VOL. 84, NO. B I3
JOURNAL
OF GEOPHYSICAL
RESEARCH
DECEMBER
10, 1979
On the Thermal Evolution of PassiveContinental Margins,
Thermal Depth Anomalies,and the Norwegian-GreenlandSea
GARY
W.
ZIELINSKI •
Department
ofGeological
Sciences
andLamont-Dohe•ty
Geological
Observatory
Columbia University,Palisades,New York 10964
A computermodelof seafloorspreading
is presented.
This time-dependent
thermalmodel,whichincludesthe presence
of an adjacentcontinent,simulatesnot only the evolutionof an oceanicregionbut
alsothe thermalevolutionof an Atlantic-typecontinentalmargin.Incorporationof the adjacentcontinentinto a seafloorspreadingmodelallowsoneto utilizegeologicaland geophysical
data from the continent and continentalmarginas constraints.In termsof the modelparametersa more completepicture
of the early spreadinghistoryand its relationto the initial rifting of the continentis provided.While vertical heat flow dominatesin both the oceanand the continentproper, severaleffectsof lateral heat flow
acrossthe ocean-continent
boundaryare seen.They are reflectedin the surfaceheatflowand topography
computedfrom the model.Owingto lateralheatflow,subsidence
of the continentalmargincanbe more
rapidthanhasbeenestimatedfrompreviousmodelsandis a strongfunctionof horizontalposition.Appliedto the Norwegian-Greenland
Sea,the modelsatisfies
all availablegeophysical
datafor that area
andproduces
oceanicdepthsnearlyI km shallowerthanfor otheroceansof comparable
age.It is consistent with the idea that thermal expansionis responsiblefor the unusuallyshallowdepthsand positive
free air gravityobservedin the Norwegian-Greenland
Sea.Theseresultsmay be applicableto partsof
otheroceanswherelargeregionsdepartfrom the normalage-depthcurve.Thermaldepthanomaliesare
not necessarily
indicativeof increased
heatinputfrombelowbut may moregenerallyreflectdifferences
in the ratio of the heat enteringthe lithosphereto the spreadingrat•. If it is correct,this conceptmay
providean originfor someof theshorter-wavelength
relief(10-100km) seenin oceanicbasement.
The
heat flow distributionacrossthe Norwegiancontinentalmargin is consistentwith a thermalmodel in
which the V•ring PlateauEscarpmentis concidentwith the ocean-continentboundary.
INTRODUCTION
THE
One method for investigatingthe implication of a surface
heat flow distribution on processesoccurring at depth in the
earth is through the use of thermal models [e.g., Langseth et
al., 1966; McKenzie, 1967]. In these models the oceanic lithosphere is assumedto behave as a moving two-dimensional
The model
envisioned
MODEL
is one in which at time zero the con-
tinent is intruded by new oceanicmaterial at the melting tem-
peratureand beginsto movelaterally at somefixed spreading
rate. As the motion continues,newly formed ocean fills the
void left by the moving continent,and the developmentof the
slabof materialwhichcool
s conductively
throughits upper area can be followed through time. The equation and boundsurfaceas it moves away from a vertical boundary held at the
melting temperature.Although such models are likely to be
grossoversimplifications
of what occursin nature, they serve
to group causesinto a finite number of categories.For this
reason they can provide a unified set of parametersfor comparing one region with another. With this in mind a thermal
model has been developed in order to compare the Norwegian-Greenland Sea, as representedby the Mohns Ridge
spreadingcenter,with other world oceanspreadingcenters.
The Mohns Ridge spreadingcenter (Figure 1) providesa
unique opportunity to constrain sea floor spreadingmodels.
Not only are there reliable heat flow measurementsdistributed uniformly over the age range of that spreading center
[Langsethand Zielinski, 1974],but alsothere are a seriesof reliable heat flow measurementson the Norwegian continental
margin, and from Swanberg et al. [1973], borehole measurements of heat flow and radioactive heat generation on the adjacent continent in Norway. Thus a two-dimensionalmodel
encompassingthe Mohns Ridge spreadingcenter, the continental margin, and the adjacent continent would be constrainedby surfaceheat flow measurementsalong its entirety.
•Now at GeologicalSciences
Department,Gulf Science& Technology Company, Pittsburgh,Pennsylvania15230.
Paper number 9B 1004.
B- 1004501.00
37+ vO•fx'
-Q
IIOT
}= O:T
O:T
K
T= 0 (z = 0), T= 1,330øC+ 0.6øC/km (x = 0) [Jordan,1975],
K(OT/Oz)-- FB (z ----L), OT/Ox-- 0 (x -- 2,000 km), where T
is temperature, t is time, K is the thermal diffusivity, K is the
thermal conductivity, V is the spreadingrate, Q is heat generation, and x and z are taken in the horizontal and vertical directions,respectively.Trn is the melting temperature, FB is the
heat flow through the bottom boundary, and L is the verticle
thickness of the region. The bottom boundary should be
placed at a depth where differencesin thermal propertiesbetween ocean and continent are sufficientlysmall that vertical
heat flow may be assumed.Froidevauxet al. [1977] argue that
the temperature beneath old oceans and stable continents
should become equal somewherebetween 200- and 400-km
depth. Since according to Clark and Ringwood [1964], heat
generation should also be equal in that range, the bottom
boundary will initially be placed at 400 km. Some consequences
of smallervaluesof L will be discussed.
Because of the large time constant for thermal processes
within the earth, heat flow data from the oceans cannot constrain the heat flux at 400 km. This can, however, be derived
from the continental geotherm if steady state one-dimensional
heat flow is assumed.
Copyright¸ 1979by the AmericanGeophysicalUnion.
0148-0227/79/009
ary conditionssolvedare
7577
7578
ZIELINSKI: THERMAL EVOLUTION OF PASSIVEMARGINS
generation
of5.0X 10
-7W/m
3(1.2HOU)andlogarithmic
decrementof 25 km. As in the caseof the continentaldistribu-
tion, a valueof 4.6 x 10-8 W/m 3 (0.11 HGU) is assumed
below the logarithmiclayer. The resultingdistributionis a good
approximationto the geochemicalmodel of Clark and Ringwood [1964] and meets the condition of constant thermal
propertiesat 400 km.
