) i 10mm/yr e 1 (undeformed) Fig. 5. Temperature,flow, and crustalstrain for a model spreadingcenter with an openinghalf-rate of 10 mrrdyr, Nu = 8 andTcutoff = 600øC.Thermal structure is shownby levelsof greyshading, crustal flow by arrows,and crustal flowlines by lightlines emanating from the intrusion region. The extent of themagma intrusion zone is shownby the heavycontour; in thiscase intrusion within the crustis limitedto a "dike"section which extends completely through the crust since none of the crust is hot enoughto sustaina quasi steadystate magma lens. Accumulatedstrain is shown at 160,000-yeartime stepsalong the crustalflow lines. In this figurethere is not nearlyas stronga gradientin accumulated crustalstrain as in Figure 4 becausethe intrusionrate is constantwith depth. A small gradientexists becausepassive mantle flow near the Moho beneaththe ridge axis moves slower than the plate openingvelocity. This flow pattern occursbecause the weak lower crusteffectively actsas a near-ridgestress free boundarycondition on manfie in responseto plate spreading. the sameNu, hydrothermalcutoff temperature, and spreading foci of axial accretionprocesses [e.g. Macdonaldet al., 1988; rate. PhippsMorgan, 1991]. Lin and PhippsMorgan [1992] note We can use Figures4 and 5 to assessthe implicationsof that while gravityand topographydata show that slow-spread- a deepermagma injection lens beneath a fast spreadingridge. ing ridgeshave a clear along-axisvariation in crustalthick- If magmainjection is relativelyuniform with depth (like in ness (i.e., integratedmagma supply varies along-axis),the Figure5) then therewill not be majordifferences in accumu- much smaller along-axisgravity and topographyvariation at lated strain with depth in a crustalor ophiolite section. In a fast spreadingridge can be explainedby either a more two- the accumulatedstrain hypothesis for the developmentof lay- dimensional(2-D) patternof upwellingand meltingbeneath a ering, it is where the flow "turns"a comer that the straining fast spreadingridge or by a well-connected,temporally per- is most intense; thus if injection occurredat the bottom of sistentmagma lens (or low-viscosityzone) that smoothsthe the crust with crustal flow to shallower levels, then we would along-axiscrustal structure at a fast spreadingridge. Within expectthe oppositesense of layer developmentto that seen this latter scenariowe can interpretthe abovemodel resultsas in the Oman Ophiolite. It is only a shallow-levelintrusive modelingcrustal flow due to along-axisfeeding of the sheeted centerthat leadsto isotropicgabbros at shallowstratigraphic dike section and the magma lens; to first order the model levelsundedain by progressivelymore deformedgabbro sec- will not be different if magma supply comesfrom the side tions. Thus the layering development,intensity, and gabbro insteadof from locally beneaththe crust. For slow spreading dips in the Oman Ophiolitesupport a scenariowhere crustal ridges, the model assumptionof a 2-D crustalflow structure injectionto form this crustoccurred by predominantmagma away from a diking regionis not as strong.Again, along-axis freezingwithin a narrow near the sheeteddike-isotropic crustalflow will preferentiallyoccur in the hottest,weakest gabbrocontact. This is in agreementwith previousassertions regionssince plate extensiontends to confineflow of stronger that this crust was createdat an analogueto a fast spreading regionsto the plate-spreadingdirection. However, the crustal ridge like the presentEPR spreadingcenter [ e.g. Nicolas, thicknessis not stronglysmoothed by along-axisflow resulting 1989]. in • 3 km along-axiscrustal thickness variation [e.g. Black- man and Forsyth, 1991]. The resultingheat transportcan be Implicationsof Along-AxisMagma Transportand Injection partially approximatedby considering2-D vertical slicesin Currently,them is a debateabout whether magma emplace- the plate spreadingdirection which vary in crustalinjection ment along a fast spreadingridge is fairy continuousalong- rate (oc crustal thickness)from a thick segment-centerslice axis or confined to a few discrete volcanic centers that are to a thinner crust segment-endslice. However, a quantitative 6290 PHIPPS MORGAN AND CHEN: GENESIS OF OCEANIC CRUST

MOR CRUSTALFLOW & TEMP (30 mm/yr) 0 •;-...... -.: '-'...... -" .' •. '• •*.,_•' •,.'•'•;•-:.,-•,.'•,,,ar-s:'.•;,x•*•', :.'.•-,:t,•.---->,_•.:=•,:,'•.' ,.*.,%**.,---•:•,,:•.,•---:

