Deuxi�eme partie

Structure des �les de Polyn�esie

Fran�caise

Chapitre 4

Les chambres magmatiques fossiles

des �les

Qui serait assez insens�e pour croire qu'il puisse exister des hommesdont les pieds seraient au-dessus de la tete, ou des lieux o�ules choses puissent etre suspendues de bas en haut, les arbrespousser �a l'envers, ou la pluie tomber en remontant ? O�u seraientles merveilles du jardin de Babylone s'il nous fallait admettrel'existence d'un monde suspendu aux Antipodes ?

Lactance

Sommaire

4.1 R�esum�e �etendu de \ Size and depth . . . gravity studies" . . . . . 76

4.2 Size and depth of frozen magma chambers under atolls and

islands of French Polynesia using detailed gravity studies,

Clouard, Bonneville and Barsczus, 2000, J. Geophys. Res.,

v 105, pp 8173-8191 . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.3 Compl�ements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.3.1 Controle des donn�ees gravim�etriques terrestres utilis�ees . . . . 97

4.3.2 D�etermination des masses volumiques . . . . . . . . . . . . . . 98

4.3.3 La loi de Gauss appliqu�ee aux champs de gravit�e . . . . . . . . 99

4.3.4 Choix de la loi liant chambre et �le . . . . . . . . . . . . . . . . 101

Nous avons r�ealis�e une �etude gravim�etrique des �les et atolls de Polyn�esie fran�caisequi a donn�e lieu �a une publication dans le Journal of Geophysical Research (vol 105, pp8173-8191). Apr�es un r�esum�e �etendu en fran�cais, ce chapitre reproduit la publication, et�nit par un compl�ement concernant certains calculs.

76 Les chambres magmatiques fossiles des �les

4.1 R�esum�e et principaux r�esultats de \ Size and depth

of frozen magma chambers under atolls and islands of

French Polynesia using detailed gravity studies"

R�esum�e

De nouvelles connaissances de l'�evolution tectonique et structurale des �les et atollsde Polyn�esie fran�caise sont obtenues �a partir de l'analyse de donn�ees gravim�etriques. Descartes de l'anomalie �a l'air libre ont �et�e r�ealis�ees avec les donn�ees acquises �a terre sur25 �les, combin�ees aux donn�ees d�eriv�ees de l'altim�etrie satellitale et aux donn�ees acquisespar bateau. Les anomalies r�esiduelles isostatiques sont alors calcul�ees suivant un mod�elecrustal en 3D et 4 couches. Ce mod�ele prend en compte la bathym�etrie, la topographiedes �les et la exure de la lithosph�ere sous la charge des �edi�ces volcaniques. 20 des 25�les �etudi�ees pr�esentent une anomalie r�esiduelle positive, allant de 9 �a 60 mGal, qui peutetre reli�ee �a la pr�esence de chambres magmatiques fossiles (et des circuits d'alimentationles plus importants) de l'ancien volcan. Des anomalies r�esiduelles n�egatives sur 4 �lescorrespondent probablement soit �a des d�epots coralliens soit �a des r�esidus fragment�es desderni�eres phases du volcanisme a�erien.

Les anomalies positives mettent en �evidence l'existence d'une chambre magmatiquefossile en profondeur sous chacune des �les de Polyn�esie fran�caise. De plus, une relationlin�eaire entre l'amplitude de l'anomalie positive et le volume de l'�le existe. Elle impliqueune relation entre la taille de la chambre magmatique qui induit l'anomalie et celle del'�le. La mod�elisation de la forme de ces chambres par un mod�ele g�eom�etrique simple (uncorps dense ellipso��dal en 3D) conduit �a une estimation de la taille et de la profondeur deschambres magmatiques. Une relation lin�eaire entre le volume des chambres et le volumedes �les est ainsi obtenue et peut etre utilis�ee pour d'autres volcans intraplaques �eteints(e.g. La R�eunion). Par ailleurs, la comparaison entre les diam�etres obtenus pour chaquechambre et leur projection �a la surface avec l'emplacement et le diam�etre des caldeirasimplique que la plupart des e�ondrements consid�er�es jusqu'alors comme des caldeiras ausens strict sont en fait des glissements des ancs des �edi�ces.

Principaux r�esultats

Les �les �etudi�ees sont Manuae, Maupiti, Tupai, Bora-Bora, Tahaa, Huahine, Maiao,Tetiaroa, Moorea et Tahiti sur la Societ�e, Nuku Hiva, Hiva Oa et Ua Pou aux Marquises,Maria, Rimatara, Rurutu, Tubuai, Raivavae et Rapa aux Australes, Moruroa et Gambierde l'alignement Gambier-Pitcairn et Mataiva, Manihi, Makatea, Rangiroa aux Tuamotu.

1. Il existe sur chaque �le une anomalie de gravit�e r�esiduelle positive, circulaire etcentr�ee sur l'�le. C'est en bon accord avec ce que l'on sait pour les volcans de typepoint chaud (e.g. Rymer et Brown, 1986) : le syst�eme d'alimentation magmatique

4.1 R�esum�e �etendu de \ Size and depth . . . gravity studies" 77

fossile, dont le principal �el�ement est la chambre, correspond �a une anomalie dedensit�e positive qui se traduit par une anomalie gravim�etrique positive, une fois lescorrections de Bouguer faites.

�! il existe une chambre magmatique unique sous chaque �le �etudi�ee.

2. les atolls �etudi�es pr�esentent les memes caract�eristiques gravim�etriques que les �leshautes, att�enu�ees en fonction de leur age, donc de leur subsidence.

�! les atolls de Polyn�esie Fran�caise, y compris ceux des Tuamotu, poss�e-

dent les caract�eristiques gravim�etriques des volcans boucliers.

3. L'emplacement du centre de l'anomalie permet de d�eterminer si ce qui est appel�ecaldeira en est vraiment une ou correspond plutot �a un e�ondrement du ancdu volcan. Une caldeira correspond �a l'e�ondrement du centre du volcan apr�esla vidange rapide de la chambre magmatique pour en combler le vide. Les paroisdoivent donc etre quasi verticales, et se situer �a l'aplomb des bords de la chambre.A l'inverse, les e�ondrements de ancs s'ouvrent vers la mer, leur diam�etre et leurcentre sont ind�ependants de l'emplacement de l'ancienne chambre.

�! la plupart des caldeiras des �les �etudi�ees sont des e�ondrements de

ancs.

4. Des mod�eles directs de chambres rendent bien compte de l'anomalie gravim�etrique.Que l'on utilise une sph�ere ou un ellipso��de de r�evolution, on obtient des r�esultatssimilaires qui permettent d'estimer le volume, le rayon et la profondeur de chaqueancienne chambre.

�! les syst�emes d'alimentation fossiles se mod�elisent bien par un ellipso��-

de de r�evolution.

5. Les volumes des chambres magmatiques obtenus sont proportionnels au volume del'�le consid�er�ee.

�! la taille de l'�le permet de conna�tre le volume de la chambre magmati-

que fossile.

6. Le choix des masses volumiques utilis�ees permet de v�eri�er l'existence d'un gradientde densit�e entre la surface et le plancher oc�eanique. La masse volumique moyennedes �edi�ces, dans leur partie sous-marine situ�ee au dessus du plancher, est de 2700kg:m�3, alors que le mat�eriau de remplissage de la d�epression cr�e�ee par la chargedu volcan sur la croute est plutot autour de 2800-2900 kg:m�3.

�! la masse volumique moyenne des �edi�ces est de 2700 kg:m�3 .

7. Le raccordement des donn�ees terrestres avec les donn�ees en mer n'a pas abouti �a lamise en �evidence de vastes glissements sous-marins, comme celui cartographi�e surle anc sud de Tahiti (voir Chapitre 5). Cela va �a l'encontre de ce qui est parfoisavanc�e (e.g. Rymer et Brown, 1986).

�! les glissements de terrain en mer ne sont pas mis en �evidence par

l'analyse gravim�etrique.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. B4, PAGES 8173{8191, APRIL 10, 2000

Size and depth of ancient magma reservoirs under atolls

and islands of French Polynesia using gravity data

Val�erie Clouard and Alain BonnevilleLaboratoire de G�eosciences Marines et T�el�ed�etection, Universit�e de la Polyn�esie fran�caise,

Papeete, Tahiti, French Polynesia

Hans G. Barsczus,1

GBE - UMR 5569 - CNRS and Universit�e de Montpellier II, Montpellier, France

Abstract. New insights into the structural and tectonic evolution of islandsand atolls in French Polynesia are derived from the analysis of gravity data.Free-air anomaly maps were constructed using gravity data from land surveysof 25 islands combined with free-air anomaly data derived from satellitealtimetry and shipborne gravimeters. Residual isostatic anomalies werecalculated using a three-dimensional (3-D), four-layer crustal model takinginto account the bathymetry of the sea oor, the topography of the islands,and the de ection of the lithosphere under the load of the volcanoes. Twentyof the 25 islands yield a positive residual anomaly, ranging between 9 and60 mGal. Negative residual anomalies over four islands probably correspondeither to limestone deposits or to fragmented material from aerial volcanism.The occurrence of a positive anomaly provides some evidence that thereis a solidi�ed magma chamber at depth beneath each of several islands inFrench Polynesia. A linear relation between the amplitude of the positivegravity anomaly and island volume is also observed. Geological features whichgenerate these positive anomalies are described by simple geometric models(3-D ellipsoidal dense bodies) which lead to a rough estimate of the size anddepth of the magma chambers. We then propose a simple linear relationbetween the volume of such magma chambers and the volume of islands thatcan be used for other extinct intraplate basaltic volcanoes. The diameter ofthe inferred magma chamber and its projection on the surface of the islandsimply that calderas correspond mostly to collapses of the anks of the edi�cesrather than to caldera vertical subsidence.

1. Introduction

French Polynesia (Figure 1) is located to the southof the central part of the Paci�c Plate, between latit-udes 5�S and 30�S and longitudes 130�W and 160�W.The Austral, Society, Pitcairn-Gambier, and Tuamotuisland chains trend N120�, the same direction of thepresent Paci�c Plate motion. The Marquesas Islandshave a N140� strike. The region is crossed by the Aus-tral and Marquesas Fracture Zones (FZ) with a N70�

strike. These FZs are the main tectonic features of thesea oor and are related to the Farallon Ridge, whichbecame extinct 9 Myr ago [Mammerickx et al., 1980].The average velocity of Paci�c Plate motion is 11 cm

1Also at Centre IRD, Montpellier, France

Copyright 2000 by the American Geophysical Union.

Paper number 1999JB9003930148-0227/00/1999JB900393$09.00

yr�1 [Herron, 1972; Minster and Jordan, 1978]. TheAustral, Society, Pitcairn-Gambier, and Marquesas is-land chains are composed mainly of islands, while theTuamotu archipelago is composed entirely of atolls. Alltogether, French Polynesia consists of 34 islands and 84atolls.

The islands rise �4500mabove the sea oor, and theirmaximum elevation above sea level, at Tahiti, is 2200m. To a �rst approximation, island ages and morpho-logies are consistent with a hotspot theory: the age ofeach island within a chain increases from the southeastto the northwest, based on radiometric dating of volcan-ism from the present to about 16 Ma (Table 1). The ageof the oceanic crust ranges between 45 and 85 Ma [Her-ron, 1972; Mayes et al., 1990; Munschy et al., 1996].The Tuamotu Islands are separated from the other is-land chains by basins exceeding 5000 m in depth. Theorigin of the Tuamotu Islands, which rise above a broadplateau, is uncertain but has been attributed to an abor-ted ridge [Pautot, 1975], a hotspot [Okal and Cazenave,

78

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 79

150˚W 140˚W30˚S

20˚S

10˚S

MooreaTahaa

Bora Bora

HuahineMaiao Tahiti

RimataraRurutu

Tubuai

Raivavae

Rapa

Ua Pou Nuku Hiva

Hiva Oa

Manihi

RangiroaMakatea

Mataiva

Moruroa Maria

Manuae

Gambier

Tetiaroa

TupaiMaupiti

Society

Tuamotu

Marquesas

Austral

Pitcairn-Gambier

Austral FZ

Marquesas FZ

500 km

-6000 -5000 -4000 -3000 -2000 -1000 0

meters

Figure 1. Bathymetric map [Sichoix and Bonneville, 1996] showing the volcanic chains of FrenchPolynesia, with archipelago names underlined. The names of the islands discussed in text areshown. FZ stands for fracture zone.