70ø . :!,;."•
In all of the computationsthe horizontalgrid spacingwas
givena value of 10km in regionssuchasnear the ridgeaxisor
the ocean-continentboundary,where large temperaturegradients were anticipated or high resolution was desired. Elsewhere, it was increased to 50 km. In the vertical direction the
grid spacingwasincreasedin an arithmeticprogression
from 3
km at the surfaceto 48 km near 400 km. The time stepwasof
m
the orderof 65,000years(for moredetails,seeZielinski
[1977]). Thermal diffusivity is taken to be a constant 0.009
cm2/s[Zielinski,1977].Partialmeltingat the baseof the litho-
I
spherewas considered,however,for valueslessthan 10%;effectswere found to be negligible.Sampletemperatureoutput
at 0, 10, 30, and 60 m.y. is shownin Figure 3, with oceanicregions shaded.
Heat flow was computedby fitting a second-orderpolynomial to the temperaturesat the upper threenodes,comput-
Fig. 1. Sketch map showingthe location of the Mohns Ridge
spreadingcenterin relation to adjacentland masses,boundingfracture zones, and the V½fing Plateau Esca•ment (vpe) [after Talwani
ing the gradientat the surface,and multiplyingby a surface
thermalconductivityof 2.9 W/møC (7 mcal/øC cm s) [Schatz
and Simmons,1972].
If densityis assumedto be a function of temperature,the
resultingsurfacetopographycan also be computedfrom the
Swanbergeet al. [1973] have repo,ed heat flow and heat temperature field [Langseth et al., 1966; Sclater and Frangeneration measurementsfrom four geologic provMces
cheteau, 1970]. In doing such computations,most workers
Noway. On the basisof their data,a heatflowvalueof 48.1 have used the steadystate ocean as a referencefrom which
and EldAolm, 1977].
roW/m: (1.15 HFU, I HFU = I •cal/cm: s) seemsreasonable changesin topographywere computed.For the model being
presented,it has been more convenientto use as a reference
an oceanat zero temperaturethroughout. Doing so allows one
to compare topographicprofiles of several modelswith differabout3.3 x 10-• W/m a (8 HGU, I HGU = 10-a cal/cm-a s-•) ing thermalregimesto a commondensityreference.
with a 1oga•thmic decrementof 8.4 • can be deducedfrom
Two mechanismsfor isostaticadjustment are considered
Swanberget al. [ 1973]. Beneath the logarithmiclayer, a con- here.The firstis the compensation
by asthenospheric
material
stantheat generationof 4.6 x 10-• W/m a (0.11 HGU) is as- for the sea water displacedby expansionand contractionof
sumed. This value correspondsto the heat generation for theoceanic
lithosphere.
Thismechanism
occurs
on theoceanpyrolite II [Sclater and Francheteau,1970] and producesa ward sideof the continentalmargin. In the secondmechanism
deep geotherm s•ilar to that of Minister and •rchambeau the densityof the continentis chosensothat for a steadystate
temperature distribution its surface is at sea level and is in
[1970]andFroide•aux
andSchubert
[1975].
With boundaw conditionsof zero surfacetemperature and isostaticequilibrium with respectto the adjacentocean.The
a heat flow of 48.1 roW/m: (1.15 HFU), the steadystateheat secondadjustmentmechanismthereforegivesrise to a differflux at depth can be solvedfor. At 4• • the modelspredict ence in elevation due to the density contrastbetweenocean
for contMentalNoway adjacentto the V½•g Plateau. If an
exponentially decreasMgheat sourcedistribution with depth
is assumed[Lachenbmch, 1970], a surfaceheat generation of
a heat flux of only about 1.7 mW/m a (0.• HFU). This heat
and continent.
flux is assumedfor the bottom boundaw,
are assumedto be completelydecoupledwith constantpres-
COMPUTATIONAL
SCHEME
The model desc•bed M the previoussectionforms an Mitial
value problem which can be solved by standard finite difference techniques[e.g., Langsethet al., 1966;Bottingaand •llegre, 1973].The Mitial temperaturedistribution(Figure 2a) is
provided by the contMentalgeothermcomputedfor Noway.
At time zero, the ocean-continent boundary, coincident
with the ridge axis boundaw, begMs to move with the entbe
slab at a spreadMgvelocity • of I cm/yr [Talwani and Eld-
The oceanic block and the continental
block
sureat a depth of 400 km.
The constantsassumedfor the topographiccalculations
presentedare as follows:the zero temperatureoceandensity
and the densityof the asthenosphere
are both taken to be 3.33
g/cm3. To producerealisticoceandepths,the zero-temperaturecontinentmusthavea densityof about2.83 g/cm3. The
densityof seawateris 1.03g/cm3, and the thermalexpansion
coefficientis assumed
to be 3.22 x 10-5 øC-' [Forsyth,1977].
The initial continental temperature distribution for most of
the models presentedis shown in Figure 2a. The left-hand
boundary of the slab is at the melting temperature. Plotted
fiolm, 1977].At subsequentt•es, on and to the fight of the
ocean-contMentboundaw, the 'contMental'heat sourcedistri- abovethe slabis the topographic
uplift dueto thermalexpanbution is roaMtaMed. To the left of the boundaw, an 'oceanic' sion. For the usualinitial conditions,the uplift is in the form
heat source distribution is roaMtaMed which is also assumed
of a spikeover the meltingtemperatureboundary.This uplift
to be exponential with depth, however, with a surface heat rapidly broadensin time, however,initially it is unrealistic.A
ZIELINSKI: THERMAL EVOLUTION OF PASSIVE MARGINS
'75'79
A
/km
200
/200
/500
400
B
/
krn
I000
km
O0
/200
/•oo øc
km
Fig. 2. The isothermsfor two continentalslabsat the onsetof seafloor spreading(left-hand edgesat the melting tem-
perature).Aboveeachslabis shownthe topographic
uplift due to thermalexpansionwith respectto a steadystatecontinent.A thermalexpansion
coefficient
of 3.22 x 10-5 øC-• is assumed.
