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Ocean Island Densities and Models of Lithospheric

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					Ocean Island Densities and Models of Lithospheric

FlexureEstimates of the Effective Elastic Thickness of the

Oceanic Lithosphere



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,

rheology



Short title: Ocean island densities



SFor submittedssion to Geophysical Journal International, December 1999.

Revised version, September 2000. Final version, January 2001.



ABSTRACT



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



                                            1
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

elastic thicknesses.



INTRODUCTION



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


                                            2
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.




                                             3
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


                                             4
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).




                                             5
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


                                             6
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

                                                           3
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).




                                             7
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

                                                                                3
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



                                            8
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

                                                          3
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

                                                                                  3
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

                                            9
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


                                             10
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
                                                                                             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


                                             11
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
                                                                                             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

of underplating.




                                             12
                                                                                              Formatted


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

                 3
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

                                                                                          3
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




                                             13
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.

96).




                                            14
                                                                                         
 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.

                                                                                             3
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




                                             15
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

                                                                                            3
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

                 3
   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).




                                             16
DISCUSSION



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

              3
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
                                                                                              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

(Fig. 1).



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-


                                            17
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.



CONCLUSION



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.



                                   3
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




                                           18
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

                             3
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

estimates.




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

available.



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.


                                            19
ACKNOWLEDGEMENTS



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###.




                                          20
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                                          27
TABLES



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




                                           28
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

HerrickRaskin (199084)


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




                                            29
FIGURE CAPTIONS



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).




                                            30
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

                                                                                     3
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

                                                             3
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

                   3                                                            3
density 2500 kg/m with a high-density cylindrical core of density 2800 kg/m . The




                                            31
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
                                                                                            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).


                                           32
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..




                                           33

				
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