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Ocean island densities and models of lithospheric flexure

T. A. Minshull1 and Ph. Charvis21 School of Ocean and Earth Science, University of Southampton, Southampton Oceanography Centre, European Way, Southampton SO14 3ZH, UK.

E-mail: tmin@soc.soton.ac.uk2 Unite Mixte de Recherche Geosciences Azur, Institut de Recherche pour le Developpement (IRD), BP48, 06235, Villefranche-sur-mer, France

Accepted 2001 January 15. Received 2000 September 21; in original form 1999 December 15

SUMMARY

Estimates of the effective elastic thickness (Te) of the oceanic lithosphere based ongravity and bathymetric data from island loads are commonly significantly lower thanthose based on the wavelength of plate bending at subduction zones. The anomalouslylow values for ocean islands have been attributed to the finite yield strength of the litho-sphere, to erosion of the mechanical boundary layer by mantle plumes, to pre-existingthermal stresses and to overprinting of old volcanic loads by younger ones. A fifthpossible contribution to the discrepancy is an incorrect assumption about the densityof volcanic loads. We suggest that load densities have been systematically overestimatedin studies of lithospheric flexure, potentially resulting in systematic underestimation ofeffective elastic thickness and overestimation of the effects of hotspot volcanism. Weillustrate the effect of underestimating load density with synthetic examples and anexample from the Marquesas Islands. This effect, combined with the other effects listedabove, in many cases may obviate the need to invoke hotspot reheating to explain lowapparent elastic thickness.

Key words: density, gravity anomalies, lithospheric flexure, ocean islands, rheology,volcanic structure.

I N T R O D U C T I O N

Our main constraint on the rheology of the oceanic lithosphere

comes from its deformation in response to applied stresses.

While 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 to the oceanic

lithosphere are applied at plate boundaries and beneath intra-

plate 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

recognized 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 the finite yield strength of the oceanic litho-

sphere can be exceeded due to plate curvature beneath volcanoes

(Bodine et al. 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 reheatingthe reduction of litho-

spheric 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 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 explanation for 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.

T H E D E N S I T Y O F O C E A N I CI N T R A P L A T E V O L C A N O E S

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

Geophys. J. Int. (2001) 145, 731739

# 2001 RAS 731

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 addi-

tional 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 else-

where (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 mx3 (e.g. Watts et al. 1975; Calmant et al. 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 cmx3 .

Independent constraints on load density and flexural para-

meters are available in the gravity and bathymetric data them-

selves. 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

Figure 1. Circles mark estimates of the effective elastic thickness of the oceanic lithosphere as a function of age, with filled symbols where the estimateis based on gravity or geoid modelling with simultaneous optimization of load density, or on seismic data, open symbols for other estimates, where in

most cases a load density of 2800 kg mx3 has been assumed, and smaller symbols where the 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 & Stein (1992). Data are from the compilation of Wessel (1992) and references therein, with additional values from Bonneville et al. (1988),

Wolfe et al. (1994), 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).

732 T. A. Minshull and Ph. Charvis

# 2001 RAS, GJI 145, 731739

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 contri-

bution to a least-squares fit is the peak amplitude of the anomaly,

and this value is highly sensitive to the load density. The trade-

off may be avoided by using an alternative optimization, for

example by 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). Except perhaps for rocks with large fracture

porosity, densities can be predicted from seismic velocity

measurements with an uncertainty of only a few per cent (e.g.

Minshull 1996). Using Carlson & Herricks preferred relation,

a density of 2800 kg mx3 corresponds to a mean seismic

velocity of 6.0 km sx1; these authors suggest a mean density

of 2860t30 kg mx3 for normal oceanic crust. However, anumber 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 sub-

aerial 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 general 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.

Figure 2. Density models derived from seismic velocity models for ocean islands and seamounts (a) Tenerife (Watts et al. 1997). (b) A modelfor La Reunion based on seismic velocities (Gallart et al. 1999; Charvis et al. 1999) and the velocitydensity relation of Carlson & Herrick (1990).

