Geophys. J. R. astr. Soc. (1980) 63, 2 3 3 - 2 5 2

On the response of the ocean lithosphere to sea-mount loads from Geos 3 satellite radar altimeter observations

Anny Cazenave, Bernard Lago and Kien Dominh Croupe de Recherches de Gdoddsie Spatiale, Centre National d'Etudes Spatiales, Toulouse, France

Kurt Lambeck Research School of Earth Sciences, Australian National University, Canberra, Australia

Received 1980 January 29;in original form 1979 September 17

Summary. Short wavelength anomalies in the geoid, derived from Geos 3 satellite radar altimeter data, have been investigated in the southern Indian Ocean and in French Polynesia. A number of these anomalies, associated with sea-mounts or volcanic islands, can be explained by regional isostatic compensation models, yielding estimates of the flexural rigidity and the effective elastic thickness H of the oceanic lithosphere. This thickness appears to be about one third of the seismic estimates for this thickness. The Halso indicates some age dependence, compatible with the models of the thermal lithosphere. These results are in agreement with the results of previous studies on the flexure of the lithosphere.

Introduction

The long-wavelength anomalies of the Earth's gravity field or of the geoid provide direct evidence for the non-hydrostatic state and, by implication, for convection in the mantle. This is particularly seen in the relation between these anomalies and the kinematic expressions of convection, namely the plate margins. Despite these correlations, however, the use of gravity or geoid data as constraints on convection models has had only a very limited success. Gravity interpretations have been more successful in the study of regional geophysical problems. Studies of the deformation of the lithosphere and mantle to surface loads, for example, give insight into the response of this upper layer to forces upon it, or it may establish values for the mantle viscosity. Examples of the use of gravity to constrain ocean lithospheric models include studies of (i) ocean ridges to determine both the ridge structure and the nature of the flow beneath it (e.g. McKenzie 1967; Lambeck 1972; Parker & Oldenburg 1973; Sclater, Lamer & Parsons 1975), (ii) loading of the ocean lithosphere by sea-mounts (e.g. Vening-Meinesz 1941; Gunn 1943; Watts & Cochran 1974; Walcott 1976) and (iii) flexure of the ocean lithosphere seawards of the ocean trench (Hanks 1971; Watts & Talwani 1974; Melosh 1978).

In the above examples, the gravity measurements are based on either surface observations or satellite results. Measurements of the shape of equipotential surfaces, specifically the

234 A. Cazenave et al.

geoid, by astro-geodetic techniques, have received only very limited attention in geo- physical studies. Recently it has been possible to measure the shape of the ocean surface directly with satellite-borne radar altimeters on Skylab, Geos 3 and Seasat. By either assimilation or reduction these measurements provide a direct estimate of the geometry of the geoid with a precision ranging from a few tens of centimetres to about a metre and with a spatial resolution of a few tens of kilometres. Geos3 and Seasat have provided homogeneous and uniformly high-quality data over the oceans, achieving within a year or two the nearly total coverage of the world's oceans that surface measurements failed to give in more than two decades of effort. The high precision, good spatial resolution and uniformity of the altimeter data makes it very useful for geophysical studies of the ocean lithosphere. Initial attempts at this have been made by Haxby & Turcotte (1978) and Roufosse (1978), using individual altimeter profiles, and by Cazenave, Lambeck & Dominh (1 979), using two-dimensional altimeter-derived geoids. Whereas altimeter profiles are adequate for linear features like volcanic chains, it appears necessary to use two-dimensional altimeter geoids for small isolated sea-mounts. We have used the latter approach, with particular emphasis on geoid anomalies over sea-mounts in the southern Indian and equatorial Pacific Oceans, in regions where surface gravity data has hitherto provided only very limited information.

The close correlation between geoid heights and sea-floor topography noted by most Gem3 investigators suggest strongly that both, in part, have a common origin, an origin intimately related to isostatic compensation of the topographic load. In regions where the load can be considered to have been placed on the ocean floor without there having been major perturbations in the thermal structure of the underlying lithosphere, a model of regional compensation may be an appropriate description of the isostatic state. This could be so for sea-mounts formed in the relatively short time interval away from active ridge crests. Where the topographic load is very much a consequence of thermal processes in the upper mantle, a local isostatic compensation mechanism may be more appropriate since the higher temperature lithosphere may not be able to support significant shear stresses. This could be the case for ocean ridge topography. Both cases can be modelled by the theory of bending of elastic plates overlying a weaker or a fluid substratum, the distinction between the two being reflected by the numerical value of the lithospheric flexural rigidity. Such a bending model appears to apply well to some of the areas studied in this paper and permits an effective flexural rigidity to be estimated, a parameter that is related to the 'elastic' thickness of the lithosphere and to the elastic moduli. A study of loads on different age lithosphere may then indicate an age dependence of this elastic thickness which in turn has consequences on the thermal state and evolution of the ocean lithosphere.

2 Geos 3 altimeter data and geoid computation

A cooperative program during 1976 and 1977 between the Terres Australes et Antarctiques FranCaises, the Groupe de Recherches de GCodCsie Spatiale and the United States Defence Mapping Agency, resulted in Geos3 altimeter data being collected in several regions not otherwise covered by the US ground-based tracking networks of this spacecraft. These areas included the Southern Indian Ocean, from about 40" to 85" east longitude and from - 30" to - 66" latitude, centred on Kerguelen and the equatorial Pacific, from 130" to 165" west longitude and from + 5" to - 35" latitude, centred on French Polynesia.