Figure2a represents
the initial conditionsassumed
for most of the modeling.Figure 2b representsa continentwhich has remainedstationaryfor a period of 20 m.y. prior to
the onsetof seafloor spreading.During that period,the continenthas undergoneheatingby lateral conductionand convectionfrom the left-hand edge.
somewhatmore realisticapproximationis exploredin Figure world oceans).The verticalsolid line within the slab shows
2b, where the onsetof sea floor spreadingis delayedby 20 the positionof the ocean-continentboundary.For the WO
m.y. During this periodof time, the stationarycontinentun- model, maximum temperaturesat 400 km are a little more
dergoesheatingby conductionand convectionassociatedwith
the intrusion of magma from the axial zone. Such a situation
might be analogousto a periodof continentalrifting prior to
seafloor spreading.Isothermsshowa shallowing,and a much
broader area is already uplifted by the time spreadingcom-
than 1,600øC,and for MR, temperaturesare lessthan 1,700øC
at 400 km. Each of thesemodelsthereforeyieldstemperatures
at 400-km depth, which is not excessively
high even beneath
the oceans.The two modelsdifferonlyin the temperaturegradientsassumedat the ridge axes,MR being greaterthan WO
mences. Some results of this case will be seen later.
by 0.2øC/km.
The most dramatic effect of the presenceof oceanic heat
TEMPERATURE
RESULTS
generationis a warmingof the oceanicmaterialwith age beFigure4 showsthe temperaturefieldsfor two modelsat 160 low about200-km depth,as seenin the riseof the deeperisom.y. for comparisonwith oceansolder than the Norwegian- thermswith age.This may, in part, be accentuated
by the parGreenland Sea (MR denotes Mohns Ridge; WO denotes ticular choice of the temperatureboundary condition at the
7580
ZIELINSKI:THERMALEVOLUTIONOF PASSIVEMARGINS
0
30
60 MY
Fig. 3. Sampletemperature
outputfromthe computer
modelof 0, 10,30, and 60 m.y.The darkenedregionis newly
formed'ocean.'(Dimensions
andisotherms
arethesameastheyarefor Figures3 and5.)
ridge axis. The effect, however, completelydisappearswhen
the oceanicheat generationis removed.
Intermediate temperaturesare also affected by the heat
source distribution. The position of the base of the oceanic
lithospherefrom a compilation of seismicsurfacewave data
[Forsyth,1977]is shownby the solid circlesplotted in each of
the slabs in Figure 4. It is in reasonableagreementwith the
roughpositionof the solidusof possiblelithosphericmaterials
(e.g., periodotite,lessthan 0.4% water), the stippledregion.
The presenceof sufficientheat generationin the oceansmaintains the temperaturefield in good agreementwith the surface
wave data. Without oceanic heat sources,more heat flux from
below would be required to prevent the thicknessof the oceanic lithospherefrom becomingtoo great.
The general featuresof the temperaturefieldsproducedby
thesemodelsare as follows:the temperaturefield in the upper
100 km reflectsthe thermal boundarylayer corresponding
to
the formation of oceanic lithosphere. Below the boundary
layer depth, the relative flatnessof the 1,400øC and 1,500øC
isothermsas followed away from the ridge indicate that no
heat is being conductedlaterally from the ridge axis. To this
approximation, for V = I ½m/yr the fact that the lower 200
km of the regionis alsoin lateral motion(i.e., notjust the lithosphere)is of little consequence
thermally. Below 200 km, the
temperaturebeneaththe ridge could be broughtinto better
agreementwith the continentalgeothermby choosing
smaller
valuesof Tm downto about1,200øCand adjustingotherparametersaccordingly.Still, the temperaturesproducedhere
are within the rangefor acceptablerheologies[Froidevauxet
aL, 1977].
Within about 300 or 400 km of the ocean-continent bound-
ary, a marked deepeningof the oceanicisothermsis seen.This
effect,corresponding
to the transitionfrom the youngerrelatively warm oceanicregion to the colder continent, continues
an equal distanceonto the continentuntil steadystateheat
flow is attained.In thesemodelsthe magnitudeand wavelengthof the temperature
transitionislargelya functionof the
agedifferencebetweentheoceanandcontinent(seeFigures3
and 4). The contrastin heat productionalsoaffectsthe transition but to a lesserdegree.
HEAT
FLOW AND TOPOGRAPHY
The twostrongest
constraints
imposed
onthemodelby geophysical data are the observedsurfaceheat flow and the to-
pography.They differfrom eachotherin that the largetime
constantassociated
with surfaceheatflow is absentin topography.Both,however,reflectthe subsurface
temperaturefield.
Figure 5 summarizesthe heat flow data associatedwith the
ZIELINSKI:THERMALEVOLUTIONOF PASSIVEMARGINS
7581
origin [Sclateret aL, 1971].It may thereforebe reasonableto
seekan explanationfor the depthanomalyin the NorwegianGreenland Sea in termsof a temperatureanomaly in the up-
200
øC
WO
perseveralhundredkilometers.
If the shallowseafloorin the
i•2oo Norwegian-Greenland
Seais in fact relatedto thermalexpan-
1500
surface
waves
ß
solidus
sion,it may be indicativeof a regional'hot spot'not evident
in the heat flow data. Conversely,any thermal mechanism
which successfully
duplicatesthe topographicanomaly must
do so without giving rise to an obviousheat flow anomaly.
One suchmechanismmay be reflectedin model MR, which
providesa goodfit of the MohnsRidgeage-depthdata (Figure 6) aswell asthe heatflowdatain Figure$.
The changein thermal regime,shownby the modelsnear
the continentalmargin, is also reflectedin the surfaceheat
2000
KM
flow. Two effectspredictedby the thermal model presented
Fig. 4. Temperaturefieldsat 160 m.y. for two thermal model out- here are illustratedin Figure 7. Isothermscomputedby the
puts.(MR denotesMohnsRidge;WO denotesworld oceans).The left
edgesrepresentridge axesat the meltingtemperature.The vertical model are shownat age 60 m.y. for slabs100 km thick (the
line through each slab marks the position of the ocean-continent isothermsextend only to 60 km). Above each slab is plotted
MR
t
boundary.The solid circlesmark the baseof the oceaniclithosphere the theoreticalheat flow through its surface.Figure 7a illusfrom seismicsurfacewave data compiledby Forsyth[1977], and the tratesan edgeeffectin the heat flow whichwill be calledthe
stippledregionis the sameapproximateparameterbasedon the wet
'long-wavelength'
edgeeffect.This effectis the resultof the
solidusof peridotite(<0.4% water).