1000

2 750

600

4

5

6 o 2 4 6 8 10 Distance from ridge axis (km) 60 mm/yr ß 1 (undeformed) Fig. 6. Temperature,flow, and crustalstrain for a modelspreading center with an openinghalf-rate of 30 mm/yr, Nu = 8 andTcutoff = 600øC.Thermal structure is shownby levelsof greyshading; crustal flow by arrows,and crustal flow lines by light lines emanatingfrom the intrusionregion. The extentof the magmaintrusion zone is shownby the heavycontour; in this caseintrusion within the crustis deeperthan in Figure4, reflectingthe reductionin magma emplacementcompared with a fasterspreading ridge. Accumulatedstrain is shownat 35,000-yeartime stepsalong the crustalflow lines. In this figurethere is a similarbut deeperand weakergradient in accumulatedcrustal strain compared to that in Figure 4. comparisonof the along-axisimplications of this model for a frequently cited explanationfor forces which lead to a me- slow spreadingridge really demandsa full three-dimensional dian valley [Sleep, 1969; Lachenbruch,1973, 1976; Sleepand (3-D) model treatmentwhich is beyondthe scopeof the cur- Rosendahl,1979]. However, the strengthvariations required rent study. In addition,transient magma injection effects will to form a conduit are difficult to explain solely on the basis becomemore importantin regionswhere a quasi-continuous of feasible near-ridgethermal structureslike those shown in along-axismagma lens doesnot exist. this study (compareFigure A1) as well as in previousstud- ies [Phipps Morgan et al., 1987; Lin and Parmentier, 1989; Implicationsfor Axial Topography Chen and Morgan, 1990]. Phipps Morgan et al. [1987] note A viscousflow-induced pressure drop due to an additionalsignificant difficulty for viscous"conduit" theo- ascendingin a narrow subridgechannel or conduit is one ries for medianvalley topography.How can they explainthe existenceof fossil median valley topographyon 10-100 Ma Magma Lens Depth' Observations and Model 0 Nu=8 EPR Fig. 7. Depth to the top of the magma lens as a function of Nu=lœ spreadingrate, all other parametersbeing held constant(the sameas in Figures 4-6, which plot as the 50, 10, and 30 mm/yr points on ..... this curve). Solid line showsresults from a suiteof numericalexper- J imentswith Nu = 8 andTcutoff = 600øC.For thesehydrothermal cooling parametersa steady state magma lens can exist within the crust only at spreadinghalf rates greater than about 20 mm/yr. A T /Lau well-developedshallow magma lens exists only for spreadingrates / I greater than 30 mm/yr. Dashed line shows results from a suite of m 4- ! iI numericalexperiments with Nu = 12 andTcutoff = 600øC.For these ! hydrothermalcooling parameters a steadystate magma lens can exist ! 0 5- within the crust only at spreadinghalf rates greater than about 30 mm/yr. A well-developedshallow magma lens exists only for spread- 0 • 6 km thick crust ing half rates greater than 40 mm/yr. Solid squares(and associated 6- no lens o uncertaintiesfrom Purdy et al. [1992]) show multichannelseismic Tcutoff=600øC observationsof the depth of the magma lens along intermediateand .,,.z 7- ß Seismic Reflector fast spreadingridges (JdF is Juande Fuca [Morton et al., 1987; Rohr et al., 1988]; Lau is Lau Basin [Collier and Sinha, 1990]; and EPR is East Pacific Rise [Detrick et al., 1987; Purdy et al., 1992]). There 8 is a good agreementbetween model predictionsof the depth depen- 0 10 20 30 40 50 60 70 80 denceof the magmalens with spreadingrate andmultichannel seismic Half-spreading rate (mm/yr) observations. PHIPPSMORGAN AND CHEN: GENESISOF OCEANICCRUST 6291 old abandonedspreading centers when the decay time for the of the relative importanceof hydrothermalcooling and mag- viscousstress supported topography above an axial conduitis matic injectionalong a given sectionof a ridge segment.Thus of the order of only 30,000 years? along-axisvariations in crustalthickness should be correlated Phipps Morgan et al. [1987] proposedthat the extension with variationsin medianvalley relief, with thicker (= hotter) of a strongridge axis lithospherelayer may be the origin axial crustat relative lows in medianvalley relief alonga seg- of medianvalley topographyas originallysuggested by Tap- ment [PhippsMorgan, 1991]. This hypothesisis supportedby ponier and Francheteau[1978]. (Note that Tapponierand currentevidence about along-axis variations in the temperature Francheteau[ 1978] actuallydevelop an elastic-isostaticmodel structureof a slow spreadingridge found from seismicveloc- for the formationof medianvalley topographythat is a differ- ity variationand along-axisvariations in maximal microearth- ent mechanismfrom their original "necking"suggestion and quakehypocentral depths. Figure 9 showsa recenthypocenter thatwrongly predicts an extremelythin crustal "hole" at a slow distributionalong a segmentof the Mid-Atlantic Ridge [Kong spreadingridge axis.) PhippsMorgan et al. [1987]show that et al., 1992]. There is a strongpositive correlationbetween momentsdue to lithosphericstresses within a brittleplate that maximumhypocentral depths and ridge axis bathymetryand a is 8 km thick at the ridge axis and thickensby only a few similar relationshipbetween along-axis velocity structure and kilometers within the 30 km halfwidth of the axial valley can ridge axis .These correlations imply that the shal- producethe typical axial topography of a slowspreading ridge. lowest sectionsof a ridge segmentare underlainby a hotter, Lin and Parmentier [1990] developedan elastic/plasticideal- weaker crust; at a given depth, a hotter temperatureleads to izationof plateextension which allows them to directlyexplore slower seismicvelocities. The axial depth/maximumhypocen- .thetransient development of extensionalrift valleytopography. tral depthrelationship shown in Figure 9 also impliesthat the They found that the form of the valley dependson the shallowestsections of a ridge segmentare underlainby a thin- thicknessand thicknessvariations in the stretchinglithosphere ner strong,brittle lithosphere,suggesting that the volume of and that the lithospherestress-supported topography remains crustalinjection (magmaticheat input) shapesthe lithosphere afterextension stops, successfully explaining the persistence of thicknessalong a spreadingcenter. failedrift topography.In thisscenario, the axialhigh typically seenat fast spreadingridges is not supportedby lithosphere DISCUSSION stretchingstresses which are very smallacross the thin, weak, axial lithosphereof a fast spreadingridge. Insteadthe axial This study has focusedon marshalingfurther evidencefor highis isostaticallysupported by the low densitymelt lens and two aspectsof an emergingparadigm for the origin of axial regionof "hot rock"directly beneath the ridgeaxis. topographyat a mid-oceanridge: (1) stretchingof strongax- This studysupports the idea that it is the balancebetween ial lithosphereis responsiblefor the origin of a medianvalley magmaticheat input and hydrothermalheat removalwhich along a spreadingcenter, and (2) the thicknessof this strong determinesthe thickness(m yield strength)of the axial litho- lithosphereis controlledby a delicate balancebetween heat sphere,which in turn controlsthe axial morphologyassoci- input by magma injection and removal by hydrothermalcir- ated with plate boundaryextension. The axial "strength"of culation so that the presenceor absenceof axial topography the lithosphereis a qualitativemeasure of the magnitudeof directly reflectsthe axial thermal structurealong a ridge. This the horizontalextensional stress that can be supportedduring paradigmis shownto be consistentwith a thermallycontrolled ridge axis extension.Figure 8 showsthe axial yield strength magma"solidus" temperature which limits the heightat which as a functionof spreadingrate for two crustaland mantlerhe- magma rises to and can exist as a quasi steadystate feature ologies: (1) where the crustand mantlerheology are both at a spreadingcenter. It is consistentwith the melt lensesre- describedby an olivinebrittle-ductile rheology, and (2) where cently imaged along fast spreadingridges but which have not the crustis describedby a weakerdiabase rheology while the been found where an axial valley morphologyis present.We mantle is describedby an rheology. (See Chen and have also shownthat the progressivedevelopment and orienta- Morgan [1990] for more discussionof an appropriateridge tion of gabbrolayering with increasingdepth within the crustal axis rheologicalstructure.) Again, in all numericalexperi- sectionof the Oman Ophiolite supportthis emergingparadigm mentsthe only physicalparameter that variesis the spreading if the developmentof layer-structureswithin the crustreflects rate. Independentof detailedcrustal rheology, there is a strong how much viscousstrain a gabbrohas experiencedrather than increasein axial yield strengthonce the half spreadingrate reflectinga cumulate"settling" mechanism. dropsbelow m 20 mm/yr. The largevariation in integrated While we feel these results are robust, there are several axial yield strengthwith spreadingrate shownin Figure8 is aspectsof this study that should be improved and explored a likely reasonfor the typicalpresence of a stronglithosphere in future studies. The first is time dependence. We chose extension-generatedmedian valley at a slow spreadingridge in this study to examine as simple a model as possibleand and its absenceat a fast spreadingridge where a shallowmelt thus parameterizedike injection above the gabbro sections lens is commonlyseen. Figure 8a showsthat the depthto of the crust as a time-averagedsteady state processdespite the 750øC isothermfound in theseexperiments correlates well the inherentlytime-dependent nature of individual dike intru- with the spreadingrate dependentmaximum slip sion episodes. Thus this study cannot addressto what extent depthsinferred from teleseismicand microseismic studies. and over what time scalesa time-dependentintrusion process would changethe temperaturestructure of oceaniccrust. See Axial Variability Along a Single Ridge Segment Henstocket al. [1992] for an initial analysisof theseeffects. This paradigmfor the origin of a median valley at a slow We also have ignoredthe possibilityof crustalmagmas assim- spreadingridge would predictthat along-axisvariations in me- ilating and reacting with gabbrosduring their ascentthrough dian valley topographyof a slow spreadingcenter reflect vari- the crustalsection; an investigationof theseprocesses will re- ationsin recent magmaticheat input along a segment,that is, quire a better descriptionof the effects of chemicalreaction that the axial topographyis a good time-averagedindicator on the densityof both magmaand hostrock. Fortunately,one 6292 PHIPPSMORGAN AND CHEN: GENESISOF OCEANIC CRUST