1985], or an emerged submarine chain which originatedclose to the East Paci�c Rise [Ito et al., 1995].

The age, petrology, and geochemistry of the FrenchPolynesian islands are relatively well known (see sum-maries by Brousse et al. [1990], Diraison [1991], andLeroy [1994]), but their subsurface structure, apart fromMoruroa and Fangataufa atolls [Guille et al., 1992,1993], remains poorly known. In this paper, we addressthe lateral density distribution using existing gravitydata, which leads to a three-dimensional model of the is-lands. Shipboard and satellite-derived gravity data aremerged with previously unpublished land data. Afteradjusting these di�erent data sets to a common ref-erence system, a free-air anomaly (FAA) map is ob-tained. We then subtract a theoretical gravity �eldcomputed using a three-dimensional, four-layer crustalmodel based on a digital terrain model (for bathy-metry and elevation). Residual isostatic anomaly maps[Blakely, 1995] are then produced for 17 islands and 8atolls to obtain insights into the makeup of shield vol-canoes.

2. Data Presentation and Processing

2.1. Gravity Data

From 1978 to 1981, 800 measurements were made byBarsczus [1979, 1980, 1981] using a Worden 600 gravi-meter at Manuae, Maupiti, Tupai, Bora-Bora, Tahaa,Huahine, Maiao, Tetiaroa, Moorea, and Tahiti in theSociety Islands; Nuku Hiva, Hiva Oa, and Ua Pou inthe Marquesas Islands; Maria, Rimatara, Rurutu, Tu-buai, Raivavae, and Rapa in the Austral Islands; Mor-uroa and Gambier Islands in Gambier-Pitcairn align-ment; and Mataiva, Manihi, Makatea, and Rangiroa inthe Tuamotu Islands. These data were merged with 137measurements made by Macheski [1965] at Tahiti andMoorea using a Worden 300 gravimeter and with 320measurements made by Leroy [1994] at Tahiti using aLacoste and Romberg model G gravimeter. All data aretied to PPT J7912, a reference station of the Interna-tional Gravity Standardization Net established in 1971(IGSN71) and located at Pamatai in Tahiti. The PPTJ7912 station (where PPT stands for Papeete and J7912

80 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

Table 1. Radiometric Ages of Aerial Volcanism in French Polynesian Studied Islands

Island Longitude W Latitude S Age, Ma Reference

Austral

Raivavae 147�390 23�520 5.6-7.6 Duncan and McDougall [1976]Rapa 144�200 27�360 5.9-5.2 Krummenacher and Noetzlin [1966]Rimatara 152�480 22�390 (4.8-28.6) Turner and Jarrard [1982]Rurutu 151�210 22�290 0.6-12.3 Dalrymple et al. [1975], Duncan and

McDougall [1976], and Turner and

Jarrard [1982]Tubuai 149�300 23�230 8.5-10.6 Duncan and McDougall [1976]

Marquesas

Hiva Oa 139�030 09�450 1.6-2.5 Duncan and McDougall [1974]Nuku Hiva 140�120 08�540 3.0-4.3 Duncan and McDougall [1974]

Society

Bora Bora 151�440 16�300 3.1-3.4 Duncan and McDougall [1976]Huahine 151�000 16�450 2.0-2.6 Duncan and McDougall [1976]Maupiti 152�160 16�270 4.0-4.5 Duncan and McDougall [1976]Moorea 149�500 17�330 1.5-1.7 Duncan and McDougall [1976]Tahaa 151�300 16�390 2.6-3.2 Duncan and McDougall [1976]Tahiti-iti 149�300 17�360 0.4-0.5 Leroy [1994]Tahiti-nui 149�150 17�480 0.19-1.37 Leroy [1994]

Pitcairn-Gambier

Gambier (Manureva) 134�570 23�090 6.2 Guillou et al. [1994]Moruroa 138�540 21�510 11.0 Gillot et al. [1992]

means that it was the twelth station made in 1979)was established by a Japanese team during a circum-Paci�c gravimetric connections campaign [Nakagawa et

al., 1983]. From this total "land data set", a FAA wasthen calculated using the GRS80 ellipsoid model. Theexperimental error e related to this land data set can beexpressed as the sum of the measurement error em es-timated to be 0.35 mGal (standard deviation [Barsczus,1980]) and a function of the barometric leveling error dzestimated to be 10 m, as follows:

e = em + 0:3086 dz �= 3:5mGal: (1)

Marine gravity data for the area compiled by Sichoixand Bonneville [1996] include 27 tracks (116,171 points)from the National Geophysical Data Center (NGDC)database which was obtained with good satellite navig-ation accuracy. After the removal of uncontrolled peaks,this set was tied to a Seasat and ERS-1 satellite-derivedFAA grid [Smith and Sandwell, 1995]. We have ad-ded data from recent cruises in French Polynesia to theSichoix and Bonneville [1996] data set: EW9602 on theR/V Maurice Ewing to the southeast of the AustralIslands [McNutt et al., 1997] and two cruises on theR/V L'Atalante, ZEPOLYF1, south of the Society Is-lands [Bonneville et al., 1997] and ZEPOLYF2, north

of the Austral Islands (A. Bonneville, personal commu-nication, 1999). The entire o�shore data set is referredto here as the "marine data set." The error on FAAsatellite-derived data was estimated to be 5 mGal bySandwell [1992]. The shipboard data error is 1 to 2mGal. Consequently, a maximum error of 5 mGal forthe whole marine data set is assumed.

2.2. Free-air Anomaly Maps

When preparing composite FAA maps, the �rst ad-justment of land and marine gravity data is controlledvisually. Close to lands, the values in the marine dataset, composed mainly of satellite data, appear systemat-ically lower by a few tens of milliGals than the grounddata set. This discrepancy may be related to (1) thehanging of radar beams on island anks [Barriot, 1987];(2) a bias introduced from the method to produce grav-ity �elds from the geoid signal due to crossover of un-evenly spaced ground tracks, especially in the vicinity ofislands where data have been removed [Filmer, 1991];and (3) the size of the island itself when its diameterranges from 5 to 15 km, which is close to the resolutionof the satellite (20-30 km, [Sandwell, 1992]).

To adjust these two data sets, we used only shipboarddata in the vicinity of islands (up to 6 km o�shore, ex-

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 81

-50 -25 0 25 50 75 100 125 150 175 200

150ºW 149ºW

18ºS

17ºS

150ºW 149ºW

18ºS

17ºS

150ºW 149ºW

18ºS

17ºS

150ºW 149ºW

18ºS

17ºS

mGal

Figure 2. Example of the derivation of the FAA map for the Tetiaroa, Moorea, and Tahitiislands. (left) Gravity satellite data only [Smith and Sandwell, 1995]. The thin black linesrepresent the shipboard pro�les along which the measured gravity values were used to producean improved �eld within the polygons shown as white lines. (right) Final FAA map producedby merging the satellite data outside the polygons with the shipborne data within the polygons.Note the improvement in anomaly resolution over and near the islands. Contour interval is 25mGal.

cept for Tahiti where this limit is extended to 60 km)because these data have the same reference bases asthe ground data and thus their datum are comparable(Figure 2). Using a continuous curvature "splines-in-tension" algorithm (GMT [Smith and Wessel, 1990]),the land data set and shipboard data in the vicinity ofislands were merged with the complete marine data setminus the data around the islands to obtain two typesof grids. The �rst grid corresponds to the completeFAA map of French Polynesia, which is a coarse grid20x20, such as is shown in the small region around theisland of Tahiti in Figure 2. The second type corres-ponds to a set of �ner grids covering each island, whichwere used in calculating the properties and geometry ofmagma chambers. These are 3000x3000grids, constrainedby good spatial coverage on land (1352 measurementsfor 2350km2, averaging about two stations within a6000x6000 area). (All the grids are available at URLhttp://www.ipgp.jussieu.fr/UFP/download.html.)

2.3. Topographic Maps

We used the synthesized database of bathymetrycompiled by Sichoix and Bonneville [1996] that wasbased on �82 cruises plus additional soundings from theFrench Service Hydrographique et Oc�eanographique dela Marine, all acquired with satellite navigation since

1967. Data were carefully checked for quality andsubjected to a crossover analysis, similar to the oneused by Smith [1993], but using Golbal Positioning Sys-tem (GPS) navigated expeditions for reference. Themost recent bathymetric pro�les used, including multi-beam soundings from EW9602 and ZEPOLYF1 cruises,are denser, often with a spacing of <500 m along theshiptrack. The older pro�les have a typical spacing of>2 km.

Elevation data on islands were obtained by digitiz-ing topographic maps of French Polynesia [ Service de

l'Urbanisme, 1992] and from maps of the Atlas de laPolyn�esie Fran�caise [ORSTOM, 1993]. For the islandof Tahiti we used a digital terrain model derived byG�eoimage (Sophia Antipolis, France) from two stereo-scopic SPOT images. The elevation on atolls was arbit-rarily set at 0 m over the lagoon (for depths between 1and 40 m) and at 1 m above sea level on the coral rim(for heights between 1 and 5 m). Topographic land dataand bathymetric data were then combined and griddedto produce a 20x20 grid for the whole area, and several3000x3000 grids covering each island.

2.4. Flexural Model

Previous studies of the gravity and topography ofthe Hawaiian archipelago [e.g.,Walcott, 1970] show that

82 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

y

z

x

flexure

6000m

bathymetry

aerial topography

mantle

crust

sea water

ρa

ρS

f

c

ρ

ρρ

ρ

ρ

c

m

w

Figure 3. The theoretical FAA is obtained by computing the gravity e�ect of volcanic construc-tion above a de ected crust. (top) The model involves six layers, with di�erent densities �. Theassumed densities for crust (�c), mantle (�m), and water (�w) are 2900, 3350 and 1030 kg m�3,respectively. The de ection is estimated using a 3-D model for a thin elastic plate loaded bythe topography (see text). The volcanic load is modeled by three layers: the subaerial volcanicconstruction (�a), the submarine volcanic construction (�s), the material �lling the exure (�f )with �a < �s < �f . (bottom) The geometry of the system is modeled by elementary prisms.

volcanic loads on the oceanic lithosphere are supportedregionally rather than locally. In response to appliedloads the lithosphere acts as a thin elastic plate overly-ing an inviscid uid [Watts et al., 1980]. The amplitudeof the de exion depends on both the size of the volcanicload and the e�ective exural rigidity of the thin elasticplate [Watts et al., 1975]. The exural rigidity is linkedto the elastic thickness of the lithosphere that corres-ponds to the upper part of the lithosphere and dependsmainly on the temperature, and hence on the age of thelithosphere at the time of loading [Watts, 1978].

Watts and Ribe [1984] obtained several values of the exural rigidity in various tectonic contexts. McNutt

[1984] introduced the concept of the "e�ective thermalage," which corresponds to the thermal age at the timeof loading. It can be less than the lithospheric age if theplate has been reheated, which is common for regions

of intraplate volcanism. Calmant and Cazenave [1986]and Young and Hill [1986] invoke this concept to explainrigidity anomalies obtained below the Cook, Austral,and Society Islands and below the Cape Verde rise.

The numerical and three-dimensional approach de-veloped by Watts et al., [1975] is used here to solve theclassical equation governing the deformationw (positivedownward) of an elastic layer under a volcanic load:

Dr4w + (�m � �l)gw = q(x; y) (2)

where �l is the load density, �m is the mantle density,D the exural rigidity of the lithosphere, r is the bi-harmonic operator, q(x; y) is the vertical load derivedfrom the topographic grid obtained previously, and g isthe acceleration due to gravity (g = 9:81ms�2).