generaldeepening
of the isotherms
as the transitionis made
Mohns Ridge spreadingcenter.While the Mohns Ridge heat from ocean to the much older continent. In the model used to
flow data, in general, fall above the Sclater and Francheteau illustrate this effect, there was no difference between ocean
[1970]North Pacificdata, when viewedin comparisonwith and continentheat production.When a differenceis assumed,
the reliable North Pacific heat flow from Sclater et al. [1976], as it is in most of the casespresentedhere, another form of
the Mohns Ridge heat flow does not appear anomalously
high. The significantdepartureof the Sclaterand Francheteau
[1970] data from the 'reliable' North Pacific data can be explained if heat lossfrom hydrothermalcirculationis present
edgeeffectarisesin the heat flow. Comparingthe continent
and ocean heat productionsdiscussedearlier, there can be
seena very largediscontinuityin crustalheat sourcesat the
dictedby slab models,the reliabledata seemto be in fairly
goodagreement.Thereforeit is possiblethat the MohnsRidge
heat flow is simply a better indicatorof theoreticalheat flow
than other oceans.This couldin turn imply that hydrothermal
circulation,consideredlikely to be taking placein many of the
world oceans,is not asprevalentin the Norwegian-Greenland
Sea. This conclusionis supportedby the fact that none of the
face or 'shortwavelength'comparedwith the previous.An example of the combinedlong- and short-wavelength
edge effects is shown in the temperature field and associatedheat
flow in Figure 7b. It is of interestto considertheseedgeeffects
ocean-continentinterface. Becauseof this discontinuity, there
is a very shallowcomponentof heat flow from the continent
in the former data set. The latter data set has been screened to
include only stationswhere hydrothermal circulation is not into the ocean,which attemptsto balance the offset in heat
likely to be occurring.Where the Sclater and Francheteau production.Only the upper 25 km or so are involvedin the
data can be shown to depart from theoreticalheat flow, pre- process,so that this edge effectcan be considerednear sur-
7
axial low heat flow valuesoften associatedwith hydrothermal
circulationhave been reportedfor the Norwegian-Greenland
Sea [Langsethand Zielinski,1974].Shownalsoin Figure 5 is
6
the theoretical heat flow curve calculated from models MR
5
and WO. (Both models produce the same theoretical heat
flow.) Sincethe data do not imply a significantheat flow differencebetweenthe Mohns Ridge and the other world oceans,
a singlecurveis sufficientto fit both data sets.
Figure6 is a compilationof topographicdata. The detailed
drawing of the crestalregion of the Mohns Ridge is from
Johnson[1974]. On the age-depthplot the solid circlesrepresent 19 data points picked off seismicprofiles acrossthe
Mohns Ridge at well-identified magnetic anomalies [from
Talwani and Eldholm, 1977] and correctedfor isostaticsediment loading. The comparabledata for the world oceans
[Parsonsand Sclater,1977]fall within the envelopeformedby
the dot-dash
curves. The relative
subsidence of the Mohns
300
-
k
-
• IVPacific
• •
- 200
N
•
[•re//ob/e
IV
P •:
-
•
I00
•
MR,
W•
Z
/
•ge
( M? ]
Ridge, basedon the data points,seemsto be no differentfrom
the subsidenceof the rest of the world ocean ridges;however, cal heat flow for the Mohns Ridge (MR) and world oceans (WO)
basementdepths for the Mohns Ridge are uniformly shal- models. Also shown are the North Pacific data from Sclater and Franlower by nearly I km. It hasbeendemonstratedthat the gross cheteau[1970] and the reliableNorth Pacificdata from Sclateret al.
oceanfloor topographycan be explainedas being thermal in [1976].
7582
ZIELINSKI: THERMAL EVOLUTION OF PASSIVE MARGINS
John s o n, 1974
3
•1 •
•\• / Taiwan/
L•E-/dholm
[Parsons
i ' !
20
•0
!
i
i
I00
L• $cla!er)
140
(My)
Fig. 6. MohnsRidgedepthversusage.Solidcirclesare from TalwaniandEldholm[1977]andthe insetprofilefrom
Johnson[1974].The solidcurvesare computedfrom thermalmodelsfor the Mohns Ridge (MR) and world oceans(WO).
The dash-dotlinesrepresentthe rangeof age-depthdata for the world oceans[ParsonsandSclater,1977].
CONTINENTAL
in examining the distributionof heat flow acrossthe V•;ring
Plateau Escarpment.
HEAT
FLOW
ACROSS THE CONTINENTAL
MARGIN
The V6ring Plateau Escarpment has been interpreted by
Talwani and Eldholm [1972] as marking the site of an Early
Tertiary openingof the Norwegian-GreenlandSea. According to their interpretation,seawardof the escarpments,normal oceaniccrust began to form via the sea floor spreading
mechanismand has continuedto do so to the present.Landward of the escarpments,one should expectto find basement
which is essentiallycontinental.
The reliable heat flow stationshave been plotted relative to
the V6ring PlateauEscarpment(Figure 8, the open symbols).
The circlesare from Haenel [1974],and the trianglesare from
MARGIN
EVOLUTION
Model MR has been shown to be in good agreementwith
all
theoretical
and
data-related
constraints
for
an ocean
formed via sea floor spreadingand bounded by an old (Precambrian to Early Paleozoic) continent. In addition, it produces ocean floor topography nearly a kilometer shallower
than for other world oceans.For these reasonsit may be consideredrepresentativeof the Norwegian-GreenlandSea and,
in particular, the Mohns Ridge spreading center. Figure 9
showsthe topographicoutputfrom MR at 10,30, and 60 m.y.,
showingthe theoretical thermal evolution of the NorwegianGreenland Sea to presenttime. In Figure 9 the evolution is allowed to continue 100 m.y. beyond present to 160 m.y. From
left to right, the early portion of the topographiccurve shows
Zielinski[1977].The solidsymbolsrepresentthe heatflow cor- the normal oceanridge subsidence.
The more rapid deepening
rected for topography and sediment refraction. Also shown at the continental margin is analogousto the heat flow edge
landward of the escarpmentis the mean regional heat flow effect (Figure 7a) and is also due to the deepening of iso(the horizontal line) estimatedfrom the measurements.