(a)

Nz• - 8 lO 750øC

12 1200øC

14 • / • I I I I o lO 20 30 40 50 60 70 (b) o

c216 3o mm/yr 50 mm/yr

20 ' ' ' ' ' ' ' 0 60 120 180 0 60 120 180 0 60 120 180 (C) (MPa) YieldStrength (MPa) lO ,,• OlivineRheology Olivine& N•z= 8

4

o o 1 0 20 30 40 50 60 70 Half-spreading rate (mm/yr) PHIPPSMORGAN AND CHEN: GENESISOF OCEANICCRUST 6293 is becomingrapidly available[cf. Ghiorso, 1987]. Quick and experimentsthat mantle upwelling is solely driven by plate Denlinger(1992) have madean initial analysisof theseeffects. spreadingand we do not treat buoyantcontributions to mantle Finally, we have neglectedthe effectsof a three-dimensional upwelling that are discussedby PhippsMorgan [1991]. In this along-axisvariation in axial lithospherestrength in shaping suite of experimentswe are trying to limit our initial model along-axisvariations in ridge morphology.While simpler2-D complexity to the oceaniccrust. modelsyield intuition into how lithospherestretching can be The above equationsare solved using a finite element for- relatedto the amplitudeand shapeof the resultingaxial val- mulation which extends the formulation ret•orted bv Chen and ley, a 3-D stretchingmodel is neededto accuratelypredict the Morgan [1990]. Since the viscosityis a functionof tempera- magnitudeof topographicvariations associated with along-axis ture which is a priori unknownwe mustsolve this problemby variationsin magma injectionand the resultingvariations in iterating to a steady state solution. For speedand computer thermallithosphere structure. These further studies are needed memory savingswe treat the temperatnre and flow subprob- to testthe conclusionsand implicationsof this work. The task lems separatelywithin a larger iterationloop. is clearly doablenow; let us do it! Weak Form of Energy Conservation APPENDIX: PROBLEM FORMULATION AND SOLUTION For temperaturewe solve the streamline-upwindPetrov- The problemwe consideris steadystate heat and mass trans- Galerkin weak form of this equationusing finite elementtech- port beneatha spreadingcenter. The temperaturestructure of niquesdiscussed by Brooksand Hughes [1982]: the ridge satisfiesa conservationequation for energydue to thermal (Fourier's Law), heat advectiondue to vis- cous fluid motions, and a latent heat releaseon cooling from a magma to "rock" phase. O=•(w+q)(-L•-T•-uiT,i)d•2-1••w,iT,id•2 Conservationof Energy L•9+ V . (fiT) = n•72T where w is the standardGalerkin weighting or basis func- tion (here the basis functionsof a bilinear quadrilateralel- where½ is themagma injection rate, L is themagma's latent ement) and q is an additional discontinuousstreamline up- heat of cooling (334 kJ/kg) convertedinto an effective'super- windweighting function given by q = where heat' of 320øC,n = 10-6 m2/s,ff is the velocity,and T is • = (•u•hxi+ •luvh•ta)/2and •, •7,in termsof a localele- the temperature.Viscous flow within the crustand mantleis ment Peclet numberPe in the local •, •7 directionare found treatedto satisfymomentum and massconservation for a vari- from• = (coth(Pe•)-Pe• -• witha similarexpression for able viscosityfluid that is incompressibleexcept in dilational •/. There are severaladvantages to this formulationas an "up- regionsof magmainjection. wind" finite element advection solver. It has no crosswind Conservationof Mass artificial diffusionbecause q actsonly in the directionof flow.