In our study the value ofD has been carefully chosenfor each island group using two methods. In the �rst

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 83

method, seismic refraction pro�les provide the Mohodepth (Society and west Tuamotu Islands [Danobeatiaet al., 1995; Talandier and Okal, 1987] and Marque-sas Islands [Caress et al., 1995]). After this depth iscompared with the Moho depth based on the exuralmodel we select the D value that minimizes the di�er-ence between observations and model. In the secondmethod, employed when seismic re ection data are un-available, we used published D values. Typical valuesof D vary from 1:5�1021 N m to 8:0�1022 N m for thesouth central Paci�c area [e.g. Calmant and Cazenave,

1987; Filmer et al., 1993; Goodwillie and Watts, 1993].These are much lower than the values expected for therange of crustal ages concerned [Watts et al., 1980].Complete discussions of the choice of exural rigidityvalues for our region are given by McNutt [1998] andSichoix [1997]. The following values for the exural ri-gidity were selected: 4:0 � 1022 N m for Society andMarquesas Islands, 3:5�1021 N m for Pitcairn-GambierIslands, 1:2 � 1022 N m for western Austral Islands,3:5 � 1021 N m for the eastern Austral Islands, and8:0 � 1021 N m for Tuamotu Islands. We assume thatthe representative densities of the mantle and the loadare �m = 3350 kg m�3 and �l = 2700 kg m�3 respect-ively [Caress et al., 1995; Sichoix, 1997]. The de ectionw is then computed for all the nodes (20x20) of the to-pographic grid.

2.5. Isostatic Residual Anomaly

A three-dimensional, four-layer crustal model (Fig-ure 3) is used to compute a theoretical FAA. The in-terface between the ocean and sea oor is given by thebathymetric grid (Figure 1). The interface between thevolcanic load, divided into three density layers, and theoceanic crust is given by the de ection grid, which isassumed also to de�ne the interface between crust andmantle. The crust is assumed to have a constant thick-ness of 6000 m. This thickness has been determinedfrom seismic refraction studies in the Society-Tuamotuarea [Danobeatia et al., 1995] and the Marquesas area[Caress et al., 1995]. The material �lling the depressionsunder the load is assumed to have a higher density (�f )than the overlying volcanic material (�s) and the aer-ial part of the volcano (�a). The sea oor normal depthis given by the deepest point of the bathymetric gridwithin the particular area being studied. The modelis divided into 20x20 square prisms extending to Mohodepth. The zero FAA is given by a at oceanic crustat the sea oor normal depth. The theoretical FAA isthen computed for each node of the 20x20 grid by sum-ming the gravity e�ects of all the prisms [Plou�, 1976]produced by the density contrasts shown in Figure 3. Asimilar computation was made for each island using the�ner grid (3000x3000).

By subtracting the theoretical FAA grid from theobserved anomaly, an isostatic residual gravity �eld[Blakely, 1995], similar to an isostatic Bouguer �eld(Figure 4), is determined and investigated below as to

-50

0

50

-100

0

100

200

300

0

-16

-12

-8

-4

000ρ w

ρ ρ f

ρ c

ρ m

18˚S

17˚S

16˚SA

152˚W 151˚W 150˚W 149˚W

152˚W 151˚W 150˚W 149˚W

152˚W 151˚W 150˚W 149˚W

6000 m

s

ρ a

40 km

A'

(a)

(b)

(c)

(d)

De

pth

(km

)F

ree

air a

no

ma

ly (

mG

al)

Iso

sta

tic r

esi

du

al

an

om

aly

(m

Ga

l)

151˚W 150˚W 149˚W

-4000

-4000

-4000

-3000

-3000

-3000

-3000-2000

-2000

-2000

-1000

-100

00

Moorea

Tahaa

Raiatea

Bora Bora

Huahine

Maiao

Tahiti

Tetiaroa

Tupai

Maupiti

152˚W

Figure 4. Residual isostatic anomaly over the Socie-ty Islands obtained by subtracting the modeled FAAfrom the observed. (a) Bathymetric map of the Soci-ety Islands. Data along the pro�le AA' (solid dashedline) are shown in Figures 4b, 4c and 4d; (b) the crustalmodel used to compute the modeled FAA. The elasticthickness is adjusted using the Moho depth given byseismic refraction pro�les; (c) comparison between ob-served (thick dashes) and computed FAA (thin line)along AA'; and (d) isostatic residual gravity anomalyalong AA'.

its utility to provide new insights on the makeup of is-lands. According to Figure 3, only contrasts betweenmantle and crustal densities and between crust and in-�ll densities are relevant in the model, not their absolutevalues. As the density contrasts are regional paramet-ers rather than speci�c to each island, we determinedthese contrasts by minimizing the di�erence betweencomputed and observed gravity anomaly for each ar-chipelago. The best estimate of the mantle-crust dens-ity contrast is everywhere 450 kg m�3. Assuming avalue of 3350 kg m�3 for the mantle density, the crustdensity is then 2900 kg m�3. Thus the volcano submar-

84 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

Table 2. Properties of Islands Showing Positive Residual Isostatic Anomalies

Island Caldera Filling Submarine Amplitude HalfIsland Volume, Diameter, Density �f , Density �s, gmax, Wavelength� Location

Vv, km3 km kg m�3 kg m�3 mGal km

Austral

Raivavae 2159 3 2900 2900 16 7 south island cent.Rapa 1500 3.5 and 5 2850 2500 17 7 caldera centeredRurutu 1950 none 2900 2900 16 7.5 island centeredTubuai 3273 2 2850 2750 26 11 west caldera cent.7 Marquesas

Hiva Oa 7628 10 and 15 2800 2700 35 18 caldera centeredNuku Hiva 5811 6 and 9 2800 2800 29 19 east caldera cent.Ua Pou 2771 none 2800 2650 10 ? not enought pts

Society

Bora Bora 2338 3 2900 2900 16 6 caldera cent.Huahine 2636 drowned 2850 2850 17 7 island centeredMaiao 1857 3 2850 2700 11 3 caldera centeredManuae 2302 atoll 2800 2550 17 7 east lagoon cent.Maupiti 2132 drowned 2900 2850 18 5 caldera centeredMoorea 3166 9 2850 2700 30 10 island centeredTahaa 2784 4 2900 2700 21 12 caldera centeredTahiti 12914 8 2900 2650 60 24 caldera centeredTetiaroa 1300 atoll 2850 2650 11 4 lagoon centeredTupai 1442 atoll 2850 2800 111 5 lagoon centered

Tuamotu-Gambier

Gambier 7287 drowned 2800 2600 34 15 caldera centeredMoruroa 4497 atoll 2600 2300 22 14 south lagoon cent.Rangiroa 14668 atoll 2750 2550 23 30 lagoon centered

�The half wavelength represents the anomaly width.

ine density �s, and, to a lesser extent, the in�ll density�f are the main factors controlling our models. Theseparameters are varied in the range 2300 to 2900 kg m�3

and the residual anomaly is minimized by the techniqueof least squares.

With this approach, we determined characteristicsubmarine and �lling densities for each of the 25 islandsconsidered (Table 2). The average values of �s and �ffor all islands are 2700 and 2800 kg m�3, respectively(discussed later).

3. Results and Analysis

Twenty of the 25 islands yield a gravity residual an-omaly >5 mGal, the assumed uncertainty. The resid-ual anomalies for these 20 islands are shown in Fig-ures 5 to 8. To a �rst approximation, the contours areconcentric, and their amplitude ranges from -20 to +60mGal. Their wavelengths are similar to the diameterof the volcanoes, suggesting that the anomalies are re-lated to density contrasts at depth within the volca-

noes. Machesky [1965] related positive Bouguer anom-alies to gabbros which outcrop in the caldera of Tahiti.More generally, Rymer and Brown [1986] proposed aclassi�cation of gravity anomalies in which positive an-omalies characterize mainly basaltic volcanoes and arecaused by a relatively dense intrusive complex/magmabody which contrasts with its surroundings. Becausethe French Polynesian islands are basaltic shield volca-noes, a pronounced positive anomaly mostly expressesthe dense cumulate core or solidi�ed magma chamberof the volcano. We will use known geological settings tore�ne the relation between a positive gravity anomalyand a dense intrusive complex, in order to establish atypology of gravity �elds over the Polynesian volcanoes.Our results are sorted by archipelago and are shown inTable 2 and Table 3 according to the sign (+/-) of theresidual anomaly.

3.1. Society Islands

The age of the oceanic crust in the chain of the So-ciety Islands ranges from 65 Ma in the south to 80 Ma

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 85

149˚36'W

17˚00'S0

2 km

151˚48'W

16˚12'S-20

0

10

2 km

149˚30'W

17˚30'S

-30

-20

-20

-10

-10

0

0

10

10

10

10

20

30

40

6 km

Tahiti Nui

Tahiti Iti

Tairapu

150˚36'W

17˚39'S

-15

05

2 km

-30 -20 -10 -5 0 5 10 15 20 25 30 40 50mGal

TETIAROA

a)

c)

b)

d) TUPAI

MAIAO

TAHITI

Figure 5. Isostatic residual anomaly over individual islands of the Society Island chain wherea residual anomaly greater than 5 mGal is observed. (a) Tahiti, (b) Maiao, (c) Tetiaroa, (d)Tupai, (e) Manuae, (f) Huahine, (g) Tahaa, (h) Moorea, (i) Bora Bora, (j) Maupiti. Black dotsrepresent land gravity stations, and black dashed lines represent caldera boundaries. Thick whitelines represent the coast, and thin white lines represent the marine gravity data.

750 km away in the north [Herron, 1972; Mayes et al.,

1990]. This island chain is composed of �ve atolls andnine islands of which Maupiti is the oldest (about 4.3 Ma[Duncan and McDougall, 1976]) and Mehetia the young-est (0 to 0.3 Ma [White and Duncan, 1996]). BecauseMehetia is associated with the present hotspot, it hasbeen intensely studied over the past 15 years [Talandierand Okal, 1984a; Chemin�ee et al., 1990; Binard et al.,

1991]. The geochronology, geochemistry, volcanology,and geology of the Society Islands have been reviewedin some detail by Diraison et al. [1991] and more re-cently by White and Duncan [1996]. The aerial activityof these volcanoes can be described by three main se-quential stages: the edi�cation of a shield volcano, theformation of a caldera, and the occurrence of postcal-dera volcanism.

Figure 5 shows the residual gravity anomaly over 10islands of the Society group. Owing to the relativelydense coverage of bathymetry and gravity data, resultsfor these islands are probably more reliable than those

for the other islands studied here. Positive anomaliesare present at all of the islands and atolls (Figure 5)and range from 60 mGal over Tahiti (Figure 5a), thelargest island, to 11 mGal over Maiao (Figure 5b), thesmallest island, and Tetiaroa (Figure 5c), the smallestatoll (Table 2). In the case of the islands the positiveanomalies are located over the inferred centers of themain feeding systems and have wavelengths similar tothe diameter of the islands or the calderas. Positiveanomalies are usually related to shield volcanoes andre ect a deep-seated, solidi�ed magma chamber or feed-ing system [Rymer and Brown, 1986]. Thus the positiveanomalies over the atolls of Tetiaroa (Figure 5c), Tupai(Figure 5d), and Manuae (Figure 5e) may express un-derlying dense magma chambers.

Tahiti is composed of two di�erent volcanoes, TahitiNui and Tahiti Iti on the peninsula. There are su�cientgravity data on Tahiti Nui to establish the existence ofa correlation between the positive anomaly and the cal-dera. On the other hand, the data coverage for Tahiti Iti

86 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

149º 48'W

17º 36'S

-30

010

20

149º 48'W

17º 36'S

149º 48'W

17º 36'S3 km

149º 48'W

17º 36'S

152º 12'W

16º 24'S

0

10

152º 12'W

16º 24'S

152º 12'W

16º 24'S

3 km

152º 12'W

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151º 00'W

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-20

0

10

151º 00'W

16º 48'S

151º 00'W

16º 48'S3 km

151º 00'W

16º 48'S

Huahine Nui

Maroe Bay

HuahineIti

Vaihi

154º 36'W

16º 36'S

-100

10

154º 36'W

16º 36'S

154º 36'W

16º 36'S 3 km

154º 36'W

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-20

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151º 48'W

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3 km

151º 48'W

16º 30'S

MANUAE BORA BORA

HUAHINE

MOOREA

MAUPITI

e)

f)

i)

h)

j)

151˚36'W

16˚48'S

16˚36'S-10

010

2 km

TAHAA

RAIATEA

g)

-30 -20 -10 -5 0 5 10 15 20 25 30 40 50mGal

Figure 5. (continued )

is poor, except for its western part, where a prominentnegative anomaly is observed. This negative anomaly isnot consistent with the existence of a third and separatevolcano as postulated by L�eotot et al. [1990]. The neg-ative anomaly of Tahiti Iti is discussed further below.The 10 mGal positive anomaly shown over the center ofTahiti Iti is not well constrained owing to the poor datacoverage on the eastern shore of the peninsula and willnot be considered further. On Manuae (Figure 5e) theanomaly is apparently located close to the eastern sideof this atoll. However, since there are no data for thewestern and southern sides, the location of the anomalyis poorly de�ned.

