Ocean Island Densities and Models of Lithospheric
FlexureEstimates of the Effective Elastic Thickness of the
T. A. Minshull, School of Ocean and Earth Sciences, University of Southampton,
Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, U.K.
Ph. Charvis, Unité Mixte de Recherche Géosciences Azur, Institut de Recherche pour
le Développement (IRD), BP48, 06235, Villefranche-sur-mer, France.
Key words: Gravity anomalies, density, flexure of the lithosphere, volcanic structure,
Short title: Ocean island densities
SFor submittedssion to Geophysical Journal International, December 1999.
Revised version, September 2000. Final version, January 2001.
Estimates of the effective elastic thickness (Te) of the oceanic lithosphere based on
gravity and bathymetric data from island loads are commonly significantly lower than
those based on the wavelength of plate bending at subduction zones. The anomalously
low values for ocean islands have been attributed to the finite yield strength of the
lithosphere, to erosion of the mechanical boundary layer by mantle plumes, and to
prexisting thermal stresses, and to overprinting of old volcanic loads by younger ones.
A fiffourth possible contributionorigin tofor the discrepancy is an incorrect assumption
about the density of volcanic loads. We suggest that load densities have been
systematically overestimated in studies of lithospheric flexure, potentially resulting in
systematic underestimation of effective elastic thicknesses and overestimation of the
effects of hotspot volcanism. We illustrate the effect of underestimating load density
with synthetic examples and an an examples from the island of the Marquesas Islands
and from La Réunion. This effect, combined with the other effects listed above, in
many cases may obviate the need to invoke hotspot reheating to explain low apparent
Our main constraint on the rheology of the oceanic lithosphere comes from its
deformation in response to applied stresses. Whilest laboratory studies make an
important contribution, empirical relations based on laboratory measurements must be
extrapolated over several orders of magnitude in order to apply them to geological
strain rates, and such extrapolations must have large uncertainties. The largest stresses
applied to the oceanic lithosphere are at plate boundaries and beneath intraplate
volcanic loads, and our understanding of its response to stresses on geological
timescales comes mainly from gravity and bathymetric studies of these features. It has
long been recognised that estimates of effective elastic thickness (Te) from oceanic
intraplate volcanoes are significantly lower than estimates of the mechanical thickness
of the lithosphere of the same age at subduction zones (McNutt 1984; Fig. 1). Part of
this difference arises because of the finite yield strength of the oceanic lithosphere ,
which can be exceeded due to plate curvature beneath volcanoes (Bodine, Steckler &
Watts 1981). Wessel (1992) attributed a further part of the discrepancy to thermal
stresses due to lithospheric cooling, which sets up a bending moment which places the
lower part of the plate in tension and the upper part in compression. Plate flexure due
to volcanic loading releases thermal stresses, so that the plate appears weakened.
Wessel (1992) found that a combination of the above effects could partly explain the
low Te values from ocean island loading studies, but not completely. The remaining
reduction was attributed to "hotspot reheating" - the reduction of lithospheric strength
by mechanical injection of heat from the mantle plumes assumed to give rise to ocean
islands. This effect has been proposed by many authors (e.g. Detrick & Crough 1978),
and was quantified by McNutt (1984), who suggested that the age of the lithosphere
was effectively "reset" by plume activity, to a value corresponding to the regional
average basement depth. A problem with this suggestion is that hotspot swells exhibit
heat flow anomalies which are much smaller than those predicted by the reheating
model (Courtney & White 1986; Von Herzen et al. 1989). More recently, anomalously
low Te values for some ocean island chains have been attributed to errors in the Formatted
inferred age of loading where older volcanic loads have been overprinted by younger
ones (e.g., McNutt et al. 1997; Gutscher et al. 1999). Here we propose an additional
explanationlternative explanation ftorfor the low apparent Te of the lithosphere
beneath many oceanic volcanoes which comes from the methods of data analysis used
rather than from geodynamic processes.
THE DENSITY OF OCEANIC INTRAPLATE VOLCANOES
Estimation of Te requires quantification of both the load represented by the volcano
and the flexure of the underlying plate. In a few cases the flexure has been quantified
by mapping the shapes of the top of the oceanic crust and the Moho by seismic
methods (e.g., Watts & ten Brink 1989; Caress et al. 1995; Watts et al. 1997). Even in
some of these studies, the shape of the flexed plate beneath the centre of the load is
poorly constrained by seismic data, since the sampling of this region by marine shots
recorded on land stations is poor, and additional constraints from gravity modelling are
needed. The vast majority of the values shown in Fig. 1 come from studies using
bathymetric and gravity or geoid data. The limitations of values based on the ETOPO5
global gridded bathymetry and low-resolution satellite gravity data have been discussed
elsewhere (e.g., Goodwillie & Watts 1993; Minshull & Brozena 1997). However, even
where values have been derived from shipboard data, significant errors can arise
because of the trade-off in gravity modelling between the shape of density contrasts
and their magnitude.
Key parameters in gravity modelling of ocean islands and seamounts are the density of
the load and the density of the material filling the flexural depression made by the load.
These two quantities are normally set to be equal because the infill material lying
beneath the load is likely to have a similar density to the load itself, and allowing the
density of the infill to vary laterally introduces significant additional complexity into
gravity and flexure calculations. Calculations are further simplified if this density is
taken to be equal to that of the underlying oceanic crust, since then if the preloading
sediment thickness can be taken to be negligible, only one flexed density contrast (the
Moho) needs to be considered. Therefore many authors make this assumption, using
typical oceanic crustal density of 2800 kg/m3 (e.g. Watts et al. 1975; Calmant, Formatted
Francheteau & Cazenave 1990; McNutt et al. 1997). Some support for this value came
from drilling studies in the Azores and Bermuda, which led Hyndman et al. (1979) to
conclude that "the mean density of the bulk of oceanic volcanic islands and seamounts
is about 2.8 g/cm3".