It also providesa numericallyß consistent weighting for the en- ergy sourceterm L•b in the equation. Conservationof Momentum Numerical Flow Problem: Solution Algorithm The finite elementsolution for viscousflow within a region with a prescribeddilatation is a new feature of this study. The problemis extremelysimilar to that for an incompressible p,i + Tij,j =0. fluid which is well summarizedby Reddy [1984] and Hughes wherep is the pressure,and/• and A are the shearand bulk vis- [1987]; the difference is that we now prescribethe dilatation cosity,respectively [cf. Tritton, 1977]. In the aboveequations to have a potentiallynonzero value. In what follows we will we use a commato representdifferentiation by the subsequent presenta penaltyfinite elementformulation for this problem. index and the summationconvection applies to an implicit A standardapproach to developinga finiteelement formulation sum of repeatedindices. While the shearviscosity of mantle is to pose the governingequations in terms of a variational and crustalrocks is poorly known, the bulk viscosityis even principle. The standardpenalty formulation for slow viscous less well known, so for this suite of numerical experiments flow (Stokes' Equation) is presentedin this way by Reddy we chooseA = /•. In addition, we considerin this suite of [1984]. The variational form

Fig. 8. Integratedaxial lithospherestrength for theseexperiments plotted as a functionof spreadingrate. (a) Depths to the750øC and 1200øC isotherm are shown from a suiteof numericalexperiments with Nu = 8 andTcutoff = 600øC. The 750øC isothermis correlateswell with the spreadingrate dependenceinferred from centroiddepths (shown by small dots and associatedbars representinginferred total rupture depth) of Huang and Solomon's[1988] teleseismicstudy. Triangles are microearthquakefocal depthsbeneath the axis of the northernMid-Atlantic Ridge [Toomeyet al., 1988; Kong et al., 1992]. There is good agreementbetween model isothermsand the spreadingrate dependenceof the depth of the seismicallyobserved brittle-ductile transition. (b) Mantle yield strengthenvelopes used in the calculationsfor 10 mm/yr, 30 mm/yr, and 50 mrn/yr. Solid lines showthe yield strengthenvelope for a crust and mantle with an assumed brittle/ductileolivine rheology. Dashedlines show the yield strengthenvelope where the crusthas a diabaserheology while the mantle has an olivine rheology(see Chen and Morgan [1990] for more detailsof this rheologicalstructure). (c) Depth-integratedtotal axial yield strengthas a functionof spreadingrate. There is a strongincrease in total axial yield strengthat spreadinghalf ratesbelow 20 mm/yr which suggeststhat extensionof strongaxial lithosphereis a likely mechanismfor the presenceof a medianvalley at slow-spreadingridges and the absenceof a medianvalley relief along fast-spreadingridges. 6294 PHIPPSMORGAN AND CHEN: GENESIS OF OCEANIC CRUST Along-AxisCross section of SeismicVelocity and MicroearthquakeHypocenters (Northern MAR) 26ON 26ø10'N

high E deep - 3.3 krn ...... •...... • ...... ß ......

- 5•-- - 6 •'• 7,•._---.---- ,a - 87• 6• o • oo - e %o• e• o o • 8

10 ! I ! I 0 5 10 15 20 25 Disfonceolong-oxis, km Fig.9. Along-axisvariations in seismic velocity and microearthquake focaldepths along the trans-Atlantic geotraverse (TAG)median valle3• near 26øN on the Mid-Atlantic Ridge. Heavy labeled contours show P wavevelocity in kilometers persecond. Filled circles show microearthquake hypocenters constrained withP and$ wavearrivals' open circles show morepoorly constrained hypocenters constrained solely by Pwave arrivals. (Events within 2 kmof the along-axis vertical planeare shown here.) Axial seafloor topography is shown as the solid line. Note the along-axis deep is roughly800 m deeperthan the along-axis high. Solid squares show the locations of the bottom hydrophones thatwere located alongthe ridge axis (two ocean bottom seismographs andseven ocean bottom hydrophones wereused in this experiment). A strongcorrelation exists between maximum microearthquake focaldepths (equal to thickness ofthe brittle lithosphere?) andridge axis bathymetry. A shallower microearthquake depthcutoff is foundbeneath this along axis depth minimum. Thealong-axis depth minimum also appears tobe seismically slower than deeper sections of the ridge axis, suggesting thatthis is thesite of hotteras well asthinner lithosphere. This evidence suggests that the lithospheric thickness at the ridgeaxis may be thermally controlled and that thicker axial lithosphere correlates with a deepermedian valley (figure modifiedfrom Kong et el. [1992]).

