GEOPHYSICAL RESEARCH LETTERS, VOL. 20, NO. 11, PAGES 1095-1098,JUNE 7, 1993
CONSTRAINTS
FOR THE INDIAN
ON LITHOSPHE•C
OCEAN
FROM
THERMAL
DEPTH
AND
STRUCTURE
HEAT
FLOW
DATA
TomShoberg
l, CarolA. Stein
2 andSethStein
1
Abstract.
Models
for
the thermal
evolution
of oceanic
lithosphere are primarily constrained by variations in
seafloordepth and heat flow with age. These modelshave
been largely based on data from the Pacific and Atlantic
Ocean basins. We constructseafloorage relationsfor the
Indian Ocean which we combine with bathymetfic, sediment isopachand heat flow data to derivecurvesfor depth
and heat flow versusage. Comparisonof thesecurveswith
predictionsfrom three thermal modelsshowsthat they are
better fit by the shallowerdepthsand higher heat flow for
the GDH1 model, which is characterizedby a thinner and
hotter lithospherethan previousmodels.
Introduction
Variations in seafloordepth and heat flow with lithospheric age provide the primary constraintson models of
thermal evolutionof oceaniclithosphere,becausethesesurface observablesreflect the evolution of the geotherm as
the lithosphereages and cools. The subsidenceand hence
seafloordepth dependon the temperatureintegratedwith
depth in the lithosphere,whereasthe heat flow dependson
the near surfacetemperaturegradient.
These variations are grossly described by a model in
which the oceaniclithospherebehavesas the cold upper
boundarylayer of a cooling halfspacesuchthat depth and
heatflowvaryas agem andage
-m, respectively
[Davis
and Lister, 1974]. However, becausefor lithosphereolder
than 70 Ma the depthand heatflow data "flatten", varying
more slowly with age, the lithosphereis typically modeled
as a cooling plate [McKenzie,. 1967]. Plate models are
characterizedby the plate thermal thicknessa which the
lithosphere
approaches
at old ages,and the temperature
Tm
at a depth equal to the plate thickness.The plate model
behaveslike a cooling halfspacefor young ages, until an
age old enoughthat the thermal effect of the lower boundary condition causes flattening. The isothermal lower
boundaryconditionmodels the additionalheat input from
below, which inhibitsthe halfspacefrom coolingfor older
ages,and thus causesflattening.
The commonlyusedplate model is a 125 + 10 km thick
plate with a 1350 +_275øC basaltemperature[Parsonsand
Sclater,1977]. Althoughthis model (heredenotedas PSM)
fits the data better than a halfspace model, it generally
1 Department
of Geological
Sciences,
Northwestern
University,Evanston,IL
2 Department
of Geological
Sciences,
University
of Il-
linois at Chicago,Chicago,IL
Copyright1993by the AmericanGeophysical
Union.
overpredictsdepthsand underpredictsheat flow for lithosphere older than 70-100 Ma [e.g. Von Herzen et al.,
1989; Stein and Stein, 1992; Johnson and Carlson, 1992].
As a result, areas with depth or heat flow that are
anomalouswith respectto the PSM model often are similar
to the averagelithosphereof that age.
A recent joint inversion of depth and heat flow data
yielded a best-fittingplate model with a thicknessof 95 +
15 km and a basaltemperatureof 1450 + 250øC [Stein and
Stein, 1992]. The primary featureof this model, GDH1 (for
Global Depth and Heat flow), is a thinnerlithospherethan
in PSM. Becausethe geothermis proportionalto Tm/a, the
thinner lithospheregives a steepergeotherm,higher temperaturesat depth, and higher heat flow. Similarly, the
thinner lithospherepredictsless subsidence,which is proportional to the heat lost in cooling, and hencethe product
T,nßa. As a result,GDH1 significantlybetterfits the depth
and heat flow data. The improvedfits reflect the predicted
higher temperaturegradient that results largely from the
thinner plate, and would occur even if the basal temperature were not somewhathigherthan in PSM.
The GDH1 and PSM modelswere generatedusing only
data from the North Ariantic and North Pacific.