Only one large positive anomaly is present over eachisland examined even though in some cases two dis-

tinct volcanoes have been postulated, such as on TahitiIti. There is some debate about Huahine (Figure 5f),which is composed of two separate islands located in thesame lagoon (Huahine Nui and Huahine Iti), separatedby Maroe Bay and a large intrusion at Mount Vaihi.Deneufbourg [1965] considers that these two islands arerelated to a single volcano separated by a large sub-merged caldera which formed Maroe Bay. In contrast,Brousse et al. [1983] postulate the presence of at leasttwo volcanoes (Huahine Nui and Huahine Iti). Figure5f clearly indicates one positive anomaly centered overMaroe Bay, which supports Deneufbourg's interpreta-tion. A di�erent interpretation may be appropriate inthe case of the islands of Tahaa (Figure 5g) and Rai-atea, which are in the same lagoon. Each island has

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 87

149˚24'W

23˚24'S

-10

20

3 km

Herani

Hanareho

151˚24'W

22˚30'S

0

0

10

3 km

144˚24'W

27˚36'S10

3 km

147˚36'W

23˚48'S

0

10

3 km

RAPA

RURUTU

RAIVAVAE

a)

b)

d)TUBUAI

c)

-30 -20 -10 -5 0 5 10 15 20 25 30 40 50mGal

Figure 6. Isostatic residual anomaly over individual islands of the Austral Island chain wherean anomaly greater than 5 mGal is observed. (a) Rapa, (b) Rurutu, (c) Tubuai, (d) Raivavae.Black dots represent land gravity stations, and black dashed lines represent caldera boundaries.Thick white lines represent the coast, and thin white lines represent the marine gravity data.

a caldera. The two calderas are separated by 25 km.Figure 5g shows a positive anomaly centered on the cal-dera of Tahaa. Unfortunately, no gravity survey hasbeen conducted on Raiatea. However the gravity resid-ual anomaly at Tahaa seems to show a separate feedingsystem.

Moorea (Figure 5h) has a 30 mGal anomaly, o�setby about 3 km from the center of a caldera, while BoraBora (Figure 5i) and Maupiti (Figure 5j) have 16 mGaland 18 mGal gravity anomalies, respectively, centeredover associated calderas.

Thus each island in the Society chain apparently hasonly one deep-seated magmachamber or feeding system.Also, it is found that a linear correlation exists betweenthe amplitude of the positive anomalies and the islandsize for both islands and atolls.

Negative anomalies (Table 3) are present over TahitiIti at Taiarapu (Figure 5a) and Moorea (Figure 5g). Onthe basis of geological data [L�eotot et al., 1990] thoseanomalies can be interpreted as the gravity e�ects ofsecondary cones producing di�erentiated lavas of relat-ively low density. A large volume of limestone deposits

could also have produced the observed negative anom-aly on the coral reef of Bora Bora (Figure 5i).

3.2. Austral Islands

The Austral Islands chain extends northwest for >1500 km from the active submarine volcano Macdon-ald [Norris and Johnson, 1969; Johnson and Malaho�,

1971; Talandier and Okal, 1984b] to the island of Rim-atara, which is about 16 Myr old [Turner and Jarrard,

1982], and the atoll of Maria (Figure 1). The chain iscomposed of �ve small islands and one atoll. The ageprogression of these islands is compatible with a hot-spot origin, with the present volcanic activity relatedto the Macdonald submarine volcano [Duncan and Mc-

Dougall, 1976]. Young radiometric ages reported forRurutu, located toward the northern end of the chain,can be explained by another hotspot located betweenRurutu and Tubuai [Turner and Jarrard, 1982]. Theexistence of this hotspot was established by demonstrat-ing the di�erences of chemical and isotopic signaturesof the recent lavas from Rurutu with those produced atthe Macdonald hotspot [Barsczus et al., 1994]. Recent

88 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

140˚00'W

9˚24'S

-40

-10

0

5 km

139˚00'W

9˚48'S

-10

010

20

30

5 km

Atuona

Ootua

Puamau

140˚00'W

8˚48'S

-30 -10

0

1020

5 km

Taiohae

a)

c)

b)

UA POU

HIVA OA

NUKU HIVA

-30 -20 -10 -5 0 5 10 15 20 25 30 40 50mGal

Figure 7. Isostatic residual anomaly over individualislands of the Marquesas Island chain: (a) Ua Pou, (b)Hiva Oa, (c) Nuku Hiva. Black dots represent landgravity stations, and black dashed lines represent cal-dera boundaries. Thick white lines represent the coast,and thin white lines represent the marine gravity data.

bathymetric and seismic data reported by McNutt et

al. [1997] reveal the complexity of overlapping volcan-ism at the southeastern end of the Austral chain. TheAustral FZ crosses the island chain between Tubuai andRaivavae, forming a western and eastern segment of theAustral island chain, each showing a distinct isotopicsignature [Barsczus et al., 1994; Hauri et al., 1997].The ages of the oceanic crust in the chain vary fromabout 35 Ma to 80 Ma [Mayes et al., 1990].

Figure 6 shows the residual anomaly over the Aus-tral Islands. Positive anomalies range from 16 mGalat Raivavae (Figure 6a) and Rurutu (Figure 6b) to 26mGal at Tubuai (Figure 6c). Rapa (Figure 6d) presentsa 17 mGal positive anomaly. These positive anomaliesare interpreted as expressing a single and deep solidi-�ed magma chamber or feeding system. No signi�cantanomalies are observed at Rimatara, the smallest and

northernmost island, and Maria, a small atoll locatedto the northwest of Rimatara.

The locations of the positive anomalies in the AustralIslands, like those in the Society Islands, are over thecenter of the island in Rapa and Rurutu but over thewestern shore in Tubuai and over the southern shorein Raivavae. The continuation of the anomaly to thesouth of Raivavae is probably due to a complex mor-phology of the southern submarine ank. The locationand uniqueness of the gravity anomaly show a singlemagma source and imply that the so-called small cal-dera (see Figure 6d) is likely related to the collapse of

148W

15 00'S

00

10 1010

10

20

148W

15 00'S

148W

15 00'S

148W

15 00'S

5 km

148W

15 00'S

138 48'W

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138 48'W

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138 48'W

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135 00'W

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-30-20

-10

0

10

20

30

135 00'W

23 12'S

135 00'W

23 12'S

5 km

135 00'W

23 12'S

a)

c)

b)

RANGIROA

MORUROA

GAMBIER

-30 -20 -10 -5 0 5 10 15 20 25 30 40 50mGal

Figure 8. Isostatic residual anomaly over (a) GambierIslands, (b) Moruroa, (c) Rangiroa. Black dots repre-sent land gravity stations. Thick white lines representthe coast, and thin white lines represent the marinegravity data.

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 89

Table 3. Properties of Islands Showing Negative Residual Isostatic Anomalies

Island Amplitude, mGal Half Wavelength, km � Location Interpretation

Bora Bora �20 4 north reef low density super�cial bodies

Moorea �10 3 Maraarii secondary cone di�erentiated lavaNuku Hiva �30 10 Topuke strombolian cone di�erentiated lavaTahiti Iti �10 6.5 NW secondary cones di�erentiated lava

�The half wavelength represents the anomaly width.

the anks of the volcano. On Tubuai the o�set of thepositive anomaly from the center of the island may in-dicate subsidence of this part of the island due to anunderlying dense source (Figure 6c), similar to that ob-served in the Marquesas Islands [Chubb, 1930; Barsczuset al., 1992]; the anomaly pattern strongly suggests thepresence of a single magma source.

3.3. Marquesas Islands

The length of the Marquesas island chain is only 350km, but it comprises a dozen islands and as many shal-low seamounts. The age of the oceanic crust ranges from50 to 55 Ma [Kruse, 1988; Mayes et al., 1990; Munschy

et al., 1996]. K-Ar ages range from about 5.5 Ma atEiao in the northwest to about 1.5 Ma at Fatu Iva inthe southeast [Brousse et al., 1990]. A basalt sampledredged 50 km southeast of Fatu Iva yielded an age ofabout 0.5 Ma [Desonie et al., 1993]. The MarquesasFZ is located southeast of the chain. To date, no activehotspot generating the Marquesas volcanism has beenidenti�ed.

Owing to the rugged topography, gravity stations aresparse (Figure 7), thus the resulting interpretations aresomewhat speculative. The shipboard data coveragearound the islands is also poor. The merging of thesetwo poor data sets probably accounts for the non cir-cular residual anomalies. The results for Ua Pou (Fig-ure 7a) will not be considered further because of thepoor distribution of data. Hiva Oa (Figure 7b) has aprominent positive anomaly (35 mGal) over the Atuonacaldera. It is possible that a separate positive anomalywith a lower magnitude exists over the Puamau valley,but the lack of o�shore data prevents any clear descrip-tion of the anomaly. The observations at Hiva Oa in-dicate that at least one deep, solidi�ed magma chamberis present at Hiva Oa. Obellianne [1955] proposed twocalderas, Atuona and Puamau. These two calderas areseparated by Mount Ootua, a trachytic diatreme, ex-pressed as 5 mGal negative anomaly.

The anomaly pattern obtained at Nuku Hiva (Figure7c) may be misleading because of the poor distributionof data. However, the positive anomaly (29 mGal) overthe southern coast, where the data coverage is relativelygood, may be associated with the caldera that formsTaiohae Bay.

3.4. Pitcairn-Gambier Islands

The Pitcairn-Gambier island chain extends over 1650km from Hereheretue atoll to Pitcairn Island. KnownK-Ar ages range from about 11 Ma at Moruroa [Guille etal., 1993] to zero in the active hotspot area, 70 to 100 kmsoutheast of Pitcairn [Binard et al., 1992]. The AustralFZ crosses this chain between Moruroa and Fangataufa.The age of oceanic crust ranges from about 25 Ma in thesoutheast to 55 Ma to the northwest [Mayes et al., 1990;Munschy et al., 1996]. The chain includes the islandsPitcairn and the Gambier and several atolls. Fangata-ufa and Moruroa have been extensively drilled and thusconsiderable data on the properties and geology of theseislands exist [see Guille et al., 1993].

Over the Gambier Islands (Figure 8a), a large posit-ive anomaly (34 mGal) occurs over the 10 islets in thecenter of a large lagoon. These islets are the emergedparts of an old volcano, and a caldera centered over thelagoon has been assumed [Guille, 1974]. The at shapeof the gravity anomaly is probably related to the lackof data in the lagoon, and the anomaly magnitude mayactually be a few milliGals more than that indicated.Over the atoll of Moruroa (Figure 8b), a positive anom-aly of 22 mGal is centered over the southern rim of theatoll. The positive gravity anomalies along the Pitcairn-Gambier island chain are interpreted as the remains ofancient magma chambers, which coincide with calderalocations for Moruroa [Buigues et al., 1992], and for theGambier Islands [Brousse et al., 1972].

3.5. Tuamotu Islands

Oriented N120�, the Tuamotu Archipelago consistsof about 60 atolls along two subparallel chains of length1200 km and width 400 km. Its northern and southerntermini are located at the Marquesas Fracture Zone andthe Austral Fracture Zone, respectively. The age of thesea oor ranges from about 30 Ma in the southeast to65 Ma in the northwest [Mayes et al., 1990; Munschy

et al., 1996]. The atolls probably formed atop buriedvolcanoes.

Among the four atolls for which gravity data areavailable, only Rangiroa (Figure 8c) shows positive an-omalies. The eastern anomaly (23 mGal) is only de�nedby one station and will not be considered further. By

90 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

-5

Dep

th (

km) ��

��yz{|ac

0

-10

0 4020 60 80 100

Sea

Crust

Mantle

(km)

Figure 9. West-east cross section along latitude 19�060N of Mauna Loa volcano, Hawai'i, extend-ing from land to sea west-east [after Moore et al., 1995]. Horizontal layering indicates subaeriallava; dashed layering indicates fragmental lava; ellipses indicate pillow lava; vertical lines indicatesheeted dikes; dotted pattern indicates gabbro; unpatterned areas are giant blocks of �rst phaseof South Kona landslide; and solid black areas are magma, or plastic core of southwest rift zoneof Mauna Loa. The 3-D ellipsoidal chamber used to model the anomaly (see Figure 11) with apositive density contrast is also drawn.