withthe definition p = -7 [Ou/Ox+Ov/Oy- A(x, y)]. From the aboverelations we find therecipe for modifyinga standard penaltyformulation for incompressibleviscous flow to solve thedilatational problem. We formthe momentum conservation +• •xx+ +f • u + f y v c•xc• y statement at an element level with• = (u, v) satisfiesmomentum conservation. This can be ke• e + gep• = f• seenby directconstruction of the Euler-Lagrangeequations. If wenow modify the variational form by addingan additional wheref• are the standardnodal loads due to bodyforces or Lagrangemultiplier surfacetractions for viscousflow, g• is the finiteelement form of thegradient operator, and k e is theelement stiffness matrix that is identical in form to that for a elastic problem with L(u,v,,•) = I(u, v) + • • +• •(x,y) •x•y Lam6parameters ,• and/• asanalogues to thebulk and ,respectively (This notationfollows that of Hughes thent•s vafiationalform will satisfyboth mass conservation [1987,chap. 4], whopresents an excellentintroduction to the penaltymethod for incompressibleviscous flow.) We nowuse • + =3(x, y) thepreviously found relation for pressurein termsof a penalty number7, P• = -7( Ou/Ox+ Ov/Oy - Ai(x, y)) tosubstitute •d momentum conservation velocityunknowns for pressureunknowns in the momentum equationwhich yields

where• = k•- 7g•(ge)•' is modifiedexactly as donefor 0 2/•-•+•+ + /• + -- =fy penalizedincompressible viscous flow andthe forcevector PHIPPS MORGAN AND CHEN: GENESIS OF OCEANIC CRUST 6295 fe = fe_ ,7g•A•is alsomodified during element formation. matrix once for this problem; thus subsequentiterations are The terms involving '7 are all evaluatedusing reducedinte- extremely cheap to compute. gration. The resultingsolution algorithm shares all of the ad- vantagesand potential pitfalls [Pelletier et al., 1989] of the Rheologyand Boundary Conditions penaltyalgorithm which is a currentworkhorse for solving2- Although we are primarily interestedhere in solving for D variable viscosityincompressible flow. See Hughes [1987] crustal flow and thermal structure, we need to also solve for for more information. mantle flow to properly treat the thermal and mechanicalef- We implementa furthermodification to the classicalpenalty fects of a growing lithosphere. Thus we solve for heat and methodto solvethis problem. Pelletier et al. [1989] showthat masstransport within a 90 x 140 km region on one side of if we implementthe penaltyformulation as a singlestep of an a symmetricridge axis as shown in Figure A1. Each of the Uzawa algorithm,then by iterationwe can find a solutionthat figuresin the main text was solvedin this largercomputational satisfiesthe continuityequation to any desiredprecision. We domain. The viscousrheology that we useis a simplificationof solve an iterative sequence that presentedby Chen and Morgan [ 1990]. For this studywe assumea Newtonianlithosphere, mantle, and crustalviscosity where we updatethe pressureafter eachiteration by structurewith a lithosphereviscosity which is 104greater than the asthenosphere(mantle) viscosity. The asthenospherevis- = + 7(V. a[_; - za) cosityis, in turn,103 times greater than the viscosity of "hot until the divergenceof the velocity field is sufficientlysmall. crust"above 750øC, resulting in a totalviscosity range of 107. For a largeenough '7 > 0( 106/•)this iteration converges ex- (The total strengthrange is limited by the dynamicviscosity tremelyrapidly (2-5 iterations).The first iterationwith a pres- rangeof a penaltyalgorithm which is about107 for a double sureguess p = 0 is simply the standardpenalty solution, which precisionnumerical code [Hughes, 1987].) The lithosphere- is alreadyquite good for large '7. Note also that in the direct asthenospheretransition within the mantleis governedby the Gaussianelimination solutionimplementation of the finite el- 750øC isotherm,and the dike injection region is set to have ement equationswe only have to form and factorthe stiffness a strength10 times less than that of the lithosphere.These