Data from
the Indian Oceanwould providean independent
testof the
models,but a depth-agecurve for the Indian Ocean has not
been presentedin the literature.We thus generatesuch a
curve and comparedepth and heat flow data with predictions of the "thin-hot"
GDH1 model, the "thick-cold"
PSM model, and the "thicker-colder"halfspacemodel.
Analysis
Oceanic lithospherein the Indian Ocean basin includes
portions of the Indian, Australian, Africa, and Antarctic
plates. A seafloor age map (Figure 1) was constructed
using magneticanomaly identificationsfrom Cande et al.
[1989] and Fullerton et al. [1989]. We estimated age
boundariesfor which no lineationswere recordedby using
plate rotationmodels[Patfiat and Segoufin,1988; Royer et
al., 1988; Royer and Sandwell, 1989; Royer and Chang,
1991]. For further interpretationwe followed Royer and
AC•. (UA)
i!• 0-3
'-• 3-10
I• 10-20
• 20-31
• 31-42
:.'.-•
42-56
•] 56--83
• 83-119
•] 119-130
[• 130-140
..:• 140-151
[• 151-160
•[ 160-165
Papernumber93GL00985
0094- 8534/93/93 GL-00985 $03.00
Fig. 1: Age provincesof the Indian Oceanlithosphere.
1095
1096
Shoberget al.: IndianOceanDepth& HeatFlow
Schlich [1988], Powell et al. [1988], Fullerton et al. [1989]
and Simpsonet al. [1979]. The seafloorwas divided into
age bins based on anomaly numbers, and absolute ages
were assignedusingthe timescaleof Haftandet al. [1990].
We used the NOAA
DBDB5
data set, which contains
depthsat grid pointsevery 5'. While this data set,which is
typically usedfor depth-agestudies,may have somebiases
due to inadequatesampling,thesedo not appearexcessive
for depth-agestudiesin the Pacific [PhippsMorgan and
Smith, 1992; Stein and Stein, 1993].
Points with depths less than 1000 m were deleted, to
eliminate
continental
shelves and islands. We
did not use
data near the Java Trench, in the Argo Abyssalplain (Figure 2), whose depths may be perturbed by near-trench
flexure.We excludedthe TasmanSea, generallyconsidered
part of the Pacific. Pointswithin 1ø squareswere averaged
to produce the uncorrecteddepth data set. A few points
are thus averagedacrossage boundaries,but this effect is
second-ordercomparedto the large age bins.
We digitized sedimentthicknesscontoursfrom the isopach maps of Rabinowitz et al. [1988] for the area west of
130øE and Ludwig and Houtz [1979] for the area between
130øE and 170øE.
Locations with sediment cover thicker
(ideally 67% of the data), whereasthe mediansare shown
with quartile ranges (50%). For comparison,basement
depthsfrom ODP/DSDP drill sitesin the Indian Oceanare
also shown.Thesedepths,from legs 22, 24, 25, 26, 27 and
119, were correctedfor sedimentsin the same manner.
We comparedthe depthsand heat flow (Figure 3) with
the predictionsof three thermalmodels,GDH1, PSM, and
a halfspace(HS) model with the PSM thermalparameters
and ridge depth.The heat flow misfit is to data with ages
older than 50 Ma in order to excludethe effect of hydrothermal circulation.The depth misfit is to data for all ages.
The improvedfit of GDH1 relative to PSM is comparable
to that for PSM relative to the halfspacemodel.
We also considered the depths after removing
anomalouslyshallow areas (Figure 2) that may reflect
excess volcanism. The remaining depths (Figure 3) are
somewhatdeeper, but the depth-agecurve is similar, and
significantlybetterfit by GDH1.
For oceaniclithosphereolder than 70 Ma both data sets
are generallyshallowerthan the GDH1 predictions.In fact,
the full depth dataset and the heat flow for ages greater
than 50 Ma are best fit by an 80 km thick plate with a
1450øCbasaltemperatureand coefficientof thermalexpan-
than 5 km, such in the western Somalia Basin, and in the
sion3.0x10
-$ øC-1. Thisresultis interesting
as GDH1
Bay of Bengal, were excluded.