0

10

20

30

40

50

60

resi

dual

isos

tatic

ano

mal

y (m

Gal

)

0 2000 4000 6000 8000 10000 12000 14000

Society IslandsGambier IslandsAustral IslandsMarquesas Islands

Rangiroa

volcano volume (km ) 3

Figure 10. Plot of the maximum intensity of the positive residual anomaly (mGal) versus islandvolume (km3). Shaded area represents the �5 mGal error associated with the observed gravityvalues. The central thick line represents the derived linear relation between volcano volume andanomaly amplitude.

analogy with results obtained for other islands (espe-cially the Moruroa atoll) we interpret the western an-omaly (17 mGal) as the gravity signature of an ancientmagma chamber and/or deep-seated feeding system. Itis possible that the amplitude of this anomaly couldhave been reduced due to the presence of a 2-km-thickcoral limestone cap [Talandier and Okal, 1987] overly-ing the proposed magma chamber. For the three other,smaller atolls of Makatea, Manihi, and Mataiva (notshown), no appreciable anomaly is observed.

4. Discussion

Current understanding of volcanic edi�ces associatedwith hotspots and their tectonic behavior has been de-rived from numerous studies, mainly of the Hawaiianvolcanoes. The �rst dynamic cross section of a typical

Hawaiian volcano [Eaton and Murata, 1960] proposedthat the magma ascends (due to buoyancy) to a depthbetween 3 and 7 km, where it forms a shallow magmareservoir. Intermittent eruptions occur within summitcalderas or laterally along rift zones. Ryan [1987] for-mulated the neutral buoyancy hypothesis in which themagma ascends to depths where its density equals thatof the surrounding material. This region of neutralbuoyancy controls the upper limit of the levels of stablemagma storage. The summit reservoir elevation followsthe buildup of the volcano, leading to the location ofthe roof at depths between 2 and 4 km, as observed onKilauea and Mauna Loa volcanoes (Figure 9) [Moore

et al., 1995]. Another characteristic of hotspot volca-noes is the existence of collapses. The Hawaiian Ridgeis characterized by giant submarine landslide debris,which played a key role in the internal makeup of the

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 91

volcanoes [Moore et al., 1989]. These landslides canhave various origins [e.g., Walker, 1988]: vertical sub-sidence by withdrawal of magma beneath the summitarea or lateral mass collapse. Using our gravity dataset, we will try to compare the Polynesian volcanoes tothis classical Hawaiian model.

4.1. Gravity Anomalies

Positive residual gravity anomalies are calculatedover 20 islands, with amplitudes ranging from 9 to 60mGal (Table 2). Generally, the anomalies are spatiallycorrelated with a known caldera (e.g., Tahiti) or theassumed main feeding conduit of volcanoes of similarwidths. Thus solidi�ed magma chambers and feedingconduits with higher densities than that of the sur-rounding rocks [Rymer and Brown, 1986; Rousset et

al., 1989] produce the observed positive gravity anom-alies. Furthermore, for each island where the gravitycoverage is good the observed single positive anomalysuggests that there is only one deep-seated, solidi�edmagma chamber or main feeding system.

We also observe a good correlation (Figure 10) bet-ween the amplitude of the positive anomaly and thevolume of the volcano. This volume is that boundedby the volcano topography and a reference plane cor-responding to the observed basis of the volcano on thesea oor. Speci�cally, the linear relation between thevolcano volume Vv and the amplitude of the positiveanomaly Ap is

Ap = 3:7� 10�3Vv + 8:9; (3)

where Vv is in km3 and Ap is in mGal. This relationfails for the Rangiroa atoll, however, where the grav-ity signal is lower than expected considering the vol-cano diameter. It has already been pointed out thatthe amplitude of the gravity anomaly at Rangiroa mayhave been reduced due to a 2 km-thick coral limestonecap. Thus the volcanic basement and the dense residueof magmatic rock are located at a greater depth thanthat for the other islands.

Negative anomalies (Table 3) are observed in a fewcases, although their magnitude never reaches that ofthe positive anomalies. Moreover, in contrast to thepositive anomalies, the negative anomalies are observedon the island or atoll edge, possibly because of lime-stone on reefs or fragmented material on the ank ofthe edi�ces.

4.2. Size and Depth of Solidi�ed Magma

Chambers

Residual gravity anomalies are associated with shal-low mass inhomogeneities. Robertson [1967] tried tomodel the gravity anomalies observed on six of the CookIslands as caused by vertical cylindrical dense cores witha radius equal to the radius of the island at sea level.Despite the simplicity of the model, which uses a uni-form density for the whole island, Robertson found a

single relation between the size of the solidi�ed magmaplumbing system and the present size of the volcano.Using a more realistic model, we examine usefulness ofthis relation.

In most cases, the amplitudes of the gravity anom-alies are based on a single pro�le across the island. Theanomaly can be modeled, in a simple way, as the ef-fect of a dense ellipsoid of revolution (Figure 11). Moresophisticated inverse or forward models would be unin-formative in the absence of any other data constraints,such as seismic or borehole data. The selected ellips-oidal body does not re ect the complexity of magmareservoirs and feeding conduits. Nevertheless, it is areasonable representation of the depth and volume ofthe main system. Using this simple approach of anellipsoidal magma chamber, the radius, the attening,and the depth of the chamber of each island can be de-rived as a function of the residual anomaly. At a pointP located at a distance r from the center of the ellipsoidthe vertical attraction gv of an ellipsoid of revolution is

gv =4�a2cG��z

3(r2 + z2)3=2[1�

3(a2 � c2)(2z2 � r2)

10(r2 + z2)2] (4)

where z is the depth of the center of the ellipsoid, 2a isthe diameter of the circular section of the ellipsoid, c isthe length of the vertical axis of revolution (see Figure9), �� is the density contrast, and G is the gravitationalconstant (6:67 � 10�11 N m). The average density forultrama�c bodies forming dense magma chambers orfeeding systems is roughly 3100-3300 kg m�3 [Rymerand Brown, 1986]: we used a value of 3100 kg m�3.The density contrast �� depends on the submarine loaddensity �s assumed for each island, except for Rangiroa,where we set �� to 500 kg m�3. To constrain our res-ults further, we also assume that the magma chamberdepth lies between 2 and 4 km, the depth of neutralbuoyancy [Ryan, 1987]. Considering that the islandshave reached an elevation of 2000 m above sea level,the magma chamber would lie at depth of 0 m to 2km below the sea level. Although the neutral buoyancyregion has been de�ned for active volcanoes, we haveassumed it applies here because of the young ages ofthe volcanoes in our study area (except Rangiroa). The�nal parameters of the ellipsoids, a, c and z, are thosethat minimize the di�erence between the isostatic resid-ual anomalies and the attraction of the ellipsoidal bodygiven by equation (4).

For each island, Table 4 gives the diameter and thedepth of the magma chamber roof. For the Society Is-lands the magma chamber roof depth varies from 100m for Maiao, Maupiti, Moorea and Tupai to 1.3 km forTahiti. The diameter of the chamber ranges from 2 kmfor Maiao to 14 km for Tahiti. For the Austral Islandsthe sizes of chamber range from 3.6 to 7 km. The Gam-bier Islands, Rangiroa, and Marquesas islands generallyhave larger magma chambers (from 8.4 to 11.6 km indiameter) lying at greater depths (up to 5.9 km). Plot-

92 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

0

-8

-4

Dep

th (

km)

0 4 8 12 16 20 24 28 32 36 40Length of the profile across Tahiti (km)

0

20

40

60

80

Gra

vity

ano

mal

y (m

Gal

)

Observed residual anomalyGravity induced by a buried ellipsoidal body

0

����yyyya

c

149W

17 30’S

149W

17 30’S

-20

0

20

Figure 11. Gravity anomaly produced by a 3-D ellipsoidal chamber with a positive densitycontrast (see text) with the surrounding rocks on Tahiti. The isostatic residual anomaly inmilliGals is represented as a dotted line, and the computed anomaly is represented as a solidline. The inset shows the location of the pro�le on Tahiti Island.

ting the magma chamber volume Vm (km3) versus thevolcano volume Vv (km3) (Figure 12) gives the followinglinear relation:

Vm = 7:14� 10�2Vv � 91: (5)

This relation gives a method to infer the rough size ofthe solidi�ed magma chamber using only the volcanovolume. To compare with other intraplate volcanoes, weplotted data from the Kilauea [Ryan, 1988] and Pitondes Neiges [Lesquer, 1990] volcanoes. Although the sizeof these volcanoes is di�cult to estimate since they cannot be easily separated from other nearby volcanoes,the Piton des Neiges point on the graph �ts well withthe linear curve determined for the islands of FrenchPolynesia. The proposed relation in equation (5) doesnot apply for Kilauea, probably because the volume ofthis volcano is very di�cult to estimate. Therefore ourmethod probably applies only to extinct volcanoes andthus entirely solidi�ed magma chambers.

4.3. Load Density

On a regional scale a submarine volcanic load densityof 2700 kg m�3 provides reasonable results for the cal-culated de ection surface and for the theoretical FAA(Figure 4). This value may thus suitably represent theactual average regional load density for volcanic islandchains. For individual islands, however, the RMS errorbetween theoretical and observed FAA leads to a rangeof submarine load densities, from 2300 to 2900 kg m�3

for all the islands (Table 2). On this local scale thedensity of the masses above sea level has a major ef-fect on the terrain correction. An average value of 2300kg m�3 for �a, the density of the aerial part of the is-lands, provides suitable results for all the islands. Thevalue of the �lling density �f was determined jointly bythe same RMS minimization method and varies from

1

1010

100

1000

mag

ma

cham

ber

volu

me

(km

)

10001000 10000

volcano volume (km )

Society IslandsGambier IslandsAustral IslandsMarquesas IslandsRangiroa

Kilauea

Reunion Island

3

3

Figure 12. Computed solidi�ed magma chambervolume versus the island volume using a logarithmicrepresentation. The trend of the plot in gray corres-ponds to a linear relation. French Polynesian volcanoesare represented by solid geometrical symbols (see le-gend), and volcanoes from Hawai'i and Reunion Islandsare plotted for comparison using open circles.

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 93

Table 4. Characteristics of Magma Chambers and Comparison With the Size of the Caldera

Caldera Solidi�ed Magma Chamber (� = 3100 kgm�3)

Island Diameter, Center Center Diameter Flattening Volume, Roof Depth,km Longitude W Latitude S a, km c=a km3 km

Austral

Raivavae 3 147�390 23�530 5.4 0.85 70 0.2Rapa 3.5 and 5 144�210 27�360 3.6 0.83 20 0.2Rurutu � � � 152�210 22�290 3.8 1.0 29 0.1Tubuai 2 149�310 23�230 7.0 0.77 138 0.2

Marquesas

Hiva Oa 10 and 15 139�030 09�480 8.4 1.52 473 0.3Nuku Hiva 6 and 9 140�060 08�540 8.4 1.43 443 0.2

Society

Bora Bora 4 151�450 16�310 6.4 0.78 107 0.2Huahine � � � 151�000 16�460 5.2 0.85 62 0.3Maiao � � � 150�370 17�400 2.0 0.9 4 0.1Manuae� � � � 154�390 16�320 4.0 0.75 25 0.3Maupiti 3 152�160 16�270 4.0 1.0 33 0.1Moorea 7 149�490 17�320 6.2 0.97 121 0.1Tahaa 4 151�280 16�380 6.2 0.81 101 0.8Tahiti 7 149�260 17�380 14.0 0.77 1108 1.3Tetiaroa � � � 149�340 17�010 2.8 1.0 12 0.3Tupai � � � 151�490 16�160 3.6 0.72 18 0.1

Tuamotu-Gambier

Gambier 12 134�580 23�090 9.6 1.04 482 1.6Moruroa � � � 138�540 21�520 7.2 0.83 163 1.8Rangiroa � � � 147�480 15�050 11.6 0.86 705 5.9

�Poorly constrained.

2800 to 2900 kg m�3, except for Moruroa and Rangiroa,where it is lower.