ProblemSolution Region and BoundaryConditions

FLOW & TEMP (10 mm/yr) w--os-O 0

Fig. A1. Problem geometryand boundaryconditions for the numericalexperiments performed in this study. The problemregion that we consideris a 140-km-wideby 90-km-deepregion on one sideof a symmetricridge axis. Mantle flow is driven solelyby plate spreading,and crustis emplacedat the ridge axis accordingto thermaland geometrical criteriadeveloped in the text. We solvethe problemon a 63(x direction)x 80(y direction)variable spacing tensor-product grid with an x and y nodalspacing shown by tick marksalong the top andright handsides of the region. The problem boundaryconditions are shownon eachside of the box. The lightly shadedbox is the subregionfrom whichthe solution is extractedto make the detail plots shownin Figures4-6. This subregioncontains 43 verticalby 30 horizontalgrid points. The exampletemperature and flow field shownhere is for a half spreadingrate of 10 mrn/yrwhere no steady statemagma lens existswithin the crust(the run from which Figure 5 was extracted).Solution isotherms are contoured at 200øC intervals. 6296 PHIPPS MORGAN AND CHEN: GENESIS OF OCEANIC CRUST strengthcontrasts roughly approximatethe rheologyin Chen Burnett,M. S., D. W. Caress,and J. A. Orcutt, Tomographicimage and Morgan's [1990] study and were chosento eliminate an of the East Pacific Rise at 12ø50'N, Nature, 339, 206-208, 1989. additional nonlinear solution iteration needed to solve a non- Caress,D. W., M. S. Burnett, and J. A. Orcutt, Tomographicimage of the axial low velocityzone at 12ø50'Non the EastPacific Rise, Newtonian flow problem [cf. Chen and Morgan, 1990]. The J. Geophys.Res., 97, 9243-9264, 1992. temperatureboundary conditions for this problemare that the Chen, Y., and W. J. Morgan, A nonlinearrheology model for mid- mantle is flowing into this region at a constanttemperature oceanridge axistopography, J. Geophys.Res., 95, 17,583-17,604, T,• = 1350øC, that heat is free to move out of the sidesof the 1990. Collier, J., and M. Sinha, Seismicimages of a magmachamber be- box, and that on the top surfaceTo = 0øC. For flow, the verti- neaththe Lau Basin back-arcspreading centre, Nature, 346, 646- cal velocity and horizontalshear stress are zero at the top of 648, 1990. the box; on the sidesof the box we assumethat passiveplate Combarnous,M., Natural convectionin porousmedia and geothermal spreadingflow occursbeneath the rigid part of the lithosphere, systems,Int. Heat TransferConf., 6th, 45-59, 1978. and we assumethe bottom of the region to be a shear and Detrick,R. S., Ridgecrest magma chambers: A reviewof resultsfrom normal stressfree surface. See Chen and Morgan [1990] for marine seismicexperiments at the East Pacific Rise, in Ophiolite Genesisand Evolution of the Oceanic Lithosphere,edited by T. furtherdiscussion of theseboundary conditions. The boundary Peterset al., pp. 7-20, Kluwer Academic,Boston, 1992. conditionthat is unique to this problemis that for the influx Detrick, R. S., P. Buhl, E. Vera, J. Mutter, J. Orcutt, J. Madsen, of magmain the crustalaccretion zone. We treat this magma, and T. Brocher,Multi-channel seismic imaging of a crustalmagma for a geometrywhich is determinedas discussedin the main chamberalong the East PacificRise, Nature, 326, 35-41, 1987. Detrick, R. S., J. C. Mutter, P. Buhl, and I.I. Kim, No evidence from body of the text, as intowing at a steadystate rate which ex- multichannelreflection data for a crustal magma chamberin the actly balancescrust leaving the region with plate spreading. MARK area on the Mid-Atlantic Ridge, Nature, 347, 61-64, 1990. The effective temperatureof this intowing materialis set to Dewey, J. F., and W. S. F. Kidd, Geometryof plate accretion,Geol. be higher than the magmasolidus by an amountequal to the Soc. Amer. Bull., 88, 960-968, 1977. energyreleased as latent heat of cooling(see PhippsMorgan Ghiorso,M. S., Modeling magmaticsystems: Thermodynamic rela- tions, in ThermodynamicModeling of GeologicMaterials: Miner- et al. [1987] for further discussionof this type of boundary als, Fluids, and Melts, edited by P. H. Ribbe, Rev. Minerol., 17, condition). All of this latent heat of coolingis releasedat the 443-463, 1987. top of the magmalens. Gregory,R., and H. P. Taylor,An oxygenisotope profile in a section of Cretaceousoceanic crust, Samail Ophiolite, Oman: Evidence Acknowledgments.This work was inspiredby extremelythought- for 6180 bufferingof the oceansby deep(> 5 km) - provokingfield tripsin the OmanOphiolite Symposium led by Adolf