Independent constraints on load density and flexural parameters are available in the
gravity and bathymetric data themselves. For example, the diameter of the flexural
node is a clear indicator of Te, and in some cases this can be defined from bathymetric
data (e.g., Watts, 1994). The shape of gravity or geoid anomalies also provides
constraints. A least-squares fitting approach where both Te and density are varied may
allow an estimate of the density to be made , but commonly there is a strong trade-off
between elastic thickness and density which leads to an ill-defined misfit function with
large uncertainties (e.g., Watts 1994; Minshull & Brozena 1997). The major
contribution to a least-squares fit is the peak amplitude of the anomaly, and this value
is highly sensitive to the load density. Studies where both . , The trade-off may be
avoided by using an alternative optimisation, for example by a including the cross-
correlation between residual gravity and topography as an additional term in the misfit
function (Smith et al. 1989).
Constraints on density can also come from wide-angle seismic studies, since for
oceanic crustal rocks there is a strong correlation between seismic velocity and density
(Carlson & Herrick 1990)., Ewhich means that xcept perhaps for rocks with large
fracture porosity, densities can be predicted from seismic velocity measurements with
an uncertainty of only a few percent (e.g., Minshull 1996) . Using Carlson and
Herrick's preferred relation, a density of 2800 kg/m3 corresponds to a mean seismic
velocity of 6.0 km/s; these authors suggest a mean density of 2860 ± 30 kg/m3 for Formatted
normal oceanic crust. However, a number of recent studies suggest that ocean islands
and seamounts have mean velocities and therefore mean densities significantly lower
than these values (Fig. 2). The mean density depends on the size of the volcanic
edifice, since smaller volcanoes are likely to have a greater percentage of low-density
extrusive rocks (Hammer et al. 1994), on its age, since erosion and mass wasting cause
a general increase in porosity as well as redistributing load and infill material, and on
its subaerial extent, since these processes act much more rapidly on a subaerial load.
Factors such as the rate of accumulation of extrusive material may also be important.
The overall correlation with load size is weak, so unfortunately the load density is not
easily estimated from its size. However, in all casesgeneral the density is significantly
lower than that of normal oceanic crust; this is not surprising because of the greater
proportion of extrusives in ocean islands and seamounts and because of the effects of
erosion and mass wasting.
EFFECT ON FLEXURE AND ELASTIC THICKNESS ESTIMATES
The above evidence suggests that load densities may be systematically overestimated
in studies of the flexural strength of the oceanic lithosphere. There are two resulting
effects on flexural modelling. Firstly, the vertical stress exerted by the load is
overestimated, so for a given Te value the depression of the top of the crust and Moho
is overestimated and the corresponding negative gravity anomaly is overestimated.
Secondly, the positive gravity anomaly of the load itself is overestimated. The latter
effect is always larger, even for Airy isostasy, since the corresponding density contrast
is closer to the observation point. The resulting effect on Te estimates may be
quantified by computing the flexure, and gravity anomalies and geoid anomalies due to
a series of synthetic loads and then estimating the corresponding elastic thickness by
least-squares fitting of the anomalies with an incorrect assumed density. The effect
varies with the size of the load, so in this study three load sizes are considered (Table
1): a small load, comparable with some seamount chains, a large load comparable to
large ocean islands such as Tenerife and La Réunion, and an intermediate load. The
result also depends on the shape of the load. The simplest shapes for computational
purposes are a cone and an axisymmetric Gaussian bell; most ocean islands and
seamounts have their mass more focused close to the volcano axis than a conical shape
would imply, so a Gaussian shape is chosen here. For simplicity, the loads were
assumed to be entirely submarine. Flexure computations used the Fourier methods of,
e.g., Watts (1994), while gravity anomalies were calculated using the approach of
Parker (1974), retaining terms up to fifth order in the Taylor series expansion to ensure
the gravity anomalies of the steeply-sloping load flanks are well represented. Geoid
anomalies were computed by Fourier methods from the corresponding gravity
anomalies. Load and infill densities of 2500-2700 kg/m were considered, with the
density of the water, crust and mantle set to 1030, 2800 and 3330 kgm/m3 respectively,
and a normal oceanic crustal thickness of 7 km (White, McKenzie & O’Nions 1992).
The crustal density used is the most commonly used value, though it is slightly lower
than Carlson &and Herrick'’s (1990) preferred value. For a series of predefined Te
values, Te was estimated using an assumed load and infill density of 2800 kg/m3.
The results of these computations (Fig. 3) confirm that in all cases Te is underestimated
because the magnitude of the plate flexure is overestimated, and the size of the
discrepancy increases with decreasing load size. In most cases the discrepancy is
comparable to or larger than commonly quoted uncertainties in Te values. The total
volume of the volcanic edifice (load plus infill) is also significantly overestimated.