4.4. Calderas or Collapses?

Are the computed locations and diameters of the an-cient magma chambers consistent with those of knowncalderas? It appears that the collapse diameter is some-times larger than the computed diameter of the associ-ated magma chamber. In addition, the collapses arenot always located directly above the chambers them-selves (e.g., north of Huahine). Considering the inferredmagma chamber location, the collapse of Tahaa is shif-ted west, that of Moorea is shifted north, and those ofHuahine and Raivavae are clearly independent of thelocation of the magma chamber. Hiva Oa, Nuku Hiva,and Rapa have outer collapses larger than the proposedsolidi�ed reservoirs. These collapses are probably notlinked to any caldera subsidence but rather to ank in-stabilities (e.g., landslides) such as described on otherintraplate volcanoes such as Hawaii or Reunion islands[Moore et al., 1989; L�enat and Labazuy, 1990]. How-ever, inner collapses of Rapa and Hiva Oa, the easterncollapse of Tahaa, and the collapses of Gambier Islands,

Tubuai, Maupiti, Tahiti Nui, and Bora Bora are prob-ably characterized by classic calderas centered above themagma chamber. Even for these edi�ces, however, thecaldera ank is always open to the sea, and this couldbe related to ank instabilities.

5. Conclusion

A gravity study of 25 volcanic islands in French Poly-nesia leads us to propose a single linear relation betweenthe island size and the solidi�ed magma chamber size,the latter being derived from the positive isostatic re-sidual gravity anomaly. This linear relation appears ap-propriate for other hotspot volcanoes, such as Piton desNeiges in Reunion Island. This relation may be used asa simple and viable tool to infer the rough size of thesolidi�ed magmatic feeding system for extinct oceanicintraplate volcano.

The results also illustrate the wide range of submar-ine volcanic load densities, from 2300 to 2900 kg m�3,and con�rm the importance of the increase of densitywith depth, from 2300 kg m�3 for subaerial lava to 2900kg m�3 for the deepest part of the volcano which �lls

94 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

the exure of the oceanic crust. On a regional scale thebest �tting load density is �2700 kg m�3.

At the island scale the residual isostatic anomalyhelps to de�ne the actual location of volcanoes. Forexample, previous studies assume multiple volcanoeson the same island (e.g., Huahine, Tubuai, Tahiti Iti).However, our results clearly demonstrate the presenceof a single volcanic system for these islands and for theatolls, except for the Marquesas Islands. Finally, weshow that the majority of the so-called calderas are re-lated to ank instabilities which induce huge landslides,rather than to caldera subsidence. Thus the calderacenter may often be a poor indicator of the locationsand other attributes of now consolidated and inactiveancient magma reservoirs.

Acknowledgments. We are grateful for ORSTOM in-stitute, now IRD, that funded all the gravity surveys con-ducted by one of us (H.G.B.) in French Polynesia between1978 and 1981 and to I. Leroy who made the complete grav-ity survey of Tahiti in 1994. V.C. is supported by a grant ofthe ZEPOLYF program. We thank particularly the associ-ate editor, T. Hildenbrand, whose remarks and suggestionshave greatly improved this paper. This work also bene�tedof the constructive reviews made by J.F. L�enat, M.P. Ryan,and H. Rymer.

References

Barriot, J.P., La d�etermination du g�eoide par altim�etrieoc�eanique et gravim�etrie : Quelques aspects du traite-ment et interpr�etation g�eologique sur l'Oc�ean Indien (partieNO) et M�editerrann�ee occidentale. Ph.D. thesis, 240 pp,Univ. des Sciences et Techniques du Languedoc, Mont-pellier, France, 1987.

Barsczus, H.G., R�esultats provisoires de quelques mesures etliaisons gravim�etriques e�ectu�ees en Polyn�esie Fran�caise,Intern. Rep., Cent. ORSTOM de Papeete, Tahiti, 1979.

Barsczus, H.G., Reconnaissance gravim�etrique de Tubuai(Iles Australes), Intern. Rep., Cent. ORSTOM de Pa-peete, Tahiti, 1980.

Barsczus, H.G., Reconnaissance gravim�etrique de Maiao(Tupai-Manu), Intern. Rep., Cent. ORSTOM de Pa-peete, Tahiti, 1981.

Barsczus, H.G., P.E. Filmer, and D.L. Desonie, Cataclys-mic collapses and mass wasting processes in the Marque-sas (abstract), Eos Trans. AGU, 73 (14), Spring Meet.Suppl., 313, 1992.

Barsczus, H.G., G. Guille, R.C. Maury, C. Chauvel, and H.Guillou, Two magmatic sources at Rurutu Island (Aus-tral Islands, French Polynesia) and the Austral "Hotline"(abstract), Eos Trans. AGU, 75(44), Fall Meet. Suppl.,323, 1994.

Binard, N., R. H�ekinian, J.L. Chemin�ee, R.C. Searle, andP. Sto�ers, Morphological and structural studies of theSociety and Austral hot spot regions in the South Paci�c,Tectonophysics, 186, 293-312, 1991.

Binard, N., R. H�ekinian, and P. Sto�ers, Morphostructuralstudy and type of volcanism of submarine volcanoes overthe Pitcairn hotspot in the South Paci�c, Tectonophysics,206, 245-264, 1992.

Blakely, R.J., Potential Theory in Gravity and Magnetic Ap-plications, 441 pp., Cambridge Univ. Press, New York,1995.

Bonneville, A., V. Clouard, P. Beuzart, I. Klaucke, R. LeSuav�e, B. Loubrieu, P. Saget, and Y. Thomas, Possiblecontrol of Society Islands volcanism by a preexisting vol-canic chain (abstract), Eos Trans. AGU, 78,(45), FallMeet. Suppl., F725, 1997.

Brousse, R., J.C. Philippet, G. Guille, and H. Bellon, G�eo-chronom�etrie des �les Gambier (Oc�ean Paci�que), C. R.Acad. Sci., Ser. D, 274, 1995-1998, 1972.

Brousse, R., C. Macherey, E. Berger, and G. Boutault,L'ile de Huahine: trois volcans successifs (Archipel dela Soci�et�e, Polyn�esie), C. R. Acad. Sci., Ser. II, 296,1559-1562, 1983.

Brousse, R., H.G. Barsczus, H. Bellon, J.M. Cantagrel,C. Diraison, H. Guillou, and C. L�eotot, Les Marquises(Polyn�esie Fran�caise): Volcanologie, g�eochronologie, dis-cussion d'un mod�ele de point chaud, Bull. Soc. G�eol.Fr., 6, 933-949, 1990.

Buigues, D., A. Gachon, and G. Guille, L'atoll de Moruroa(Polyn�esie Fran�caise): Structure et �evolution g�eologique,Bull. Soc. G�eol. Fr., 5, 645-657, 1992.

Caress, D.W., M.K. McNutt, R.C. Detrick, and J.C. Mutter,Seismic imaging of hotspot-related crustal underplatingbeneath the Marquesas Islands, Nature, 373, 600, 1995.

Calmant, S., and A. Cazenave, The e�ective elastic litho-sphere under the Cook Austral and Society Islands, EarthPlanet. Sci. Lett., 77,, 187-202, 1986.

Calmant, S., and A. Cazenave, Anomalous elastic thicknessof the oceanic lithosphere in the south central Paci�c,Nature, 328, 236-238, 1987.

Chemin�ee, J.L., R. H�ekinian, J. Talandier, F. Albar�ede,C.W. Devey, J. Francheteau, and Y. Lancelot, CampagneTeahitia-1, G�eologie d'un point chaud actif: Teahitia-Mehetia, �les de la Soci�et�e (Paci�que Central Sud), Ocea-nol. Acta, 10, 225-239, 1990.

Chubb, L.J., The geology of the Marquesas Islands, Bull.68, B.P. Bishop Mus., Honolulu, Hawaii, 1930.

Dalrymple, G.B., R.D. Jarrard, and D.A. Clague, Potas-sium-argon ages of some volcanic rocks from the Cookand Austral Islands, Geol. Soc. Am. Bull., 86, 1463-1467,1975.

Danobeitia, J.J., et al., Deep seismic reconnaissance beneathSociety Archipelago (South Paci�c), paper presented atEGS Assembly, Eur. Geophys. Soc., Hamburg, Germany,1995.

Deneufbourg, G., Carte g�eologique, Notice explicative sur lafeuille Huahine, Bur. des Rec. G�eol. et Mini�er., Paris,1965.

Desonie, D. L., R.A. Duncan, and J.H. Natland, Temporaland geochemical variability of volcanic products of theMarquesas hotspot, J. Geophys. Res., 98, 17,649-17,665,1993.

Diraison, C., Le volcanisme a�erien des archipels polyn�esiensde la Soci�et�e, des Marquises et des Australes-Cook, Ph.D.thesis, 413 pp, Univ. de Bretagne Occidentale, Brest,France, 1991.

Diraison, C., H. Bellon, C. Leotot, R. Brousse, and H.Barsczus, L'alignement de la Soci�et�e (Polyn�esie fran-�caise): Volcanologie, g�eochronologie, proposition d'unmod�ele de point chaud, Bull. Soc. G�eol. Fr., 162, 479-496, 1991.

Duncan, R.A., and I. McDougall, Migration of volcanismwith time in the Marquesas Islands, French Polynesia,Earth Planet. Sci. Lett., 21, 414-420, 1974.

Duncan, R.A., and I. McDougall, Linear volcanism in FrenchPolynesia, J. Volcanol. Geotherm. Res., 1(3), 197-227,

CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS 95

1976.Duncan, R.A., M.R. Fisk, W.M. White, and R.L. Nielsen,

Tahiti: Geochemical evolution of a French Polynesian vol-cano, J. Geophys. Res., 99, 24,341-24,357, 1994.

Eaton, J.P., and K.J. Murata, How volcanoes grow, Science,132, 925-938, 1960.

Filmer, P.E., Flexure of the oceanic lithosphere in the vicin-ity of the Marquesas Islands, Ph.D. thesis, 234 pp, Mass.Inst. of Technol., Cambridge, 1991.

Filmer, P.E., M.K. McNutt, and C.J. Wolfe, Elastic thick-ness of the lithosphere in the Marquesas and Society Is-lands, J. Geophys. Res., 98, 19,565-19,577, 1993.

Gillot, P.Y., Y. Cornette, and G. Guille, Age (K-Ar) et con-ditions d'�edi�cation du soubassement volcanique de l'atollde Moruroa (Paci�que Sud), C. R. Acad. Sci., Ser. II,314, 393-399, 1992.

Goodwillie, A.M., and A.B. Watts, An altimetric and ba-thymetric study of elastic thickness in the central Paci�cOcean, Earth Planet. Sci. Lett., 118, 311-326, 1993.

Guille, G., Contribution �a l'�etude g�eologique des �les dePolyn�esie fran�caise: Les Gambiers, Ph.D. thesis, 215 pp,Univ. Paris XI, Orsay, France, 1974.

Guille, G., R.C. Maury, D. Buigues, H. Bellon, A. Gachon,and M. Caro�, L'Atoll de Moruroa (Polyn�esie fran�caise);III, Conclusions g�en�erales, Bull. Soc. Geol. Fr., 163,681-685, 1992.

Guille, G., G. Gouti�ere, and J.F. Sornein, Les atolls deMururoa et de Fangataufa (Polyn�esie Fran�caise), vol I.G�eologie, P�etrologie, Hydrog�eologie, 168 pp., Masson, Pa-ris, 1993.

Guillou, H., P.Y. Gillot, and G. Guille, Age (K-Ar) et pos-ition des �les Gambier dans l'alignement du point chaudde Pitcairn (Paci�que Sud), C. R. Acad. Sci., Ser. II,318, 635-641, 1994.

Hauri, E.H., J.C. Lassiter, and H.G. Barsczus, Lithosphericcontrols on the compositions of Austral Islands lavas: Iso-topic evidence from Raivavae and the southern Australs(abstract), Eos Trans. AGU, 78(46), Fall Meet. Suppl.,F828, 1997.

Herron, E.M., Sea- oor spreading and the cenozoic historyof the east-central Paci�c, Geol. Soc. Am. Bull., 83, 1671-1692, 1972.

Ito, G., M. McNutt, and R.L. Gibson, Crustal structure ofthe Tuamotu Plateau, 15�S, implications for its origin, J.Geophys. Res., 100, 8097-8114, 1995.