The thermsas the continentis approached.
dominant feature of the data, the marked decrease in heat
As the seafloor adjacentto the continentdeepenswith age,
flow as the V6ring Plateau Escarpmentis approachedfrom the edgeeffectbroadensand becomeslesspronounced.To the
seaward, cannot be significantlyreduced by environmental right of the ocean-continentboundary, the uplifted continent
correction.For comparison,the solid line marked 'no conti- (shaded)is also seento undergoa changein time. The amplinent' showsthe slopethe heat flow would have due to simple tude of the uplift diminishesdue to cooling;however,the upocean cooling in the absenceof an adjacent continent. The lifted area becomesbroader as heat is diffused laterally into
theoretical heat flow from the models in Figure 5 has been the interior of the continent.
continued onto the continentalmargin in Figure 8, assuming
Several processessuchas erosion,deposition,and sediment
that the theoretical ocean-continentboundary is coincident loading have been ignoredin thesemodels.Those parts of the
with the V6ring Plateau Escarpment.The dashedcurve is for continental margin which are thermally uplifted above sea
a model with no oceanicheat sources.In Figure 8 the decrease level would be expectedto simultaneouslyundergo considin heat flow from the ocean to the escarpmentpredicted by erable erosion [Foucher and Le Pichon, 1972]. As a result of
the modelsis significantlygreaterthan the 'no continent'de- the removal of the eroded material, isostatic rebound would
crease,providinga much better fit to the data in that region. then result in further uplift. Subsequentdepositionof the
Sinceit is unlikely that the heat flow distributionis causedby eroded material onto the adjacentoceanicarea also playsan
the local environment, some deeper causemust be sought. important part in shapingthe continental slope. None of the
One interpretation is that it is an expressionof a heat flow featuresare included in the modelspresentedhere. In this reedgeeffectdue to the ocean-continentboundarybeing coinci- spect,the model topographyrepresentsa fundamentalprofile
dent with the V6ring Plateau Escarpment.
governedprimarily by a responseto temperature. Never-
ZIELINSKI: THERMAL EVOLUTION OF PASSIVE MARGINS
7583
Earlier, it was mentioned that a model was tested in which
A
the continentwasallowedto heat up during a periodof rifting
20 m.y. prior to the onsetof seafloor spreading.The resulting
topographyat 60 m.y. for this caseis shownin Figure 9, the
dashedcurve.Note the absenceof the edgeeffectat the continental margin, apparentlyoffsetby the higher initial temperatures in the trailing edge of the continent. Over the continent, the remnantof greaterinitial uplift is still quite strongat
60 m.y.
Holtedahl [1960] publisheda map of Cenozoicuplift, believed to be of tectonicorigin, acrossScandanavia.In Figure
10 the Holtedahldata.alongsectionAA' is plottedon a graph
of uplift versusdistance.The zero point on the horizontalaxis
is the Norwegian shoreline, and the vertical axis coincides
with the positionof the V6 ring PlateauEscarpment.The continental uplift from Figure 9 at 60 m.y. is plotted along with
the Holtedahl data. The solid curve is for the simple initial
condition(Figure 2a), and the dashedcurvea for the 'rifting'
initial condition (Figure 2b). Note that the solid.curve is considerablymore displacedfrom the data than dashedcurve a.
This implies that with the simple initial condition an insufficientportion of the continentis affectedthermally. The
better fit of dashedcurve a can be improvedif it is assumed
that all materialuplifted abovesealevel is rapidly eroded,and
more uplift is allowedvia isostaticrebound(dashedcurveb).
In light of the crudeverticaltemperatureboundarycondition usedfor the ridge axis, there is reasonablygood agreement betweenthe slopeof the theoreticaluplift curvesand the
data. Use of an axial boundary condition as in the work of
Langsethet al. [1966] and Bottingaand •tllegre [1973] which
distributesthe ridge axis meltingtemperatureover a sloping
(not vertical)surfacewouldprobablycausethe theoreticaluplift to be lesssteepthan in Figure 10and providea betterfit to
the data.
It may also be seenin Figure 10 that theoreticalmaximum
uplift of the continentedge can be of the order of 5 km or
more. WidespreadTertiary uplift is reportedfor East Greenland [Hailer, 1971]with amountsof up to 8 km inferred for
someareas[Wager,1947](someof thismay postrifting).Reference made to the Miocene-to-recent
Baikal
arch and rift
systemwith upliftsof 5-7 km furtherseemsto agreein magnitude with the uplift predictedby the theoreticalmodels.Despitetheseexamplesthere are areaslike the North Sea where
Fig. 7. Temperaturefieldswith heat flowsplottedabovefor two
100-km-thickslab modelsat 60 m.y., illustratingthe effectson the
temperature
field of transitionfrom oceanridgeto continent(left to
right). Figure7a showsan exaggerated
drop in heat flow acrossthe
the geologicdatashowno evidencefor large-scale
uplift associatedwith a rifting thermalevent.Suchareashaveprompted
alternate mechanisms, such as lithospheric stretching
[McKenzie, 1978], to explain the observedpostrifting subocean-continent
boundarywith no discontinuity
in heatgeneration sidence. The need for these alternate mechanisms on most At(the long-wavelength
effect).Figure 7b combinesthe above effect lantic-type continental margins and rift zones,however, is a
(unexaggerated)
with a shorter-wavelength
effectdue to the discontipoint still in question,awaitingfurthersynthesis
of the data in
nuity in heatgeneration(oceanto continent)assumed
for the models
these areas.
presented(the short-wavelength
effect).
theless,severalfeaturesof the model may be directly relatable
to actual continental margins. Walcott [1972] has shown that
it is difficult
to account for thick sediments found on some
While the computedoceanfloor topographyrapidly assumessteadystatefrom point to point (i.e., the oceandepth
300 km from the ridgeaxisis the sameat 160m.y. asit is at 60
m.y.), the sameis not true for pointson the continentalmargin. In this regionthe model may be usedto computesubsidencerates.Someresultsare shownin Figure 11, a plot of
thermal subsidenceof the edge of the continentas a function
of age.The subsidence
curvesin Figure 11 alsoignorethe effectsof erosionand sedimentdeposition.They are in a form,
however,which can be directlycomparedwith recentlypublished data basedon deep wells and seismiclines that have
been 'backstripped'[Wattsand Ityan, 1976].Curve a is for a
narrow marginsby loadingalone.This leavesopen the possibility that somecontrolmightbe exercisedby the temperature
field, i.e., a deepeningof oceanicbasementbeneathcontinental marginsmay be an expressionof a thermal edge effect.