hydrothermalcirculation at mid-oceanridges, J. Geophys. Res., Nicolas, John Pallister,Georges Ceuleneer, and Thierry Juteau. De- 86, 2737-2755, 1981. velopmentof the computercode was completedduring the 1990 Harding,A. J., J. A. Orcutt,M. E. Kappus,E. E. Vera, J. C. Mutter, RIDGE Theoretical Institute in Boulder. We thank Kristin Rohr for P. Buhl, R. S. Detrick, and T. M. Brocher, Structure of young helpful discussionsand input abouther seismicreflection work on the oceanic crust at 13øN on the East Pacific Rise from expanding Juande Fuca Ridge. During the 1992 RIDGE TheoreticalInstitute in spreadprofiles, J. Geophys.Res., 94, 12,163-12,196,1989. Tucsonwe were alertedto parallel effortsin this areaby Jim Quick Harper,G. D., J. R. Bowman,and R. Kuhns,A field, chemical,and (whose "Gabbro Glacier" computervideo is a visually compelling stableisotope study of subseafloormetamorphism of the Josephine "proof" that lower crustalflow from a shallowintrusive center is a ophiolite, California-Oregon,J. Geophys. Res., 93, 4625-4656, 1988. viable means of generatingthe observedgabbro layering structure) and by Tim Henstock,Andrew Woods, and RobertWhite, who have Henstock, T. J., A. W. Woods, and R. S. White, The accretion of developeda similar model for oceaniccrustal accretion. Before the oceaniccrust by episodicsill intrusion,J. Geophys.Res., in press, revisionof thispaper we alsobecame aware of preprintsof their work 1992. and have tried to refer in the text to where thesestudies complement Huang,P. Y., and S.C. Solomon,Centroid depths of mid-oceanridge and extendthe presentwork. (Quick and White were also at Oman :Dependence on spreadingrate, J. Geophys.Res., 93, - coincidence?)We thank Norm Sleep, Doug Toomey,and an asso- 13445-13477, 1988. ciate editorfor helpful, constructivereviews of this study.This work Hughes,T. J. R., The Finite ElementMethod, Prentice-Hall,Engle- was supportedby NSF (bothdirectly as well as indirectlythrough its wood Cliffs, 1987. supportof the aboveworkshops and symposia)and ONR. Kent, G. M., A. J. Harding, and J. A. Orcutt, Evidencefor a smaller magmachamber beneath the EastPacific Rise at 9030' N, Nature, 344, 650-653, 1990. Kong, L. S. L., S.C. Solomon,and G. M. Purdy, Microearthquake characteristicsof a mid-oceanridge along-axishigh, J. Geophys. REFERENCES Res., 97, 1659-1685, 1992. Lachenbruch,A. H., A simplemechanical model for oceanicspread- Bergman, E. A., and S.C. Solomon, Source mechanismsof - ing centers,J. Geophys.Res., 78, 3395-3417, 1973. quakesnear mid-oceanridges from body waveforminversion: Im- Lachenbruch,A. H., Dynamicsof a passivespreading center, J. Geo- plicationsfor the early evolutionof oceaniclithosphere, J. Geophys. phys. Res., 81, 1883-1902, 1976. Res., 89, 11,415-11,441, 1984. Lin, J., and E. M. Parmentier,Mechanisms of lithosphereextension Bischoff, J. L., and R. J. Rosenbauer,The critical point and two- at mid-oceanridges, Geophys. J., 96, 1-22, 1989. phaseboundary of seawater,200-500øC, Earth Planet. Sci. Lett., Lin, J., andE. M. Parmentier,A finite amplitudenecking model of rift- 68, 172-180, 1984. ing in brittle lithosphere,J. Geophys.Res., 95, 4909-4923, 1990. Blackman,D. K., and D. W. Forsyth,Isostatic compensation of tec- Lin, J., andJ. PhippsMorgan, The spreadingrate dependenceof three- tonic featuresof the Mid-Atlantic Ridge: 25-27ø30'S, J. Geophys. dimensionalmid-ocean ridge gravitystructure, Geophys. Res. Lett., Res., 96, 11,741-11,758, 1991. 19, 13-16, 1992. Brooks, A. N., and T. J. R. Hughes, Streamline upwind Petrov- Macdonald, K. C., The crest of the Mid-Atlantic Ridge: Models for Galerkin formulationfor convectiondominated flows with particu- crustalgeneration processes and tectonics, in The Geologyof North lar emphasis on the incompressible Navier-Stokes America: The WesternNorth Atlantic Region,vol. M, editedby P. equation,Comput. MethodsAppl. Mech. Eng., 32, 199-259, 1982. Vogt andB. Tucholke,pp. 51-68, Geol. Soc. Am., Boulder,Colo., Browning, P., Cryptic variationwithin the cumulatesequence of the 1986. Oman ophiolite: magmachamber depth and petrologicalimplica- Macdonald,K. C., P. J. Fox, L. J. Perram,M. F. Eisen, R. M. Haymon, tions,in Ophiolitesand OceanicLithosphere, edited by I. G. Gass, S. P. Miller, S. M. Carbotte, M.-H. Cormier, and A. N. Shor, A S. J. Lippard, and A. W. Shelton,Geol. Soc. London,Spec. Publ., new view of the mid-oceanridge from the behaviourof ridge-axis 71-82, 1984. discontinuities,Nature, 335, 217-225, 1988. PHIPPS MORGAN AND CHEN: GENESIS OF OCEANIC CRUST 6297