(c) Great Meteor seamount (Weigel & Grevemeyer 1999). Note that the horizontal scale varies from one plot to another.

Ocean island densities 733

# 2001 RAS, GJI 145, 731739

E F F E C T O N F L E X U R E A N D E L A S T I CT H I C K N E S S E S T I M A T E S

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. First, 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 corres-

ponding negative gravity anomaly is overestimated. Second,

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, 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 sea-

mount chains, a large load comparable to large ocean islands

such as Tenerife and La Reunion 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 more

of their mass 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 were well represented.

Geoid anomalies were computed by Fourier methods from

the corresponding gravity anomalies. Load and infill densities

of 25002700 kg mx3 were considered, with the densities of

the water, crust and mantle set to 1030, 2800 and 3330 kg mx3,

respectively, and a normal oceanic crustal thickness of 7 km

(White et al. 1992). The crustal density used is the most

commonly used value, although it is slightly lower than Carlson

& Herricks (1990) preferred value. For a series of pre-defined

Te values, Te was estimated using an assumed load and infill

density of 2800 kg mx3.

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 isostasy, 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 mx3 this ratio is 1.55, while

for a density of 2500 kg mx3 the ratio is 1.89. Estimates of

Te are slightly improved if the geoid rather than the gravity

anomaly is used, because the geoid anomaly is more sensitive to

the shape of the flexed surfaces beneath the load. However, 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 be

recovered by simultaneous optimization of both Te and load

density (Fig. 4). The misfit minimum is fairly flat and a small

Table 1. Synthetic Gaussian load sizes. Scale length is the radius at which the height decreases to 1/e ofits maximum. All calculations use a square grid of 256 by 256 nodes

Load Height (km) Scale length (km) Volume (km3) Grid interval (km)

Small 4 15 2827 2

Medium 5 25 9817 4

Large 6 45 30159 8

Figure 3. (a) True elastic thickness versus estimated elastic thickness from gravity anomalies for the large Gaussian load of Table 1, if a load densityof 2800 kg mx3 is assumed. Curves are annotated with the true density in kg m x3. 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 mx3 is assumed and the true load density is

2600 kg mx3. Here the solid curves result from fitting gravity anomalies and the dashed curves from fitting geoid anomalies.

734 T. A. Minshull and Ph. Charvis

# 2001 RAS, GJI 145, 731739

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.

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 com-

puted for a large load with a density of 2500 kg mx3 except

in a central core with a radius 80 per cent of the Gaussian

decay length and reaching 50 per cent of the height of the load

above the surrounding ocean floor, which was assigned a

density of 2800 kg mx3. This structure is loosely based on that of

Reunion 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. 5)

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.

R E A L E X A M P L E : T H E M A R Q U E S A SI S L A N D S

We further illustrate the problem of assuming a standard oceanic

crustal density with a real example from the Marquesas Islands,

for which the elastic thickness is constrained independently

by seismic determinations of the shape of the flexed oceanic

basement and the shape of the flexed Moho beneath the load.

Two further effects must be considered here. The first is that of

inferred magmatic underplating (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.

A comprehensive gravity and bathymetric data set for the

Marquesas Islands (Fig. 6) was published by Clouard et al.

(2000). 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 1u inall directions beyond the edges of the region shown in Fig. 6, to

avoid edge effects. Models assumed an oceanic crustal thick-

ness of 6 km, consistent with sonobuoy refraction data (Wolfe

et al. 1994; Caress et al. 1995), an oceanic crustal density of

2800 kg mx3, and a range of elastic thickness and load and

infill densities. The root-mean-square misfit was evaluated for

the region shown. Our purpose here is not to place new con-

straints 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,

although 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 mx3,

slightly smaller than the 2650 kg mx3 used by Wolfe et al.