The topographicdiscontinuitybetweenoceanand continent
in the modelsrepresentsa region of decouplingbetweenthe
two. Geologically,thiscouldbe picturedasa zoneof marginal
400-km slab and curves b, c, and d are for a 60-km slab. In the
faulting.
7584
ZIELINSKI:THERMALEVOLUTION
OF PASSIVEMARGINS
corrected
/•
Verna cruise 30
0
Haenel, 1974
mean
- (42)
heat
&
flaw
122
•/2/
/28
----..._.
.•
'•".•
•.•••.•••O••
l•/
•IH6•12
.•
l/•151
(21)
I
I
I00
s e o word
0
D/stance
I
I
/on dword
I00
(kin)
Fig. 8. Heatflowdata(opensymbols)
on theV6ringPlateauplottedwithrespect
to theV6ringPlateauEscarpment
(verticaldashedline). Solidsymbolsare correctedfor maximumtopographyand sedimentrefractioneffects.The circles
areheatflowmeasurements
fromHaenel[1974].Thehorizontal
linelandwardof theV6ringPlateauEscarpment
indicates
themeanregional
heatflowfromthedata.Thesolidline(seaward)
marked'nocontinent'
shows
thehorizontal
change
in
heatflowa modelwouldhavein theabsence
of thecontinent.
Theoretical
heatflowsfor MohnsRidgeandworldoceans
(solidcurve)andfor anoceanwithnoheatgeneration
fromradioactive
sources
(dashed
curve)areshown.
IO my
first 10 m.y., curve a shows over 3 km of subsidence.Subsequentto that time, there is little differencebetween the subsidenceshownby a and b.
_.k
CON
TINEN
Sleep[1971]successfully
utilizeda thermalmodelin analyzing subsidence
of the Atlantic continentalmargin,but argued
that one-dimensionalmodelswere sufficientto explain subsidencedue to thermal contraction.For the purposeof comparing a one-dimensionalmodel with the model presented
here the early subisdence
of a comparablecoolinghalf space
is alsoplottedin Figure 11 (solidcircles).With respectto the
half space,curveb appearsto havelosta largerproportionof
T
$o my
GO my
m;
---
IGO
my
3
i
i
i
i
i
Holtedahl, 1960
/Am
I
2000
Am
]
I
1000
Fig. 9. Topographycomputedfrom the thermal model MR at 10,
30, 60, and 160m.y. The shadedregionsare the portionsof the conti-
DISTANCE
(KM)
nentthermallyupliftedabovesealevel.The dashedcurveat 60 m.y. is
Fig. 10. Obliqueuplift across
Scandanavia
[afterHoltedahl,1960]
for the 'rifting' initial condition(Figure 2b), wherebythe continent alongsectionAA •. Plottedalongwith the dataare theoretical
curves
undergoesa 20-m.y.-longperiodof heatingprior to seafloor spread- from modelMR. Curve a is replottedfrom Figure9 (dashed),and
ing.
curveb showsadditional uplift due to erosion.
ZIELINSKI:THERMALEVOLUTIONOF PASSIVE1V[ARGINS
7585
•pace.
correspondingamountsindicatea differentsituation.At that
time, the heat lossthrough the oceanfloor crestalregion may
be ashigh as300 mW/m'- througha 50-km-widesurface.The
lateral heat flow, while only averagingabout 21 mW/m',
would yield heat lossof comparablemagnitudeif it occurred
througha 400-km interface.The strongdependenceof initial
subsidenceon sla_b.
thicknessL (Figure 11) can be explained
by the distributionof horizontal thermal gradient with depth
in Figure 12. The average heat flow acrossthe interface
changeswith the particular thicknessassumed.This is due to
the changein gradient with depth. However, by increasingor
decreasingthat thickness,the 'window' through which heat is
transferredis alsoopenedor closed.
The lateral heat flow indicated in Figure 12 is for models
startingwith the simple initial conditionof the left edge of a
cold continentbeing at the melting temperature.The more realistic rifting initial condition would causea shift in the time
axis, producinga smaller ocean-continenttemperaturecontrast for a given interval of spreading.Figure 12, for that reason,probably illustratesmaximum horizontal gradients.
Curves a and b in Figure 11 have been computed for a
point exactlyat the edgeof the continent,and curvesd and c
illustrate the vertical motion for points 10 and 50 km farther
onto the continent. Both latter points becomeuplifted sometime after the onsetof sea floor spreading(best illustrated by
heat within the first 20 m.y. This is evidencedby the greater
subsidence
in that interval. Subsidence
data from the Gulf of
Lion [Watts and Ryan, 1976] show more rapid initial subsidencewhen comparedwith the empirical oceanridge subsidencecurve of Hays and Pitman [1973].
The more rapid initial subsidence
shownpossiblein Figure
11 can be attributed to early lateral heat loss through the
ocean-continentboundary.Figure 12 is a plot of horizontal
curve c). It is evident from Figure 11 that one point on a margin could be undergoingthermal uplift while another point
somelateral distanceaway is subsiding.The absoluteratesof
vertical motion are also seento diminish rapidly with distance
from the continent edge.
The resultsshownin Figure 11 are alsofor the simple initial
condition. One effect of using the rifting initial condition
would be that the decreasingsubsidencewith distancefrom
the continentedge would be more gradual and probably, for
ß
ß 1D
COOLING
b
0
5'0
AGE
1•0
150
(MY)
Fig. 11. Thermally inducedsubsidence
(relative to positionat
time zero)of the continentedgeversusagefor (a) L -- 400 km and
(b), (c), and(d) L -- 60 km for severalmodels(solidcurves).Curvesd
and c are for points 10 and 50 km inland. The solidcirclesshowthe
first 60 m.y. of subsidencepredictedby a comparablecooling half
temperaturegradientsacrossthe ocean-continent
interfaceat
5, 10, 30, and 60 m.y. The dashedlinesindicateheat flow, assuminga thermal conductivityof 2.9 W/møC (7 mcal/øC cm
s). At 60 m.y., it can be seenthat heat lossdue to conduction
acrossthe continentalmargin is only a fractionof the heat loss
throughthe ocean floor (less than 4.2 mW/m2 vertically
througha 600-km-wideoceanfloor). At 5 m.y., however,the
o
that reason, more realistic.