We estimatedsedimentcover by locating each depth
point with respectto the appropriate
'isopachcontourusing
an algorithm of Bevis and Chatelain [1989]. The basement
depthwas then found by applyinga correctionfor isostatic
unloading of sediment [Le Douaran and Parsons,1982].
was constructedusing depth data that included swells and
regions of possible excess volcanism, because their
suppressionwould bias the model to greaterdepths.As a
The heat flow data were taken from the data set discussed
by Stein and Stein [1992] and separatedinto the sameage
bins as the depths.
result, GDH1 could be considered biased somewhat toward
shallowdepths[Stein and Stein, 1993].
Discussion
The fact that GDH1 bestfits the Indian Oceandepthand
heat flow data arguesfor sucha model, in which the litho-
sphereis thinner and hotter at depth than traditionally
Results
thought.This is an independenttest of the PSM and GDH1
Figure 3 shows the mean and median depths for 1ø
squareswithin each age bin. The two values are similar.
The apparentdifference in the uncertaintiesis largely
because the means are shown with one standard deviation
models, which were derived without Indian Ocean data.
We alsoconsiderit significantthat althoughno geoiddata
wereusedto deriveGDH1, it betterfits fracturezonegeoid
data,whichreflecta depth-weighted
integralof the geotherm [Stein and Stein, 1993].
We thus expect the GDH1 thermal structure to be a
20
40
60
60
100
12•
140
160
180
Fig. 2: Map of the Indian Ocean showingthe location of
areas that were excluded
from the entire data set or were
treated as perturbed by excess volcanism. Rectangular
regionsof exclusionwere chosenfor simplicity. In the primary data set, only the Tasman Sea (1) and Argo Abyssal
Plain (2) were excluded.For the "No hot spot" data set,
the Kerguelen(3), NinetyeastRidge (4), BrokenRidge (5),
Chagos-LaccadiveRidge (6), Mascarene Plateau (7) and
(8), Reunion (9), Crozet Plateau and Conrad Rise (10), and
Agulhas Plateau (11) areaswere also excluded.
better approximationof that within oceaniclithosphere.
Both becausethe data are satisfiedby a range of similar
plate models[Stein and Stein, 1992; 19931,and the plate
model is the simplestmodel that can fit both heat flow and
depth data, we do not ascribegreat significanceto the
detailsof the predictedtemperature
structurebeyondthe
generalpropertythat it is somewhathotterat depththan
earlier models. We anticipatethat a thinner and hotter
lithospherewill be a generalfeatureof modelsfoundfrom
analysisof depth,heatflow, or geoiddatawith age.
It is, of course,impossibleeither to constructa single
bestmodelor for a singlemodelto fit the dataperfectly.In
constructinga model, we chosethe form of the model and
the data it shouldfit. GDH1 was constructedusing the
plate formulation, such that depth and heat flow are fit
joinfly. Even within this formulation, the best fitting
modelswill differ dependingon the dataselectionandprocessing(e.g. sedimentcorrectionand spatialaveraging),the
modelingassumptions,
and the fitting procedure.
Whether to exclude shallow areas such as swells and hot
spot tracksis crucial. The choiceis not clear-cut;exclusion
of shallow areas inserts a bias about what is "anomalous,"
Shoberget al.' IndianOceanDepth& HeatFlow
PRIMARY
2
3
i
,
•
,
....
PS•
,
,
i
0•-•
I
•00
DATA SET
i
I
,
/
ß ----I-IS ßDSDP/ODP
t •' 150
i
25
I
õ0
ß ........
t 'I
i
75
I
100
1097
I %150I"-125
0
GDH1
,
•M
GDH1
•MODi•
50
AGE(Ma)
100
•
150
(Ma)
NO HOT SPOT DATA
I
I
I
GDH1
....
3
,
PSM
--- -- HS
I
I
io
I
• MEAN
0 MEDIAN
ßDSDP/ODP
.
, GDH1
}o
ß
ß &
.