(1994). The fit between observed 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

Figure 4. Contoured root-mean-square gravity misfit (in mGal) fora series of models with different assumed load densities compared

with the medium Gaussian load of Table 1 with a load density of

2600 kg mx3. The misfit is evaluated for a 308 km by 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 thickness and higher densities.

Figure 5. True elastic thickness versus estimated elastic thickness for aGaussian load of density 2500 kg mx3 with a high-density cylindrical

core of density 2800 kg mx3. The solid curve represents results from

fitting gravity anomalies and the dashed curve represents results

from fitting geoid anomalies.

Ocean island densities 735

# 2001 RAS, GJI 145, 731739

separating a regional bathymetric signal such as a hotspot swell

from a residual due volcanic loading by using a median filter

which maximizes the residual volume above a particular con-

tour 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 filter length corresponding to the

maximum 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 con-

sidered here (Sichoix et al. 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 per cent 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 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). These analyses show that

the optimum load density required to fit the gravity data is

always significantly less than 2800 kg mx3 and that if a load

density of 2800 kg mx3 were assumed for the Marquesas, the

elastic thickness would be underestimated by ca. 2540 per cent.

Calmant et al. (1990) made just such an assumption and found

a Te value of 14t2 km, significantly less than the seismicallyconstrained 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.

D I S C U S S I O N

The above results show that great care should be taken

in interpreting estimates of Te, and hence of the amplitude of

lithospheric flexure and the volume of volcanic edifices, from

gravity- or geoid-based seamounts loading studies of oceanic

lithosphere unless there are independent seismic constraints,

or at least the load density has been optimized to match the

gravity data. Values are likely to be underestimated by large

amounts, particularly for small loads, if a density of 2800 kg mx3

has been assumed. Most recent studies have indeed taken a

more rigorous approach, with the use of seismic constraints

(e.g. Watts et al. 1997), or simultaneous optimization of load

density and elastic thickness (e.g. Smith et al. 1989). In some of

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-airgravity 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 50 mGal intervals.

736 T. A. Minshull and Ph. Charvis

# 2001 RAS, GJI 145, 731739

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

approach simplifies gravity calculations, but its effect on the

estimation of Te is not yet quantified. Even ignoring such

problems, the published global data set 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 resolve statistically a bias towards

lower values by comparison with the better-constrained values

(filled symbols). 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 2-D analysis (Lyons et al. 2000). However,

it is clear from the above analysis that such a bias is likely to

be present frequently. Most published values for ocean islands

could be considerably improved by a reanalysis using ship-

board 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 constrains it from seismic data. Without such reanalysis,

and given the variety of other possible explanations 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.

C O N C L U S I O N S

From our study we draw the following conclusions.

(1) Ocean islands and seamounts commonly have a mean

density which is significantly lower than that of the oceanic

crust beneath.

(2) If a load density of 2800 kg mx3 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. The infill

volume can be overestimated by a factor of at least 50 per cent,

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

Figure 7. Contoured root-mean-square gravity misfit (in mGal) for a series of flexural models of the Marquesas Islands with different elasticthickness (incremented in 1 km intervals) and load densities (incremented in 50 kg mx3 intervals). Circles mark best-fitting model in each case, and

triangles mark the elastic thickness which would be inferred if a load density of 2800 kg mx3 were assumed. (a) All material above 4200 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 per cent of the density contrast of the top load. This basal load approximates the underplate

inferred by Wolfe et al. (1994).

Ocean island densities 737

# 2001 RAS, GJI 145, 731739

of 2800 kg mx3 is much larger than biases which would be

introduced by 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.

(4) Few flexural 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 plumelithosphere interaction.

A C K N O W L E D G M E N T S

TAM is supported by a Royal Society University Research

Fellowship. We thank A. Watts and I. Grevemeyer for supply-

ing 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

initiated during visits by both authors to the Instituto de

Ciencias de la Tierra (Jaume Almera), Barcelona, Spain. UMR

Geosciences Azur contribution 356.

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