Johnson, R.H., and A. Mahalo�, Relation of Macdonald vol-cano to migration of volcanism along the Austral chain,J. Geophys. Res., 76, 3282-3290, 1971.

Krummenacher, D., and J. Noetzlin, Datations de coul�ees�eruptives dans di��erents archipels de la Polyn�esie Fran-�caise, Bull. Soc. Geol. Fr., 3, 131, 1966.

Kruse, S.E., Magnetic lineations on the anks of the Mar-quesas swell: Implications for the age of the sea oor, Geo-phys. Res. Lett., 15, 573-576, 1988.

L�enat, J.F., and P. Labazuy, Submarine morphologies andstructures of Reunion, in Le Volcanisme de la R�eunion-Monographie, edited by J.F. L�enat, pp. 43-74, Cent.Rech. Volcanol., Clermont-Ferrand, France, 1990.

L�eotot, C., P.Y Gillot, F. Guichard, and R. Brousse, Le vol-can de Taravao (Tahiti): Un exemple de volcanisme poly-phasique associ�e �a une structure d'e�ondrement, Bull.Soc. Geol. Fr., 6, 951-961, 1990.

Leroy, I., Evolution des volcans en syst�eme de point chaud:Ile de Tahiti, archipel de la Soci�et�e (Polyn�esie Fran�caise),Ph.D. thesis, 271 pp, Univ. Paris XI, Orsay, France, 1994.

Lesquer, A., Deep structure of Reunion Island from grav-ity data, in Le volcanisme de la R�eunion-Monographie,edited by J.F. L�enat, pp 19-27, Cent. Rech. Volcanol.,Clermont-Ferrand, France, 1990.

Macheski, L.F., Gravity relations in American Samoa andthe Society Islands, Paci�c Sci., 19, 367-373, 1965.

Mammerickx, J., E. Herron, and L. Dorman, Evidence fortwo fossil spreading ridges in the southeast Paci�c, Geol.Soc. Am. Bull., 91, 263-271, 1980.

Mayes, C.L., L.A. Lawver, and D.T. Sandwell, Tectonic his-tory and new isochron chart of the south Paci�c, J. Geo-phys. Res., 95 8543-8567, 1990.

McNutt, M.K., Lithospheric exure and thermal anomalies,J. Geophys. Res., 89, 11,180-11,194, 1984.

McNutt, M.K., Superswells, Rev. Geophys., 36(2), 211-244,1998.

McNutt, M.K., D.W. Caress, J. Reynolds, K.A. Jordahl, andR.A.Duncan, Failure of plume theory to explain midplatevolcanism in the southern Austral islands, Nature, 389,479-482, 1997.

Minster, J.B., and T.G. Jordan, Present-day plate motions,J. Geophys. Res., 83, 5331-5354, 1978.

Moore, J.G., W.B. Bryan, M.H. Besson, and W.R. Normark,Giant blocks in the South Kona landslide, Hawaii, Geo-logy, 23, 125-128, 1995.

Moore, J.G ., D.A. Clague, R.T. Holcomb, P.W. Lipman,W.R. Normark, and M.E. Torresan, Prodigious submar-ine landslides on the Hawaiian ridge, J. Geophys. Res.,94, 17,465-17,484, 1989.

Munschy, M., C. Antoine, and A. Gachon, Evolution tecto-nique de la r�egion des Tuamotu, oc�ean Paci�que central,C. R. Acad. Sci., Ser. II, 323, 941-948, 1996.

Nakagawa, I., et al., Precise calibration of scale values ofLacoste & Romberg gravimeters and international gravi-metric connections along the circum-Paci�c zone, Tech.Rep. Kyoto Univ., Kyoto, Japan, 1983.

Norris, A., and R.H. Johnson, Submarine volcanic eruptionsrecently located in the Paci�c by SOFAR hydrophones,J. Geophys. Res., 74, 650-664, 1969.

Obellianne, J.M., Contribution �a l'�etude g�eologique des �lesdes Etablissements Fran�cais de l'Oc�eanie. Sci. Terre, 3,1-146, 1955.

Okal, E.A., and A. Cazenave, A model for the plate tec-tonic evolution of the east-central Paci�c based on Seasatinvestigations, Earth Planet. Sci. Lett., 72, 99-116, 1985.

ORSTOM, Atlas de la Polyn�esie Fran�caise, Paris, 1993.Pautot, G., Analyse structurale de l'archipel des Tuamotu:

Origine volcano-tectonique, paper presented at 3�eme Col-loque des Sciences de la Terre, Univ. Montpellier, Mont-pellier, France, 1975.

Plou�, D., Gravity and magnetic �elds of polygonal prismsand application to magnetic terrain corrections, Geophys-ics, 41 (4), 727-741, 1976.

Robertson, E.I., Gravity e�ects of volcanic islands, N. Z. J.Geol. Geophys., 10(6), 1466-1483, 1967.

Rousset, D., A. Lesquer, A. Bonneville, and J.F. L�enat,Complete gravity study of Piton de la Fournaise volcano,Reunion Island, J. Volcanol. Geotherm. Res., 36, 37-52,1989.

Ryan, M.P., Neutral buoyancy and the mechanical evolutionof magmatic systems, in Magmatic Processes: Physico-chemical Principles, edited by B.O. Mysen, Geoch. Soc.Spec. Pub. 1, 259-287, 1987.

Ryan, M.P., The mechanics and three-dimentional internalstructure of active magmatic systems : Kilauea Volcano,

96 CLOUARD ET AL.: GRAVITY SIGNATURE OF MAGMA RESERVOIRS

Hawaii, J. Geophys. Res., 93, 4213-4248, 1988.Rymer, H. and G.C. Brown, Gravity �elds and the inter-

pretation of volcanic structures: Geological discrimina-tion and temporal evolution, J. Volcano. Geotherm. Res.,27, 229-254, 1986.

Sandwell, D.T., Antartic marine gravity �eld from high-density satellite altimetry, Geophys. J. Int., 109, 437-448,1992.

Service de l'Urbanisme, Carte topographique 1:20,000, Pa-peete, Tahiti, French Polynesia, 1992.

Sichoix, L., Le volcanisme de Polyn�esie Fran�caise : Ca-ract�erisation des points chauds et du superbombement�a partir d'une nouvelle synth�ese bathym�etrique, Ph.D.thesis, 297 pp, Univ. Fr. du Pac., Papeete, Tahiti, 1997.

Sichoix, L., and A. Bonneville, Prediction of bathymetry inFrench Polynesia constrained by shipboard data. Geo-phys. Res. Lett., 23, 2469-2472, 1996.

Smith, W.H.P., On the accuracy of digital bathymetric data,J. Geophys. Res., 98, 9591-9603, 1993.

Smith, W.H.P., and D.T. Sandwell, Marine gravity �eld fromdeclassi�ed Geosat and ERS-1 altimetry (abstract), EosTrans. AGU, 76 (46), Fall Meet. Suppl., F156, 1995.

Smith, W.H.P., and P. Wessel, Gridding with continuouscurvature splines in tension, Geophysics, 55, 293-305,1990.

Talandier, J., and E.A. Okal, The volcanoseismic swarms of1981-1983 in the Tahiti-Mehetia area, French Polynesia,J. Geophys. Res., 89, 11,216-11,234, 1984a.

Talandier, J., and E.A. Okal, New surveys of Macdon-ald seamount, southcentral Paci�c, following volcanoseis-mic activity, 1977-1983, Geophys. Res. Lett., 1, 813-816,1984b.

Talandier, J., and E.A. Okal, Crustal structure in the Societyand Tuamotu Islands, French Polynesia, Geophys. J. R.Astron. Soc., 88, 499-528, 1987.

Turner, D.L., and R.D. Jarrard, K-Ar dating of the Cook-Austral island chain: A test of the hot spot hypothesis,J. Volcano. Geotherm. Res., 12, 187-220, 1982.

Walcott, R.I., Flexure of the lithosphere at Hawaii, Tectono-physics, 9, 435-446, 1970.

Walker, G.P.L., Three Hawaiian calderas: An origin throughloading by shallow intrusions?, J. Geophys. Res., 93,14,773-14,784, 1988.

Watts, A.B., An analysis of isostasy in the world's oceans,1, Hawaiian-Emperor seamount chain, J. Geophys. Res.,83, 5989-6004, 1978.

Watts, A.B., and N.M. Ribe, On geoid heights and exureof the lithosphere at seamounts, J. Geophys. Res., 89,11,152-11,170, 1984.

Watts, A.B., J.R. Cochran, and G. Selzer, Gravity anom-alies and exure of the lithosphere: A three-dimensionalstudy of the Great Meteor Seamount, northeast Atlantic,J. Geophys. Res., 80, 1391-1399, 1975.

Watts, A.B., J.H. Bodine, and N.M. Ribe, Observations of exure and the geological evolution of the Paci�c Oceanbasin, Nature, 283, 532-537, 1980

White, W.M., and R.A. Duncan, Geochemistry and geo-chronology of the Society Islands: New evidence for deepmantle reclycling, in Earth Processes: Reading the Iso-topic Code, Geophys. Monogr. Ser. vol 95, edited by A.Basu and S. Hart, pp. 183-206, AGU, Washington, D.C.,1996.

Young, R.Y., and I.A. Hill, An estimate of the e�ectiveelastic thickness of the Cape Verde Rise, J. Geophys. Res.,91, 4854-4866, 1986.

V. Clouard and A. Bonneville, Laboratoire de G�eo-sciences Marines et T�el�ed�etection, Universit�e de la Poly-n�esie Fran�caise, BP 6570 Faaa A�eroport, Tahiti, FrenchPolynesia. (e-mail:clouard@ufp.pf; bonneville@ufp.pf)H.G. Barsczus, GBE - UMR 5569 - CNRS, and Uni-

versit�e de Montpellier II, 34095 Montpellier Cedex 5.(e-mail:barsczus@dstu.univ-montp2.fr)

(Received January 29, 1998; revised October 8, 1999; acceptedNovember 4, 1999.)

This preprint was prepared with AGU's LATEX macros v5.01.File jgr99_pp formatted July 11, 2000.

4.3 Compl�ements 97

4.3 Compl�ements

4.3.1 Controle des donn�ees gravim�etriques terrestres utilis�ees

Les donn�ees terrestres proviennent d'une part de l'IRD1, anciennement l'ORSTOM2

(Barscsuz, donn�ees non publi�ees), et d'autre part, de l'UPF3, anciennement l'UFP4 (Leroy,1994).

Les donn�ees de l'UPF (315 mesures) ont �et�e acquises en mai 1994, sur l'�le de Tahiti,avec un gravim�etre Lacoste et Romberg, mod�ele G, un r�ecepteur GPS5 et un altim�etre.Elles ont �et�e acquises et trait�ees par Leroy (1994).

Les donn�ees terrestres de l'IRD ont �et�e acquises �a la �n des ann�ees 1970. Ellesnous ont �et�e transmises sous forme de �ches de terrain manuscrites et de �ches desynth�ese dactylographi�ees. Les donn�ees comprennent pour chaque station de mesure : laposition en coordonn�ees UTM6 et/ou g�eographiques, l'altitude, la mesure instrumentale,les corrections instrumentales et luni-solaires, le rattachement �a la base locale, la valeurde g mesur�ee en mGal. Ces donn�ees n�ecessitent un pr�e-traitement.

{ Le positionnement de toutes les stations de mesures est v�eri��e en les faisant�gurer sur les cartes. Des erreurs de conversion UTM/Longitude-latitude sontrecti��ees pour Huahine. Quatres mesures �gurant en mer sont supprim�ees, tandisque celles r�ealis�ees dans les lagons de Rangiroa, Manihi et Moruroa, prises �a mar�eebasse sur des rochers a�eurants non cartographi�es sont conserv�ees (Barscsuz,communication personnelle, 1996).

{ Altitude : Les mesures ont �et�e r�ealis�ees �a l'aide d'un altim�etre Nadeau, �etalonn�eaussi souvent que possible aux bases. Des v�eri�cations statistiques sont r�ealis�eespar rapport aux cartes topographiques IGN7 et montrent la coh�erence des valeursrapport�ees.