The ratio between the inferred infill volume and the true volume deviates little from
the ratio for Airy isostascy, whatever the value of Te , because the total compensating
mass must be the same in all cases. For a mean edifice density of 2600 kg/m this ratio
is 1.55, while for a density of 2500 kg/m3 the ratio is 1.89. Estimates of Te are slightly
improved if the geoid rather than the gravity anomaly is used, ; this is because the
geoid anomaly is more sensitive to the shape of the flexed surfaces beneath the load.,
However,but the difference is small and in real applications the geoid may be more
strongly influenced by deeper, long-wavelength effects which are not accounted for in
the flexural model. For these synthetic examples, the correct value of Te can of course Formatted
be recovered by simultaneous optimisation of both Te and load density (Fig. 4). The Formatted
misfit minimum is fairly flat and a small amount of noise due to density variations not
considered in the flexural model may shift the minimum away from its true value, but
no systematic bias is expected. A further effect which has not been included is that of
any magmatic underplating, such as has been inferred beneath the Hawaiian and
Marquesas Islands (Watts & ten Brink 1989; Caress et al. 1995). Magmatic
underplating places a negative load on the base of the plate which reduces its
downward flexure, but also increases the Moho depth and hence the apparent flexure
of the base of the plate; the trade-off between these effects depends on the size, shape
and density contrast of the underplate.
The uniform density models used for these calculations are somewhat oversimplified;
seismic experiments indicate that ocean islands commonly have a high-density
intrusive core (Fig. 2). To simulate this type of structure, gravity anomalies were
computed for a "large" load with a density of 2500 kg/m except in a central core with
a radius 80% of the Gaussian decay length and reaching 50% of the height of the load
above the surrounding ocean floor, which was assigned a density of 2800 kg/m . This
structure is loosely based on that of Réunion Island (Fig. 2). In this case the flexure
computation is iterative since the overall height of the cylindrical core depends on the
amplitude of the flexural depression. The results (Fig. 54) again show that Te is
systematically underestimated, and the results from this composite load are very
similar to those of a uniform load of the same mean density.
REAL EXAMPLE: THE MARQUESAS ISLANDSS FROM LA REUNION
We further illustrate the problem of assuming a standard oceanic crustal density with
atwo real examples from the Marquesas Islands, (one from the literature and one
involving new data) for which the elastic thickness is constrained independently by
seismic determinations of the shape of the flexed oceanic basement and/or the shape of
the flexed Moho beneath the load. Two further effects must be considered herefor real
examplessome results from the island of La Réunion, where vertical multichannel
seismic data and wide-angle seismic data give a well-constrained model both of the
internal structure of the volcanic load (Gallart et al. 1999), and of the three-
dimensional shapes of the top and base of the oceanic plate beneath (Charvis et al.
1999; de Voogd et al., 1999).
. The first is that of inferred magmatic underplating , such as has been inferred beneath
the Hawaiian and Marquesas Islands (Watts & ten Brink 1989; Caress et al. 1995).
Magmatic underplating places a negative load on the base of the plate which reduces
its downward flexure, but also increases the Moho depth and hence the apparent
flexure of the base of the plate; the trade-off between these effects depends on the size,
shape and density contrast of the underplate. The second is that of the assumed depth
of the top of pre-existing oceanic crust, which defines the size of the load. Both effects
are explored below.
AOur first example is that of the Marquesas Islands, for which a comprehensive
gravity and bathymetric dataset for the Marquesas Islands (Fig. 6) was recently
published by Clouard et al. (2000). THere, the depth to pre-existing oceanic basement
has been determined by multichannel seismic reflection profiling and by coincident
sonobuoy wide-angle seismic data (Wolfe et al. 1994), and an elastic thickness of 18
km has been determined. Gravity anomalies were computed for a region extending one
degree in all directions beyond the edges of the region shown in Figure 6, to avoid edge
effects. Models assumed an oceanic crustal thickness of 6 km, consistent with
sonobuoy refraction data (Wolfe et al. 1994; Caress et al. 1995), an oceanic crustal Formatted
density of 2800 kg/m3, and a range of elastic thicknesses and load and infill densities. Formatted
The root mean square misfit was evaluated for the region shown. Our purpose here is
not to place new constraints on the rheology of the lithosphere in this region, but rather
to illustrate the bias that may be introduced by an incorrect choice of load density.
The island chain forms a well-defined bathymetric feature, though there is some
interference from the Marquesas Fracture Zone in the south-east corner of the region.
If a horizontal base level is used for the load, there is an uncertainty of a few hundred
metres in what this base level should be. The smallest root-mean-square misfit was
found for a base level of 4200 m (Fig. 7a) and this corresponds to a Te of 19 km,
similar to the seismically constrained value, and a density of 2550 kg/m3, slightly Formatted
smaller than the 2650 kg/m3 used by Wolfe et al. (1994). The fit between observed Formatted
and calculated gravity is good, with the misfit only exceeding 20 mGal locally around
some islands and seamounts, where density variations within the volcanic edifices
make a significant contribution (Clouard et al. 2000). A slightly shallower base level
of 4000 m results in a slightly larger misfit, but no significant difference in Te or the
best-fitting load density (Fig. 7b).
An alternative possibility is that part of the seabed relief is due to a long-wavelength
swell. Inclusion of the swell in the load could result in a biased Te value. An objective
method for separating a regional bathymetric signal such as a hotspot swell from a
residual due volcanic loading by using a median filter which maximises the residual
volume above a particular contour was suggested by Wessel (1998). The method
places a clear lower limit on the optimal filter length, but unfortunately the residual
volume changes slowly at large filter lengths, so that small changes due to the choice
of area included in the analysis can change significantly the optimal filter length
corresponding to the maximum residual volume, and an upper limit is less clearly
defined. To illustrate the effect of accounting for a swell, we analysed a series of
models using a residual load after removing a regional defined by a 500 km median
filter, which gives a peak swell amplitude of about 500 m relative to the abyssal plain
at the edge of the area considered. This regional relates to the central part of the swell
only, since the swell extends well beyond the area considered here (Sichoix et al. Formatted
1998). In this case the best-fitting Te is slightly larger, while the best-fitting load
density is unchanged (Fig. 7c).