THERMAL
ANOMALIES
Model MR and model WO differ in only one of their input
parameters,the magnitudeof the linear temperaturegradient
assumedat the ridge axis.This difference-0.2øC/lorn (greater
for MR) resultsin oceandepthsnearly a kilometer shallower
5
GRADIENT
DEPTH
io
1,5
(oC/KM)
Fig. 12. Horizontalthermalgradientacross
theocean-continent
interfaceversusdepth,computedfrommodelWO at
5, 10,30, and60 m.y.The verticaldashedlinesshowcorresponding
heatflowfor a thermalconductivity
of 2.9•W/møC(7
mcal/s øCtcm).
7586
ZIELINSKI: THERMAL EVOLUTION OF PASSIVEMARGINS
would have to increasethe gradientby an additional3øC/km.
In other words, the plume must provide an additional heat
flowof 8.8mW/m2 (0.21HFU) for a thermalconductivity
of
2.9 W/møC (7 mcal/øC cm s). A very detailed and accurate
regionalheat flow surveywould be requiredto resolvesuchan
anomalyat the surface.Even if all thecompensation
for Ice-
.!
o
4
land is placedwithin the upper 100km, a 10%or 20% increase
in ocean ridge heat flow could produce the excesselevation
according to Figure 13. The numbers involved in each of
theseexamplesare relatively small and do not appearto rule
out the possibilityof this mechanism.
If excessthermal expansiondown to somedepth of compensationis called upon to explain the depth anomalyin the
Norwegian-Greenland Sea, then the correspondingdensity
field should produce gravity anomalieswhich are consistent
with the observationaldata. Cochranand Talwani[1978]have
compiled the existing gravity and bathymetric data in the
North Atlantic including the Norwegian-Greenland Sea. On
the basisof 5ø x 5ø averages,they found that a positiveregional depth anomaly of roughly 1 km extendingnorthward
into the Norwegian-Greenland Sea from about 30øN coincideswith consistentlypositivefree air gravity.A residualfree
air gravity anomaly of about 20 mgalsseemsto correlatewith
the depth anomaly. Computer anlaysislead Cochranand Talwani [1978]to further concludethat at leastpart of the compensationfor excesselevation in the Norwegian-Greenland
Sea extendsto depths of the order of 300 km. These results
canbe usedto testthe thermaldepthanomalymodel•The
Fig. 13. Compensated
thermalexpansion
AL as functionof tem- density distribution computed from the thermal model has
peraturegradientincreaseAI• for severalslabthicknessL predicted
by the modelspresented.
for MR than for WO when topography is computed to 400km depth. The increased temperature gradient at the ridge
axis boundary resultsin newly intruded oceanicmaterial having a temperature excess.This temperature excessin turn
gives rise to additional isostaticallycompensatedthermal expansionwhich accountsfor the depth anomaly. Sincecooling
of oceanicmaterial as it movesaway from the ridge axis takes
place predominantly in the vertical direction, an element of
masswill retain its temperatureexcessabovethe temperature
of normal oceanas spreadingcontinues(i.e., each follows the
same family of cooling curves).Thus the depth anomaly will
persistas long as the gradient differenceat the axis is maintained. Should this differencecease,subsidenceof the ridge
axis would precede eventual subsidenceof the rest of the
ocean to normal depths.Since an increasein the gradient of
been enteredinto a computerprogram[Takin, 1967]to compute the gravity anomaly due to excesstopographyand its
compensationfor a sphericalcap the sizeof the NorwegianGreenland Sea. The resultsare shownin Figure 14 for L =
400 kin. The amplitudeof the computedgravityanomalyover
the center of the topographicanomaly is consistentwith ,the
observations. Values for L of less than about 300 km will not
producelargeenoughgravityanomaliesto comparewith the
observed,becausecompensation
of the depthanomalyis too
shallow.(It should be pointed out that the Cochranand Tal-
wani[1978]compilation
is basedon shipboard
gravitydata.
Strictly speaking, a more rigorous treatment of the above
would incorporatea correctionto the geoid.) In the above
sense,L, whichis obtainedfrom thermalmodelingindependent of the gravity, may be considered the 'thermal compensationdepth.' In the Norwegian-Greenland Sea, it seems
0.2øC/kin is equivalentto 0.59 mW/m 2 (0.014 HFU) for a
conductivityof 2.9 W/møC (7 mcal/øC cm s), there is no discernible heat flow anomaly.
The responseof elevation to a gradient change of only
0.2øC/km was computed for a full 400-km-thick slab. A thinner slab would require a greatergradientincreaseto produce
the sameelevation.The interrelationof slab thicknessL, gradient increasesAI•, and the amount of seafloor shallowingAL
is shownin Figure 13. Any point along a given curve specifies
the gradient increasewhich producesa given depth anomaly.
It can be seenthat for L -- 120 km and shallowerthe gradient
increase is large enough that even for AL = 0.1 km a dis-
cerniblesurfacehe•at
•flowanomalymaybe produced.
In the
Norwegian-Greefiland Sea (AL -- 1 kin), a compensation
depth of 200 km requiresa 1øC/km gradient increaseto that
depth. In turn, to raise Iceland above sea level, a 'mantle
pl•ume'giving rise to a temperatureexcessdown to 200 km
- 40
mgal
-1500
•
.
.
1500
#m
- -20
I `2.
roam/co
1 /•m T
/k I-= 0.,25 øC/#m
.
•. •
gm/cc
L
,
•ig. 14. Gravity anomalycomputedfor a l-km thermaldepth
anomaly.
ZIELINSKI: THERMAL EVOLUTION OF PASSIVEMARGINS
7587
to coincidewith the compensationdepth derived from gravity ever, this short-wavelengthtopographywould be expectedto
analysis.
ßdecaysubstantially
in 10m.y.(shorterwavelengths
decaying
more rapidly). So, this mechanism for generating rugged
DISCUSSION
AND SPECULATION
oceanridge topographysuffersfrom the sameproblem as the
Thermal expansionmechanismsmay be capableof repro- elevated continental margins. That is, while thermal expanducing topographic features other than ocean floor sub- sion provides a convenient means for generating these feasidence.Such a mechanismwas used to simulate the depth tures,it doesnot predict that they will be maintained.