{ Corrections et calibration instrumentales : les valeurs de la d�erive luni-solaire�edit�ees en quelques points �a la date des mesures montrent la validit�e de la correctiond�ej�a e�ectu�ee. Les valeurs de la d�erive instrumentale, suppos�ee lin�eaire, sont recalcu-l�ees �a partir des mesures �a la base locale faites toutes les demi-journ�ees. Nousretrouvons les valeurs utilis�ees dans les �ches dactylographi�ees.

{ Rattachement au r�eseau gravim�etrique international : la seule correction apport�eeaux donn�ees est �nalement le changement de valeur de la gravit�e absolue de labase du LDG8 de Pamata��, Tahiti. Cette base fait partie du r�eseau gravim�etrique

1Institut de Recherche pour le D�eveloppement2Institut Fran�cais de Recherche Scienti�que pour le D�eveloppement en Coop�eration3Universit�e de la Polyn�esie Fran�caise4Universit�e Fran�caise du Paci�que5Global Positioning System6Universal Transverse Mercator7Institut G�eographique National8Laboratoire de G�eophysique du Commissariat �a l'Energie Atomique

98 Les chambres magmatiques fossiles des �les

international de la zone circum Paci�que (Nakagawa et al., 1983), sous le nom dePPT J7912. Sa mesure absolue vaut 978 627.249 mGal. La valeur utilis�ee par l'IRDest 978 627.35 mGal, soit un �ecart de 0.1 mGal qui est report�e sur l'ensemble desvaleurs.

4.3.2 D�etermination des masses volumiques

Les masses volumiques sont d�etermin�ees dans le calcul de l'anomalie r�esiduelle isosta-tique en minimisant l'�ecart entre l'anomalie �a l'air libre observ�ee et l'anomalie gravim�etri-que calcul�ee en tenant compte de la topographie, la bathym�etrie et la exure de lalithosph�ere. Il nous faut d�eterminer la masse volumique de la croute, �c, celle du remplissa-ge de la croute �a la suite de sa exure, �f , et celle de la partie sous-marine de l'�edi�ceavec �c � �f � �s.

Le calcul est e�ectu�e tout d'abord au n�ud de grilles r�egionales pour chaque archipel.Ainsi, la masse volumique de la croute est obtenue partout �egale �a 2900 kgm�3. Cettevaleur est en bon accord avec des r�esultats r�ecents obtenus sur la portion sup�erieure dela croute oc�eanique (Gilbert et Johnson, 1999; Johnson et al., 2000) : la valeur mesur�ee�a petite �echelle (grain density) de la masse volumique de la roche est de l'ordre de 2960kg m�3, mais la porosit�e �etant importante dans le premier kilom�etre, sa masse volumiquee�ective est diminu�ee.

1520

20

25

25

2600

2700

2800

2900

3000

Rho

_fill

ing

(kg.

m-3

)

2600 2700 2800 2900 3000

Rho_sous-marine (kg m-3)

Fig. 4.1 { D�etermination des massesvolumiques sous-marine �s et deremplissage �f de Tahaa : isocontours tousles 5 mGal du RMS entre les anomaliesobserv�ees et calcul�ees en fonction desdi��erentes valeurs de �s et �f .

Un calcul similaire est ensuite e�ectu�e aux points des stations de mesure �a terrea�n de d�eterminer la masse volumique de l'�edi�ce sous-marin. La �gure 4.1 repr�esente lesvariations du RMS en fonction des couples (�s,�f) choisis. On peut noter tout d'abordqu'une variation de 50 kgm�3 induit une variation du RMS de l'ordre de 5 mGal. C'estla valeur de l'erreur initiale sur les donn�ees, le pas de variation des masses volumiquesest donc correctement choisi. Dans l'exemple de Tahaa pr�esent�e sur la �gure 4.1, deuxcouples ont un RMS inf�erieur �a 10 mGal, (2750,2850) et (2700,2900), nous avons conserv�e

4.3 Compl�ements 99

le second couple puisque son RMS est le plus faible.

La �gure 4.2 montre les r�esultats du calcul gravim�etrique, toujours sur l'�le de Tahaa,pour les deux couples (�s,�f ) qui pr�esentaient les plus petits RMS. Ces deux couplesfournissent chacun une anomalie gravim�etrique tr�es voisine. Le r�esultat du calcul pourune masse volumique sous-marine de 100 kg m�3 plus �elev�ee est �egalement repr�esent�e. Ilmontre qu'il se produit un d�ecalage r�egulier de 10-15 mGal en plus �a chaque station demesure. Comme l'analyse porte sur l'anomalie r�esiduelle isostatique, qui est la di��erenceentre l'anomalie observ�ee et l'anomalie calcul�ee, le choix des masses volumiques quiproduisent le plus petit RMS s'impose donc.

Données observéesDonnées calculées (rs=2700 kg m-3, rf=2900 kg m-3)Données calculées (rs=2750 kg m-3, rf=2850 kg m-3)

Nombre de stations

AA

L (m

Gal

)

Données calculées (rs=2800 kg m-3, rf=2900 kg m-3)260

160

240

220

200

180

10 20 30 40

Fig. 4.2 { E�et des variations des masses volumiques dans le calcul gravim�etrique : valeursde l'anomalie gravim�etrique aux stations de mesure en fonction des di��erents couples demasse volumique utilis�es. En dehors des deux couples mis en �evidence sur la �gure 4.1, cegraphique montre qu'une augmentation de 100 kgm�3 de �s produit un d�ecalage de 10-15mGal.

4.3.3 La loi de Gauss appliqu�ee aux champs de gravit�e

Lors des di��erentes revues de l'article sur l'�etude gravim�etrique des �les de Polyn�esiefran�caise, il nous a �et�e sugg�er�e par T. Hildenbrand d'utiliser la loi de Gauss appliqu�eeaux champs de potentiel pour d�eterminer la masse en exc�es qui a engendr�e l'anomalie degravit�e. La loi de Gauss dit que M, la masse totale, dans une r�egion R est proportionnelle �ala composante normale de l'attraction g somm�ee sur S, la fronti�ere ferm�ee de cette r�egion(e.g. Blakely, 1995).

ZSg:ndS =

ZR5gdv; (4.1)

= �4�GMT :

Cette loi se transforme si l'on consid�ere que le volume est ferm�e par une surface plane

100 Les chambres magmatiques fossiles des �les

(altitude z=0), et que l'on suppose que la masse est su�samment loin pour que les termesen r puissent sortir de l'int�egrale. g se d�ecompose en une composante calcul�ee �a traversla surface plane, gz, et une �a travers un h�emisph�ere

ZSg:ndS = �

ZSpgzdS �

Z2�

0

Z �

�=2

@U

@rr2sin�d�d� (4.2)

= �ZSpgzdS � 2�GMT

Z �

�=2sin�d�

= �ZSpgzdS � 2�GMT :

En rempla�cant l'�equation 4.1 dans 4.2, il vient que I, la valeur de la composanteverticale de la gravit�e gz somm�ee sur un plan in�ni, est proportionnelle �a la masse MT

situ�ee sous ce plan :

I =ZSpgzdS = 2�GMT : (4.3)

L'avantage de cette m�ethode est de conduire �a une estimation de la masse ayantengendr�e l'anomalie ind�ependamment de la g�eom�etrie de cette masse. En pratique, les 2inconv�enients de la formule 4.3 sont que la zone d'int�egration est une aire limit�ee et que lescorrections r�egionales d�ej�a prises en compte dans l'anomalie r�esiduelle ont probablementtronqu�e son extension verticale. On peut rem�edier �a ces 2 probl�emes en utilisant plutotla formule suivante (Grant et West, 1965) :

4GM = (arctanXY

zpX2 + Y 2

)�1I (4.4)

o�u [-X,X] et [-Y,Y] correspondent �a la taille du plan horizontal utilis�e dans le calcul de4.1, et z la profondeur de la source. Pour obtenir une estimation de la profondeur, lar�egle g�eom�etrique simple suivante est souvent ad�equate : z = 0:6w1=2. Cette r�egle d�erivede la d�etermination g�eom�etrique de la profondeur du centre de la sph�ere z = 0:65w1=2

et de celle d'un cylindre horizontal in�ni, z = 0:5w1=2 o�u w1=2 est la distance du centrede l'anomalie au point o�u la valeur de l'anomalie vaut la moiti�e de la valeur maximum.En d'autres termes, on introduit une notion de g�eom�etrie sur le corps dont on cherche lamasse.

Nous avons appliqu�e les formules 4.3 et 4.4 aux �les de Tahiti et Bora Bora et compar�eles r�esultats avec ceux obtenus avec le mod�ele de l'ellipso��de. Les r�esultats sont pr�esent�esdans le tableau 4.1. Pour le passage de la masse au volume, les masses volumiques utilis�eessont de 300 kgm�3 pour Bora Bora et 400 kgm�3 pour Tahiti.

L'�evolution des r�esultats pour ces 2 �les est comparable, quelle que soit la m�ethode.La m�ethode de calcul utilisant la loi de Gauss corrig�ee fournit des r�esultats tr�es similaires�a ceux obtenus dans le cas o�u l'on consid�ere a priori la forme de la chambre connue etellipso��dale.

4.3 Compl�ements 101

Tab. 4.1 { Comparaison des volumes des chambres magmatiques obtenus par di��erentesm�ethodes.

Formule de Gauss Formule de Gauss corrig�ee Ellipso��deMasse totale Volume (km3) Masse totale Volume Volume

Bora Bora 1.354E+13 45 2.795E+13 93 107Tahiti 2.715E+13 678 4.274E+13 1068 1108

4.3.4 Choix de la loi liant chambre et �le

La repr�esentation du volume de la chambre magmatique fossile par rapport au volumede l'�le implique qu'il existe une relation entre ces 2 param�etres, valable pour chaque�edi�ce. Nous avons test�e di��erentes possiblit�es :

{ loi polynomiale d'ordre 1 et 2 ;{ loi exponentielle d'ordre 1 et 2.

0 5000 10000 15000−200

0

200

400

600

800

1000

1200

Volume ile, en km3

Vol

ume

cham

bre

Correlation volume ile et chambre

0 5000 10000 15000−300

−200

−100

0

100

200

300

Volume ile, en km3

Res

idus

en

poly

nom

e

Residus

0 5000 10000 150000

500

1000

1500

2000

2500

3000

Volume ile, en km3

Vol

ume

cham

bre

0 5000 10000 15000−2000

−1500

−1000

−500

0

500

Volume ile, en km3

Res

idus

en

expo

nent

iels

Fig. 4.3 { R�egression suivant une loi polynomiale (en haut) et suivant une loi exponentielle(en bas) et repr�esentation des r�esidus. Les points les plus �a droite de chaque courbe sontTahiti et Rangiroa.

Plusieurs crit�eres permettent de s�electionner une loi : (1) la distance entre les donn�eesobserv�ees et celles obtenues en utilisant la loi doit etre la plus petite possible ; (2) lesr�esidus doivent etre d�ecorr�el�es. Dans le cas o�u plusieurs lois satisfont ces 2 premiers

102 Les chambres magmatiques fossiles des �les

crit�eres, on peut choisir de mani�ere subjective la loi la plus simple pour l'esprit : unordinateur ne fait pas de di��erence entre un polynome d'ordre n et une droite, en revanche,pour l'�il humain, une droite se repr�esente plus facilement.

La �gure 4.3 pr�esente les r�esultats obtenus d'une part avec un polynome d'ordre 1 etune exponentielle d'ordre 1. Nous avons �elim�e les ordres 2 : les RMS pour un polynomed'ordre 1 et pour un polynome d'ordre 2 valent respectivement 95 et 89 km3, il n'y adonc pas de raison de choisir l'ordre 2. La courbe en exponentielle d'ordre 2 s'approchedu point haut qui repr�esente Tahiti et s'in �echit vers le point bas qui repr�esente Rangiroa.Ce changement de direction n'a probablement pas de r�ealit�e car lorsque l'on ajoute l'�lede la R�eunion dans la �gure �nale de l'article, la courbe se prolonge bien vers le haut. Sil'on compare maintenant les r�esultats dans le cas d'une loi polynomiale ou exponentielle(Figure 4.3), les r�esidus sont bien d�ecorr�el�es du volume de l'�le, et le meilleur RMS estcelui de la loi polynomiale avec 95, tandis que la loi exponentielle pr�esente un RMS de 417.Ainsi, une relation lin�eaire entre le volume de l'�le et le volume de la chambre magmatiquefossile est mise en �evidence.