Wolfe et al. (1994) found that the observed basement deflection could be matched by
the addition of a basal load equal to 25% of the low-pass filtered top load, with a filter
cut-off at 300 km, and interpreted as due to magmatic underplating. McNutt &
Bonneville (2000) have suggested recently that such underplating could be the origin
of the long-wavelength swell. Including such a basal load also has little effect on the
optimal Te and load density (Fig. 7d). TIn all cases, these analyses show that the Formatted
optimum load density required to fit the gravity data is always significantly less than
2800 kg/m3, and that if a load density of 2800 kg/m3 were assumed for the Marquesas, Formatted
the elastic thickness would be underestimated by ~25-40%. Calmant et al. (1990) Formatted
made just such an assumption, and found a Te value of 14±2 km, significantly less than
the seismically constrained value. This bias in elastic thickness is much greater than
the bias which would arise due to reasonable errors in the base level or due to the effect
Our second example is taken from the island of La Réunion, where multichannel
seismic reflection data and wide-angle seismic data give a well-constrained model both
of the internal structure of the volcanic load (Gallart et al. 1999), and of the three-
dimensional shapes of the top and base of the oceanic plate beneath (Charvis et al.
1999; de Voogd et al. 1999).
ADD SECTION ABOUT WHAT HAPPENS IF YOU ASSUME A DENSITY OF
2800, WITH SOME FITTING OF GRAVITY DATA.
For La Reunion, wWe can independently estimate the density of the volcanic load from
wide-angle seismic velocities using the preferred relations of Carlson and
HerrickRaskin (199084) (Table 2). The submarine part of the volcanic edifice has a
density as low as 2500 kg/m3. Beneath the island a body with a density of 2900
kg/m3, similar to the average density of the oceanic crust, is interpreted as an intrusive
core of dense volcanic material. Its shape and volume were further defined by gravity
modelling (Charvis et al. 1999). We estimate the average density for the volcanic load
to be 2600 kg/m . The top of the load is define by the topography of the aerial and
submarine parts of the volcanic edifice down to isobath 4000 m which represents its
outer limit (Fig. 85a). The base of the load is the top of the oceanic sedimentary layer
deposited prior to volcanic activity at Réunion which was images by multichannel
seismic data (Fig. 85b). The volume of the volcanic load, so defined, is 75,000 km
(de Voogd et al. , 1999). Seismic data also showevidenced the presence of an
underplated layer located at the base of the prexisting oceanic crust with a density of
~3 000 kg/m3 (Gallart et al., 1999). Theis underplatelayer, which is up to 3 km thick
and 200 km wide, has a volume ofis 50,000 to 70,000 km3, shifted by and is centred 25
km to the sSouthwest of the centre of Lawith regard to the Réunion Island (Charvis et
al., 1999). It will act as a negative load placed the base of the plate and will reduce the
downward flexure. PlateThe flexure of the plate will then results from the positive
load of the volcanic edifice lying on the top of it and from the negative load of the
underplated material located at the base of the crust. We computed the resulting
deflectionflexure for elastic thicknesses of the lithosphere varying from 12 to 38 km
(Fig. 96). We compared the shape of the flexed plate to lithospheric interfaces well
constrained by seismic data: the top and the base of the oceanic crust. These interfaces
existed prior to the volcanic activity at Réunion, and they likely recorded the flexure of
the plate due the emplacement of the volcanic edifice. The base of the oceanic crust is
located at the top of the underplated body where it is present, whereas the present day
Moho is located deeper, at the base of the underplating, and is deepensing from 10 km
beneath the oceanic basin to 15 km beneath La Réunion (Fig. 2). To compare the
computed shape of the flexed plate to the top and the base of the oceanic crust with the
observed shapes, we subtracted a best-fitting planlinear trend from both to the top and
base of the oceanic crust in order to remove long-wavelengththe effects such as those
due related to the varying age of the plate. This was also applied, for consistency, to
the computed flexed plate, as part of the flexure could also be removed in this process.
The different surfaces are We compared the two surfaces along two seismic profiles,
located over seismic lines where they lithospheric interfaces are best constrained (Fig.
The fit between lithospheric interfaces and the flexed surface is characterised by
for different values of the elastic thickness (Fig. 7).
An adequate fit is achieved ifThe main result of this study is that the elastic thickness
of the lithosphere beneath La Réunion is 25 ± 5 km, though larger values cannot be
excluded (Fig. 107). However, much ofBut the topography of the top and base of the
oceanic crust is also clearly related to the formation emplacement and tectonic history
of the oceanic crust prior to load emplacement rather than to flexural effectsvolcanic
activity (the oceanic crust is ~62 Ma and the earliest known volcanic activity is 2 Ma).
The volcanic edifice of La Réunion liesn volcanic edifice is built at the intersection
between a NW-SE trending spreading centre and a SW-NE trending fracture zone
(Charvis et al., 1999; de Voogd et al., 1999; Dyment et al., 1991). Tthe oceanic crust
isbeing older south of the fracture zone and this age difference partly accounts for the
depression observed beneath the volcanic edifice.
Our estimate of TeThe flexure we computed is not very different from the result of
Bonneville et al. (1988), who which calculated an elastic thickness of 28 ± 4 km for
the lithosphere beneath La Réunion from modelling of GEOS3 and SeaSat geoid data.