Macdonald,K. C., R. M. Haymon,and A. N. Shor,A 220km 2 re- crustal structureacross the Juan de Fuca Ridge, Geology, 16, 533- centlyerupted lava field on the EastPacific Rise near8øS, Geology, 537, 1988. 17, 212-216, 1989. Ryan, M.P., Neutral buoyancyand the mechanicalevolution of mag- Madsen, J. A., R. S. Detrick, J. C. Mutter, P. Buhl, and J. A. Orcutt, A matic systems,in MagmaticProcesses: Physiochemical Principles, two- and three-dimensionalanalysis of gravityanomalies associated Geochem.Soc., Spec. Pub. 1, 259-287, 1987. with the East Pacific Rise at 9øN and 13øN, J. Geophys.Res., 95, Sinton, J. M., and R. S. Detrick, Mid-ocean ridge magma chambers, 4967-4987, 1990. J. Geophys.Res., 97, 197-216, 1992. McKenzie, D. P., Finite deformationduring fluid flow, Geophys.J. Sleep, N.H., Sensitivityof heat flow and gravity to the mechanism R. Astron. Soc., 58, 689-715, 1979. of -floorspreading, J. Geophys.Res., 74, 542-549, 1969. McKenzie, D., The generationand compactionof partially molten Sleep, N.H., Formationof oceaniccrust: Some thermal constraints, rock, J. PetroL, 25, 713-765, 1984. J. Geophys. Res., 80, 4037-4042, 1975. Morton, J. L., and N.H. Sleep, A mid-oceanridge thermal model: Sleep,N.H., Thermalstructure and kinematics of the mid-oceanridge Constraintson the volumeof axial hydrothermalflux, J. Geophys. axis, someimplications to basalticvolcanism, Geophys. Res. Lett., Res., 90, 11,345-11,353, 1985a. 5, 426-428, 1978. Morton, J. L., and N.H. Sleep, Seismicreflections from a Lau Basin Sleep, N.H., Hydrothermalcirculation, anhydrite precipitation, and magma chamber, in Geology and OffshoreResources of Pacific thermal structureat ridge axes, J. Geophys. Res., 96, 2375-2387, Arcs - TongaRegion, Earth Sci. Ser.,edited by D.W. Scholl 1991. and T. L. Vallier, pp. 441-453, CircumPacific Council for Energy Sleep,N.H., and B. R. Rosendahl,Topography and tectonicsof mid- and Mineral Resources, Houston, Tex., 1985b. oceanicridge axes,J. Geophys.Res., 84, 6831-6839, 1979. Morton, J. L., N.H. Sleep, W. R. Normark, and D. H. Tomkins, Small, C., and D. T. Sandwell,An abruptchange in ridge axis gravity Structureof the southernJuan de FucaRidge from seismicreflection with spreadingrate, J. Geophys.Res., 94, 17,383-17,392, 1989. records,J. Geophys.Res., 92, 11,315-11,326, 1987. Smewing,J. D., Mixing characteristicsand compositionaldifferences Mutter, J. C., G. A. Barth, P. Buhl, R. S. Detrick, J. Orcutt, and A. in mantle-derivedmelts beneath spreadingaxes: Evidence from Harding, Magma distributionacross ridge-axis discontinuities on cyclicallylayered rocks in the ophioliteof North Oman,J. Geophys. the East Pacific Rise from multichannelseismic images, Nature, Res., 86, 2645-2659, 1981. 336, 156-158, 1988. Sparks,D. W., and E. M. Parmentier,Melt extractionfrom the mantle Natland, J. H., Effect of axial magma chambers beneath beneathspreading centers, Earth Planet. Sci. Lett., 105, 368-377, spreadingcenters on the compositionsof basalticrocks, Initial Rep. 1991. Drill. Proj., LIV, 833-850, 1980. Tapponier,R., and J. Francheteau,Necking of the lithosphereand the Nehlig, P., and T. Juteau,Flow porosities,permeabilities, and prelim- mechanicsof slowly accretingplate boundaries,J. Geophys.Res., inary data on fluid inclusionsand fossil thermalgradients in the 83, 3955-3970, 1978. crustal sequenceof the Sumail Ophiolite (Oman), Tectonophysics, Toomey,D. R., S.C. Solomon, and G. M. Purdy, Microearthquakes 151, 199-221, 1988. beneaththe medianvalley of the Mid-Atlantic Ridgenear 23øN: To- Nicolas, A., Structuresof Ophiolitesand Dynamicsof OceanicLitho- mographyand Tectonics,J. Geophys.Res., 93, 9093-9112, 1988. sphere,Kluwer Academic, Boston,Mass., 1989. Toomey,D. R., G. M. Purdy, S.C. Solomon,and W. S. D. Wilcock, Nicolas, A., I. Reuber, and K. Benn, A new magma chambermodel The three-dimensionalseismic velocity structure of the EastPacific basedon structuralstudies in the Oman ophiolite,Tectonophysics, Rise near latitude 9ø30'N, Nature, 347, 639-645, 1990. 151, 87-105, 1988. Tritton, D. J., Physical Fluid Dynamics, Van Nostrand Reinhold, Pallister,J. S., and C. A. Hopson, Samail Ophiolite plutonic suite: Princeton, N.J., 1977. Field relations,phase variation, cryptic variation and layering,and Vera, E. E., J. C. Mutter, P. Buhl, J. A. Orcutt, A. J. Harding, M. a model of a spreadingridge magma chamber,J. Geophys. Res., E. Kappus, R. S. Detrick, and T. M. Brocher,The structureof 0- 86, 2593-2644, 1981. to 0.2-m.y.-oldoceanic crust at 9øN on the East PacificRise from Pelletier, D., A. Fortin, and R. Camarero, Are FEM solutions of in- expandedspread profiles, J. Geophys. Res., 95, 15,529-15,556, compressibleflows really incompressible?(Or how simple flows 1990. can cause headaches!),Int. J. Numer. Methods Fluids, 9, 99-112, Wiens, D. A., and S. Stein, Intraplateseismicity and stressesin young 1989. oceaniclithosphere, J. Geophys.Res., 88, 6455-6468, 1983. PhippsMorgan, J., Mid-oceanridge dynamics: Observations and the- Wilson, D. S., D. A. Clague, N.H. Sleep, and J. L. Morton, Im- ory, U.S. Nat. Rep. Int. Union Geod. Geophys.,Rev. Geophys., plications of magma convectionfor the size and temperatureof 29, Suppl., 807-822, 1991. magma chambersat fast spreadingridges, J. Geophys. Res., 93, PhippsMorgan, J., E. M. Parmentier,and J. Lin, Mechanismsfor the 11,974-11,984, 1988. origin of mid-ocean ridge axial topography:Implications for the thermaland mechanicalstructure at accretingplate boundaries,J. Geophys. Res., 92, 12,823-12,836, 1987. Purdy, G. M., L. S. L. Kong, G. L. Christeson,and S. Solomon, Y. J. Chen, College of Oceanography,Oregon State University, Relationshipbetween spreading rate and the seismicstructure of OceanAdmin. Bldg. 104, Corvallis,OR 97331-5503. mid-oceanridges, Nature, 355, 815-817, 1992. J. PhippsMorgan, Instituteof Geophysicsand PlanetaryPhysics, Reddy,J. N., An Introductionto the Finite ElementMethod, McGraw- 0225, ScrippsInstitution of Oceanography,La Jolla, CA 92093-0225. Hill, New York, 1984. Riedesel, M. J., J. A. Orcutt, K. C. Macdonald, and J. S. McClain, Microearthquakesin the black smokerhydrothermal field, East Pa- (ReceivedApril 28, 1992; cific Rise and 21øN, J. Geophys.Res., 87, 10,613-10,623, 1982. revised November 3, 1992; Rohr, K. M. M., B. Milkereit, and C. J. Yorath, Asymmetric deep acceptedNovember 3, 1992.)