Taken at face value, the changesin temperature gradient
anomaly in the Norwegian-Greenland Sea in agreementwith
required
to produce the topographicflucuationsmentioned
the long-wavelengthgravity field in that area. The symptoms
of this anomaly seemto appear in other broad regionsof the above would imply corresponding fluctuations in magma
worldoceans.
Menard[1973],
for'example,
citespositive
depth chemistry.This couldprovidea testfor muchof the above
and gravity anomalieswith no apparentheat flow anomaly in speculation.Alternately, it may be more realistic to explore
the northern Pacific-Gulf of Alaska region. A similar situa- whether or not similar topographicfluctuationsmight be produced by incorporating a resistive term into the differential
tion seems to exist in the central Pacific for the Hawaiian swell
based on compilations of residual gravity and topography equation.with a flux boundary condition at the ridge axis in[Watts, 1976]and regionalheat flow [Sclaterand Corry, 1967; stead of the temperature boundary condition which has been
Sclater et aL, 1970].
In the model for the Norwegian-GreenlandSea the depth
anomaly originated at the ridge axis. This doesnot necessitate
that all large-scaledepth anomalies originate at ridge axes.
The relationshfpshownin Figure 13is equallyapplicableto a
mid-plate thermal anomaly, provided that heat can be
used here.
IMPLICATION
OF CONVECTION
Apart from the advectiveterm in the conductionequation
used here, the model presentedignoresheat convectionin the
earth.Thisis largely•/mathematical
convenience.
In viewof
likelihood•'•that
in theregion
beneath
thelithobrought
to thenearsurface
•rapidlyenough.
Often,simplethe,strong
conductionthroughthe lithosphereis too slowto meet thisre-
quirement
unless
largequanti•ties,
ofheatareintroduced
from
below (Birch, 1975). However, in the case of the Hawaiian
swell and other mid-plate 'hot spots,'surfacevolcanismis vi-
sualevidencethat somehearis beingtransported
to the sUr-
sphere(below100-200•)
convection
is thedominantmode
of heat transfer, some discussionof the validity of the results
presentedis warranted.
Thermal models of the lithosphere regardlessof whether
they are conductiveor convectivemust produce similar temperaturefieldsin the upper 100 km. This is constrainedby ob-
face by means other than conduction.
Thermal expansionmay also be reflectedin shorter-wave- servationsof gravity, topography,surfacewaves, and geolength features.It was shownthat much of Iceland's present thermometry.Most of the topographicresultspresentedhere
elevation,for example,could be accountedfor by thermal ex-
havebeencomputed
fromthe full 400-km-thick
temperature
field; however,severalcaseswere discussed
in which only the
pansion
without
requiring
great
amounts
ofadditional
heat •pper
60kmofthe region
wasused
tocompute
topography.
from below.
:
•
Thatthermalanomalie
s associated
withspread•gcentersAll
may result from changesor differencesin the forcesresisting
plate motion was first put forth by Langseth and Zielinski
[1974]. Increasedresistance,accordingly,implies more thermal expansion. South of the SoutheastIndian Ridge, the
oceanflooris significantly
shallower
thanit is tc•'thenorth
[e.g.,Hayes,1976].Thiscouldbetheresultof Antarctica,
often assumedfixed in plate motion studies,affording more re-
sistanceto seafloor spreadingthan Australia.
Alsosuggested
isai!•ans bywhichoceanic
material
ona
continental margin might be elevated above normal ridge
crestheightsduring rifting. (It is conceivablethat stressesre-
quired
to tearplates
apartmight
be•greater
thanthose
involvedin normalseafloorspreadingS)
Changes
in ridgeaxis
elevationwith time, from oceanto oceanor along a ridge axis,
might also reflect different amountsof resistanceto plate motion.
deepertemperaturedifferenceswere ignored.The effectof
varying L for the topographic computation is discussedin
more detail in the•work of Zielinski [1977]. The important result is that, with the exceptionof the thermaldepth anomaly,
all featuresproducedby the model remain presentas L is reduced to about 100 km. This magnitudesof both the ocean
and the topographic edge effect are in fact
floorsubsidence
•:
greaterwhen only the upper 160km of the temperaturefield is
usedfor the computation than when the entire 400 km is used.
In view of thesefacts,it seemslikely that the topographygenerated from the temperature field of a purely convective
model which simultaneouslyincorporatesocean and continent would exhibit effectssimilar to thosepresentedhere.
The lower half of the 400-kin temperaturefield contributes
little to the topographic effects.This is becausethe mean lateral heat transfer in this region is considerablylessthan for
ß
theupper200km. To thisapproximation,
aswasstatedear-
Supposethat seafloor spreadingtakesplace not in a contin- lier, the lateral motion of the lower half of the region is inuous fashion but in a seriesof rapid surges.Between surges, significant(i.e., the model is not meant to suggesta 400-kmforces build
until
the resistive forces are overCOme and the
thicklithosphere).
Below200km,themodelproduces
•ertical
platecan moveforward.As a resultof the motion,energyis temperaturegradientswhich are nearly adiabatic, so the tem-
dissipatedso that driving forcesagain must build. During the peraturefield in the lower regionis not greatly differentfrom
more or lessstationaryperiod,materialcouldriseto a greater that producedby someconvectivemodels[e.g.,Schubertet aL,
the modelpresented
heremay be
heightat the axis than when the motionis occurring.By add- 1978].For thesereasons,
considered
an
approximation
to
its
more
elegant
but lesstracing a periodic.
componentto the ridgeaxisboundarytemper-
cOUnterpart.
ature to simulate this, thermal models could be constructed tableconvective
which reproducethe shorter-wavelength(,--10 km) ruggedto-
Acknowledgments. I am grateful for the assistanceand comments.
pographycommonto ridgeaxessuperimposed
on th• usual of my colleagues
'• Lamontandwouldparticularly
like to thankM.
oceanfloor subsidencecurve. Becauseof lateral cooling,how-
G. Langsethand A. B. Watts.
7588
ZIELINSKI: THERMAL EVOLUTION OF PASSIVE MARGINS
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