However, Nevertheless Bonneville et al. (1988), who assumed a density of 2800 kg/m
for the volcanic load, carried out a two-dimensional analysis which causes a
systematic bias to higher elastic thicknesses (e.g., Lyons et al., 2000); in this case the
downward bias in Te due to an incorrect density estimate was fortuitously cancelled out
by the upward bias in Te due to the two-dimensional approach. In addition, Bonneville
et al. (1988) inferred a maximum Moho deflection of 4 km beneath the island, using an
assumed density of 2800 kg/m3 for the volcanic load, which is much larger than the
observed deflection inferred from the geometry of the top and bottom of the prexisting
oceanic crust, of less than 2 km (Charvis et al. 1999; Gallart et al., 1999). The volume
of the load and infill associated with a 4 km deep flexural depression is ~240,000 km ,
approximately three times the volume to compare with the 75,000 km3 inferred from
seismic studies. The volume discrepancy is larger than in the above synthetic models,
and. t The inferred elastic thickness inferred by the two approaches differs less from
the true valueis fortuitously similar in this case, because of the effects of the
underplating. The difference between maximum deflections calculated in this study
and in Bonneville et al. (1988) could be related to:
1. density used for the computation of the load: Bonneville et al. (1988) used a density
of 2800 kg/m for the volcanic load, the sediments infilling the flexural depression
around the edifice and the oceanic crust as well; then the gravity anomaly is only
related to the flexure of the Moho and the volcanic load itself;
2. the lack of on-land gravity data to constrained densities in the volcanic edifice in
Bonneville et al. (1988);
3. the effect of underplating: which compensates for part of the volcanic load and
reduces the amplitude of the flexure.
The seismic Moho, 4 to 5 km deeper beneath the south-eastern part of the volcanic
edifice because of the presence of magmatic underplating (Charvis et al. 1999; Gallart
et al., 1999) has a depth similar to the one expected for a 4 km deflection of the plate.
We show from this study that the seismic structure of La Réunion is compatible with a
25 km thick flexure, which is only slightly smaller than the one inferred from geoid
data modelling (Bonneville et al., 1988).
The above results show that great care should be takaken in interpreting estimates of Te
, and hence of the amplitude of lithospheric flexture , and of the volume of volcanic
edifices,estimates from gravity or geoid-based seamount loading studies of oceanic
lithosphere unless there are independent seismic constraints, or at least the load density
has been optimised to match the gravity dataindependently constrained. Values are
likely to be underestimated by large amounts, particularly for small loads, if a density
of 2800 kg/m has been assumed. Most recent studies have indeed taken a more
rigorous approach, with the use of seismicindependent constraints from seismic data
(e.g. Watts et al. 1997), or or simultaneous optimisation of load density and elastic
thickness (e.g., Smith et al. 1989)the use of a composite misfit function which Formatted
emphasises the shape of gravity anomalies more than does a simple least-squares misfit
(e.g. Smith et al., 1989). In some of these studies the crustal density has been fixed
equal to the load density (e.g., Filmer et al. 1993; Lyons et al. 2000). Such an Formatted
approach simplifies gravity calculations, but its effect on the estimation of Te is not yet Formatted
quantified. Even ignoring such problems, tHowever, the published global dataset for
seamount loading (as compiled by, e.g., Wessel 1992) is reduced to very few points
(the filled circles and squares of Fig. 1) if values using assumed densities and values
derived from ETOPO5 bathymetry and/or low-resolution satellite gravity are excluded
The less well-constrained values of Te (open symbols of Fig. 1) are too scattered to Formatted
resolve statistically a bias toward lower values by comparison with the better-
constrained values (filled symbols). In all cases the seamount loading , but it may be
possible to explain a reduced difference In some cases the bias due to using an
assumed density may be counteracted by an upward bias due, for example, to the use of
a two-dimensional analysis (Lyons et al. 2000). However, it is clear from the above Formatted
analysis that such a bias is likely to be frequently present. Most published values for
ocean islands could be considerably improved by a reanalysis using shipboard
bathymetry and a combination of shipboard, land, and high-resolution satellite
gravity/geoid measurements and, using an approach which maintains the load density
as a free variable or constraints it from seismic data. Without such reanalysis, and
given the variety of other possible explanations causes for reduced elastic thickness
beneath ocean islands and seamounts, suggestions that the mechanical thickness of the
lithosphere is eroded significantly by plumes must be treated with some caution.
From oura study of gravity and geoid anomalies of synthetic loads flexing the oceanic
lithosphere, we draw the following conclusions:
1.1. Ocean islands and seamounts commonly have a mean density which is
significantly lower than that of the oceanic crust beneath.
22. If a load density of 2800 kg/m is assumed in gravity studies of flexure due to
seamount loading, effective elastic thicknesses are significantly underestimated, by an
amount which can be up to a factor of three or four for smaller loads., Twhile the total
infill volume of load plus infill can be overestimated by a factor of at least 50%, or
more in the presence of underplating.
3. For the Marquesas Islands, where the elastic thickness is independently constrained
by seismic data, the bias in elastic thickness which would be introduced by assuming a
load density of 2800 kg/m3 is much larger than biases which would be introduced by Formatted
reasonable variations in the chosen base of the load or by failing to allow for the
contribution of underplating with a volume consistent with seismic data.up to *..
4. 3. From seismic data we estimates anthe average density of the volcanic load of La
Réunion ofto be 2600 kg/m in La Réunion and athe maximum deflection of the top
and the base of the oceanic crust ofto be less than 2 km beneath the island, compared
with an earlier estimate based on geoid anomalies of 4 km. Theis deflection is
compatible with an elastic thickness of 25 ± 5 km only slightly smaller than previous
4. Least-squares fitting of geoid anomalies is a slightly more robust process than least-
squares fitting of gravity anomalies if no independent constraints on density are
445.5. Few flexurale studies of ocean islands and seamounts have used data of
sufficient resolution and with sufficient constraint on load densities to give an accurate
estimate of the effective elastic thickness; the paucity of reliable values severely limits
their use in constraining models of plume-lithosphere interaction.