)o
•o
PSM
GDH1
TtiKRMAL MODKL
o
o
•o
•o
AGE(Ma)
•us (•a)
Fig.3: (top)Depth-age
curves,
heatflow-age
curves,
andReduced-x
2 misfits
fortheprimary
Indian Oceandata set comparedwith predictionsof the GDH1 and PSM plate models,and a
halfspace(HS) model. (bottom) Samecomparisons
usinga data set with regionsof excess
volcanism(Figure 2) removed.
and forces the model toward deeper values, whereasinclusion of these areasforces it toward shallow depths.Moreover, becauseolder lithospherehas had more opportunity
to be perturbed,a significantportion of it may be per-
turbed.Such shallowareaswere not excludedin developing GDH1, becausethe goal was to developa model for
averagethermal structureto be usedfor identifyingperturbations.The alternativesare to develop models using the
deepestdepths [Parsonsand Sclater, 1977], or to use a
halfspacemodel which treatsall shallowerdepthsas perturbations [Davies and Pribac, 1993].
The Indian Ocean illustrates these difficulties.
Even after
excluding the excessvolcanism,the Indian Ocean is shallower than GDH1 predicts.One could argue that most of
We vicw thcscdifferences
asperturbations
on an average
thermal structure which GDH1
or similar models seek to
characterize.Depthvariationsalongridgesor on opposing
ridge flanks have been attributedto variationsin manfie
temperature[Cochran,1986; Many and Cazenavc,1989] or
to asthenosphcric
flow [PhippsMorgan and Smith, 1992].
These alternativesparallel the two primary proposed
mechanismsfor flatteningthe depth-agecurve, heat addition from below or asthenospheric
flow [Schubertet al.,
1978]. Our senseis that both mechanisms
may contribute
to perturbingthe depth-age
variation.The overalldepth-age
flatteningseemsto us, however,difficultto interpretas due
to asthcnosphcric
flow alone,as proposedby PhippsMor-
the remainingold lithosphere,such as the ExmouthPla-
I
teau, is anomalouslyshallow and shouldbe excluded.This
exclusionwouldleavelittle old lithosphere,
andthusmake
it difficult to resolveany thermalstructurebeyondthat
expectedfor halfspacecooling.We thus face the philosophicalchoiceof acceptinga halfspaceas the reference,
.......
--
---
-
ß South SEIR
PSM
ß North SEIR
HS
ß South
SWIR
ß North
SWIR
O East CIR
or usinga reference
like GDHi whichattempts
to describe
the averagetopographyfor older lithosphere.
Given that GDH1 providesa better averagefit to the
I
GDH1
•
ß West CIR
4
IndianOceanlithosphere,
it is interesting
to consideithe
remainingmisfit. Some may be due to anomalouslyshallow areasof old lithospherebeyondthoseexcludedas due
to excessvolcanism. Much of the remainingmisfit reflects
the differences in subsidence rates between and within
plates. Such variationsoccur for the Indian Ocean Basin,
as shownby comparisonof depthson oppositeflanksof
the differentridges (Figure 4). Some of thesedifferences
appear significanteven given the scatter(+ -500 m) of
depthsfor a givenagerangeon anyridgeflank.
6
0
I
50
100
A•e (•a)
Fig. 4: Depth-agecurvesfrom the "No hot spot" data set
on oppositeflanksof the IndianOceanridges.
1098
Shoberget al.: IndianOceanDepth& Heat Flow
gan and Smith [1992]. The facts that both the depth and
geoid for old lithospherefiatten in a consistentfashion
[Colin and Fleitout, 1990] and that the depth, heat flow,
and geoid data are reasonablywell fit by a singlethermal
model like GDH1 [Stein and Stein, 1993] favor the flatten-
ing being primarily a thermal effect. Obviously much
remains to be done before either the flattening or the
along-ridge and across-ridgedepth variationsare understood.
,
AcknOwledgements.
'We thank Lute Fleitout for helpful
discussions,and two anonymousreviewersfor usefulcomments. This researchwas supportedby NSF grantsOCE9019572 and EAR-9022476, and NASA grant NAG-51944.
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(Received March 5, 1993;
acceptedApril 12, 1993)