TAM is supported by a Royal Society University Research Fellowship. We thank A.
Watts and I. Grevemeyer for supplying digital data used in Fig. 2, and P. Wessel and
M. McNutt for constructive reviews. The GMT package of Wessel & Smith (1998)
was used extensively in this study. This research was initiatedconducted during visits
by both authors to the Instituto de Ciencias de la Tierra (Jaume Almera), Barcelona,
Spain. UMR Géosciences Azur contribution 356###.
Bonneville, A., Barriot, J.P. & Bayer, R., 1988. Evidence from geoid data of a hot spot
origin for the southern Mascarene Plateau and Mascarene Islands (Indian Ocean), J.
Geophys. Res., 93, 4199-4212.
Bodine, J. H., Steckler, M. S. & Watts, A. B., 1981. Observations of flexure and
rheology of the oceanic lithosphere, J. Geophys. Res., 86, 3695-3707.
Calmant, S., Francheteau, J. & Cazenave, A., 1990. Elastic layer thickening with age of
the oceanic lithosphere: a tool for the prediction of the ages of volcanoes or oceanic
crust, Geophys. J. Int., 100, 59-67.
Caress, D.W., McNutt, M.K., Detrick, R.S. & Mutter, J.C., 1995. Seismic imaging of
hotspot-related crustal underplating beneath the Marquesas Islands, Nature, 373, 600-
Carlson, R. L. & Herrick, C. N., 1990. Densities and porosities in the oceanic crust
and their variations with depth and age, J. Geophys. Res., 95, 9153-9170.
Charvis, P., Laesanpura, A., Gallart, J., Hirn, A., Lépine, J.-C., de Voogd, B.,
Minshull, T.A., Hello, Y. & Pontoise, B., 1999. Spatial distribution of hotspot material
added to the lithosphere under La Réunion, from wide-angle seismic data, J. Geophys.
Res., 104, 2875-2893.
Charvis, P., Laesanpura, A., Gallart, J., Hirn, A., Lépine, J.-C., de Voogd, B.,
Minshull, T.A., Hello, Y. &, Pontoise, B. & Minshull, T.A., 1999. Spatial distribution
of hotspot material added to the lithosphere under La Réunion, from wide-angle
seismic data, J. Geophys. Res., 104, 2875-2893.
Clouard, V., Bonneville, A. & Barsczus, H. G., 2000. Size and depth of ancient
magma reservoirs under atolls and islands of French Polynesia using gravity data, J.
Geophys. Res., 105, 8173-8191.
Courtney, R. C. & White, R. S., 1986. Anomalous heat flow and geoid across the Cape
Verde Rise: evidence of dynamic support from a thermal plume in the mantle,
Geophys. J. R. Astr. Soc., 87, 815-868.
Detrick, R. S. & Crough, T., 1978. Island subsidence, hotspots and lithospheric
thinning, J. Geophys. Res., 83, 1236-1244.
de Voogd, B., Pou, S., Hirn, A., Charvis, P., Gallart, J., Rousset, D., Dañobeitia, J. &
Perroud, H., 1999. Vertical movements and lateral transport during hotspot activity:
seismic reflection profiling offshore La Réunion, Journal of Geophysical Research,
Dyment, J., 1991. Structure et évolution de la lithosphère océanique dans l’océan
Indien: apport des anomalies magnétiques, Thesis, Université Louis Pasteur,
Strasbourg, 374 pages.
Filmer, P.E., McNutt, M.K. & Wolfe, C.J., 1993. Elastic thickness of the lithosphere in
the Marquesas and Society Islands, J. Geophys. Res., 98, 19565-19577.
Gallart, J., Driad, L., Charvis, P., Hirn, A., Lépine, J.-C., Diaz, J. & de Voogd, B.,
1999. Perturbation to the lithosphere along the hotspot track of La Réunion from an
onshore-offshore seismic transect, J. Geophys. Res., 104, 2895-2908.
Goodwillie, A. M. & Watts, A. B., 1993. An altimetric and bathymetric study of
elastic thickness in the central Pacific Ocean, Earth Plan. Sci. Lett., 118, 311-326.
Gutscher, M.-A., Olivet, J.-L., Aslanian, D., Eissen, J.-P. & Maury, R., 1999. The
"“lost Inca Plateau"”: cause of flat subduction beneath Peru?, Earth Plan. Sci. Lett.,
Hammer, P.T.C., Dorman, L.M., Hildebrand, J.A. & Cornuelle, B.D., 1994. Jasper
Seamount structure: seafloor seismic refraction tomography, J. Geophys. Res., 99,
Harris, R. N. & Chapman, D. S., 1994. A comparison of mechanical thickness
estimates from trough and seamount loading in the southeastern Gulf of Alaska, J.
Geophys. Res., 99, 9297-9317.
Hyndman, R. D., Christensen, N. I., & Drury, M. J., 1979. Velocities, densities,
electrical resistivities, porosities, and thermal conductivities of core samples from
boreholes in the islands of Bermuda and the Azores, in: Deep Drilling Results in the
Atlantic Ocean: Ocean Crust, Am. Geophys. Union Maurice Ewing Ser., 2, 94-112.
Kruse, S. E., Liu, Z. J., Naar, D. F., & Duncan,.R. A.,1997. Effective elastic thickness
of the lithosphere along the Easter Seamount Chain, J. Geophys. Res., 102, 27305-
Lénat, J.F. & Labazuy, P., 1990. Morphologies et structures sous-marines de La
Réunion, Le volcanisme de La Réunion, Monographie, Centre de Recherche
Volcanologique de Clermont-Ferrand, 43-74.
Lyons, S. N., Sandwell, D. T. & Smith, W. H. F., 2000. Three-dimensional estimation
of elastic thickness under the Louisville Ridge, J. Geophys. Res., 105, 13239-13252.
McNutt, M., 1984. Lithospheric flexure and thermal anomalies, J. Geophys. Res., 89,
McNutt, M. K., Caress, D. W., Reynolds, J., Jordahl, K. A., & Duncan, R. A.., 1997. Formatted
Failure of plume theory to explain midplate volcanism in the southern Austral islands,
Nature, 389, 479-482.
McNutt, M. and Bonneville, A., 2000. A shallow, chemical origin for the Marquesas
Swell, Geochem. Geophys. Geosys., 1, paper 1999GC000028. Formatted
Minshull, T. A., 1996. Along-axis variations in oceanic crustal density and their
contribution to gravity anomalies at slow-spreading ridges, Geophys. Res. Lett., 23,
Minshull, T. A. & J. M. Brozena, 1997. Gravity anomalies and flexure of the
lithosphere at Ascension Island, Geophys. J. Int., 131, 347-360.
Parker, R. L., 1974. A new method for modeling marine gravity and magnetic
anomalies, J. Geophys. Res., 79, 2014-2016.
Parsons, B. & Sclater, J. G., 1977. An analysis of the variation of ocean floor
bathymetry and heat flow with age, J. Geophys. Res., 82, 803-827.
Peirce, C. & Barton, P.J., 1991. Crustal Structure of the Madeira-Tore Rise, eastern
North Atlantic—results of DOBS wide-angle and normal incidence seismic experiment
in the Josephine Seamount region, Geophys. J. Int., 106, 357-378.
Recq, M., Goslin, J. & Charvis, P., 1998. Small scale crustal variability within an
intraplate structure: the Crozet Bank (southern Indian Ocean), Geophys. J. Int., 134,
Sichoix, L., Bonneville, A. & McNutt, M. K., 1998. The seafloor swells and
Superswell in French Polynesia, J. Geophys. Res., 103, 27123-27133.
Smith, W. H. F., Staudigel, H., Watts, A. B., & Pringle, M. S., 1989. The Magellan
seamounts: Early Cretaceous record of the south Pacific isotopic and thermal anomaly,
J. Geophys. Res.,94, 10501-10523.
Von Herzen, R. P., Cordery, M. J., Detrick, R. S. & Fang, C., 1989. Heat flow and the
thermal regime of hotspot swells: the Hawaiian swell revisited, J. Geophys. Res., 83,
Watts, A. B., 1994. Crustal structure, gravity anomalies and flexure of the lithosphere
in the vicinity of the Canary Islands, Geophys. J. Int., 119, 648-666.
Watts, A. B., & ten Brink, U. S., 1989. Crustal structure, flexure and subsidence
history of the Hawaiian islands, J. Geophys. Res., 94, 10473-10500.
Watts, A. B., Cochran, J. R., & Selzer, G., 1975. Gravity anomalies and flexure of the
lithosphere: a three-dimensional study of the Great Meteor seamount, northeast
Atlantic, , J. Geophys. Res., 80, 1391-1398.
Watts, A.B., Peirce, C., Collier, J., Dalwood, R., Canales, J.P. & Henstock, T.J., 1997.
A seismic study of lithospheric flexure in the vicinity of Tenerife Canary Islands, Earth
Planet. Sci. Lett., 146, 431-447.
Weigel, W., & Grevemeyer, I., 1999. The Great Meteor seamount: seismic structure of
a submerged intraplate volcano, J. Geodynamics, 28, 27-40..
Wessel, P., 1992. Thermal stresses and the bimodal distribution of elastic thickness
estimates of the oceanic lithosphere, J. Geophys. Res., 97, 14177-14193.
Wessel, P., 1993. A reexamination of the flexural deformation beneath the Hawaiian
islands, J. Geophys. Res., 98, 12177-12190.
Wessel, P., 1998. An empirical method for optimal robust regional-residual separation
of geophysical data, Math. Geol., 30, 391-408.
Wessel, P. & Smith, W. H. F., 1998. New, Improved Version of Generic Mapping
Tools Released, EOS Trans. AGU, 79 (47), 579. Formatted
White, R. S., McKenzie, D. & O’Nions, R. K., 1992. Oceanic crustal thickness from
seismic measurements and rare earth element inversions, J. Geophys. Res., 97, 19683-
Wolfe, C. J., McNutt, M. K., & Detrick, R. S., 1994. The Marquesas archipelagic
apron: seismic stratigraphy and implications for volcano growth, mass wasting, and
crustal underplating, J. Geophys. Res., 99, 13591-13608.
Table 1: Synthetic Gaussian load sizes. "Scale length" is the radius at which the height
decrease to 1/e of its maximum. "Characteristic size" is the cube root of the volume.
All calculations use a square grid of 256 by 256 nodes.
Load Height Scale Length VolumeCharacte Grid Interval
(km) (km) ristic Size (km3) (km)
Small 4 15 282710 2
Medium 5 25 981715 4
Large 6 45 3015921 8
Table 2: Densities at and beneath La Réunion deduced from seismic velocities (Gallart
et al., 1999; Ccharvis et al., 1999) using the preferred relation of Carlson and
Layer Average seismic velocity (km/s) Density (kg/m3)
Water 1.5 1030
Volcanic edifice 4.5 2500
Oceanic sediments 3.9 2300
Oceanic crust 6.5 2900
Underplating 7.5 3000
Upper mantle 8.0 3300
Figure 1. Circles mark estimates of the effective elastic thickness of the oceanic
lithosphere as a function of age, with filled symbols where the estimate is based on
gravity or geoid modelling with independent constraints onsimultaneous optimisation
of load density, or on seismic data, open symbols for other estimates, where in most
cases a load density of 2800 kg/m3 has been assumed, and smaller symbols where the Formatted
value is based on low-resolution satellite altimetry and/or ETOPO5 bathymetry.
Squares mark values from French Polynesia, with the same convention. Triangles
mark estimates of the mechanical thickness of the lithosphere from subduction zones.
Solid isotherms are from the plate model of Parsons & Sclater (1977) and dashed
isotherms are from the model of Stein and Stein (1992). Data are from the compilation
of Wessel (1992) and references therein, with additional values from Bonneville et al.
(1988), WolfeFilmer et al. (19943), Goodwillie & Watts (1993), Harris & Chapman
(1994), Watts et al. (1997), Minshull & Brozena (1997), Kruse et al. (1997) and
McNutt et al. (1997). Where there is more than one published value for the same
feature, only the most recent has been retained, except in a few cases where a value
based on shipboard data is followed later by a value based on low-resolution satellite
data. The large, filled symbols are considered the most reliable (see text).
Figure 2. Density models derived from seismic velocity models for ocean islands and
seamounts (a) Tenerife (Watts et al. 1997). (b) A model for La Réunion based on
seismic velocities (Gallart et al., 1999; Charvis et al., 1999) and the velocity-density
relation of Carlson and Herrick (1990)(this study). (c) Great Meteor seamount (Weigel
& Grevemeyer 1999). Note that the hHorizontal scale varies from one plot to another.
Figure 3. (a) True elastic thickness vs estimated elastic thickness from gravity
anomalies for the “large” Gaussian load of Table 1, if a load density of 2800 kg/m .is
assumed. Curves are annotated with the true density in kg/m3. The behaviour at very
low true values of Te (less than 5 km) is complex and not fully sampled. (b) Results
for three different load sizes if a load density of 2800 kg/m is assumed and the true
load density is 2600 kg/m3. Here the solid curves result from fitting gravity anomalies
and the dashed curves from fitting geoid anomalies.
Figure 4. Contoured root mean square gravity misfit (in mGal) for a series of models
with different assumed load densities compared with the “medium” Gaussian load of
Table 1 with a load density of 2600 kg/m3. The misfit is evaluated for a 308 km by Formatted
308 km box at the centre of the 508 km box for which the gravity calculations are
done. Note the elongation of the misfit contours in the direction of lower elastic
thicknesses and higher densities.
Figure 54. True elastic thickness vs estimated elastic thickness for a Gaussian load of
density 2500 kg/m with a high-density cylindrical core of density 2800 kg/m . The
solid curve represents results from fitting gravity anomalies and the dashed curve
represents results from fitting geoid anomalies.
Figure 6. (a) Bathymetry around the Marquesas Islands (Clouard et al. 2000). Land
areas are shaded in grey. Contour interval is 500 m (b) Free air gravity anomalies,
contoured at 50 mGal intervals. (c) Residual gravity for best-fitting flexural model
(Fig. 7a), contoured at 20 mGal intervals. (d) Free air gravity anomalies of best-fitting
flexural model contoured at 20 mGal intervals.
Figure 7. Contoured root mean square gravity misfit (in mGal) for a series of flexural
models of the Marquesas Islands with different elastic thicknesses (incremented in 1
km intervals) and load densities (incremented in 50 kg/m3 intervals). Circles mark Formatted
best-fitting model in each case, and triangles mark the elastic thickness which would
be inferred if a load density of 2800 kg/m3 were assumed. (a) All material above 4200 Formatted
m depth is included in the load. (b) All material above 4000 m depth is included in the
load. (c) The load is considered to overly a hotspot swell defined by the application of
a 500 km median filter to the bathymetric data. (d) The top loading is as in (a), but in
addition there is a basal load with an amplitude equal to the amplitude of the top load
for wavelengths larger than 350 km, of zero amplitude for wavelengths less than 250
km, and tapering between these wavelengths, and with a density contrast equal to 25%
of the density contrast of the top load. This basal load approximates the underplate
inferred by Wolfe et al. (1994). Formatted
Figure 85. Topography of the top and the base of the volcanic edifice at La Réunion:
(a) bathymetric map of La Réunion volcanic edifice (after Lénat and Labazuy, 1990).
Contours interval isare 2500 m interval. The 4000 m bathymetric contour is used as
the outer limit of the loadvolcanic edifice. Profiles 1 and 2 are respectively located
over along seismic lines R23-R4 and R24-R18, respectively (Gallart et al, 1999;
Charvis et al, 1999); (b) topography of the base of the volcanic edifice from
multichannel seismic profiling (de Voogd et al., 1999).
Figure 96. Computed plate flexure compared to the topography of the top and base of
oceanic crust along profiles 1 and 2 (Fig. 51). Thick solidPlain heavy line marks:
topography of the base of the oceanic crust. Dashed line marks: topography of the top
of the oceanic crust. The assumed uncertainties on these values are shown in gray.
Thin line marks: computed plate flexure for different values of effectivethe lithospheric
elastic thickness (labelled from 12 to 38 km).
Figure 107. MNormalised misfit ( ) of the horizons plotted in Fig. 6 as a function of
versus the lithospheric elastic thickness Te. The Mminimum values of are obtained
for Te valueselastic thicknesses ranging from 20 to 30 km, though larger values also
produce acceptable fits..