Balmino et al. (1979) have described the successive steps required to compute the geoids from the altimeter data; the methods for preprocessing, filtering and adjusting the altimeter profiles and the Bjerhammar-type predictor used to estimate the geoid heights over a regular

Response of ocean lithosphere to sea-mount loads 23 5

236 A. Cazenave et al.

WEST LONGITUDE Figure 2. Geos 3 altimewt geoid over the equatorial Pacific (1 rn contour interval).

grid - in these cases with a step size in latitude and longitude of 0.5". Figs 1 and 2 illustrate the results for The two regions. The contour interval is 1 m and heights are referenced to an ellipsoid of semi-major axis 6 378 155 m and a flattening of 1/298.255. The geoid precision is estimated to be about 50cm. The spatial resolution is dependent upon the spacing between nearby altimeter profiles and varies from about 50 km to about 200km in the less well sampled areas. Hence the detail in geoid varies somewhat over the two areas.

3 Structure of the two oceanic areas

3.1 S O U T H INDIAN OCEAN

The bathymetry of the southern part of the Indian Ocean is illustrated in Fig. 3 and is based on the regional maps of Schlich (1975) and Goslin & Schlich (1979). Several aseismic ridges

Response of ocean lithosphere to sea-mount loads 23 7

I

23 8 A. Gzzenave et al.

c .s 3

Response of ocean lithosphere to sea-mount loads 239 occur of which the Kerguelen plateau, including the Kerguelen and Heard Islands, is the longest in the area. This plateau is believed to be oceanic in origin, rather than continental (see Watkins et aZ. 1974; Houtz, Hayes & Mark1 1977; Luyendyk & Rennick 1977) although Dosso et al. (1979) conclude that the petrological and geochemical evidence remains incon- clusive. The plateau is associated with distinct positive geoid anomalies, To the south of Kerguelen, at about - 57' latitude and between about 67" and 7 1" east longitude, a number of sea-mounts (USSR Academy of Sciences 1975) of unknown ages are associated with smaller geoid anomalies.

Towards the west of the Kerguelen-Heard plateau lies the Crozet plateau and the Ob-Lena-Marion Dufresnes seamounts. Despite some recent work (Schlich 1975; Goslin & Schlich 1979) the region south of Crozet is still poorly understood. Crozet Island itself is on the eastern limit of a fairly extensive submarine plateau extending to Prince Edward Island and the western branch of the Indian Ocean Ridge. These islands appear to be remnants of shield volcanoes dating from the Pliocene or more recent (Gunn et el. 1970). The Ob, Lena and Marion Dufresnes sea-mounts, with a fourth sea-mount between the last two, run in a west-east direction, roughly parallel to the magnetic anomalies, and they all

240 A. Cazenave et al.

appear to sit on lithosphere that is of the same age, probably upper Cretaceous (Schlich 1975). This is unlike most sea-mount chains where the age of the lithosphere changes systematically from one end of the chain to the other. Their age is unknown although Goslin & Schhch (1979), from the shallow seismic structure around the base of Marion Dufresnes, interpret them as being old structures. The Crozet plateau, the sea-mount chain to the south, and the intervening Crozet basin, are also associated with a broad positive gravity anomaly of magnitude and wavelength comparable to that found over the Kerguelen-Heard plateau. To the north, the area includes part of the eastern branch of the Indian Ocean Ridge but there is no clear geoid anomaly associated with t h s feature. In particular the Ile d ’hs t e rdam and Ile St Paul do not result in geoid deflections, even for those altimeter profiles that pass immediately over the islands, indicating that these features are locally compensated at shallow depths as befits their ridge position.

c I-

Q,

WEST LONGITUDE Figure 6. Residual geoid over the equatorial Pacific.

Response of ocean lithosphere to sea-mount loads 24 1 The geoid is dominated by a steep slope in the north-eastern corner and by the broad

highs over the Kerguelen-Heard plateau and over the Crozet basin. These features are also clearly seen in all the recent free-air satellite-based global gravity solutions and they would appear to originate from density anomalies that lie mainly in the upper mantle (Lambeck 1976). These long wavelength features appear to be only partly correlated with the sea- floor topography. Fig. 4 illustrates the geoid after the low degree harmonics, of degree Q 10, of Balmino, Reigber & Moynot (1978) have been removed.

3.2 E Q U A T O R I A L P A C I F I C

The schematic bathymetry of the region, redrawn from the charts by Mamerickx et al. (1973) is illustrated in Fig. 5. Several linear volcanic chains, occur in this area and include the Society, Tuamotu, Line and Marquesas Islands. They form nearly parallel traces which intersect the East Pacific Rise at approximate right angles. Generally the islands are much younger than the ocean floor on which they are situated and rise above the sea-floor as distinct volcanic cones rather than as peaks of a prominent submarine ridge. The Marquesas chain, for example, consists of six main islands, separated from each other by a few tens of kilometres with ages ranging from 3.8 to 1.3 Myr (Duncan & McDougall 1974) while the lithospheric age upon which they sit is estimated to be about 45 f 5 Myr from the magnetic lineations of Pitman, Larson & Herron (1974) and from the results of sites 74 and 75 of the Deep Sea Drilling Project (Tracey et al. 1971). The Society Islands range in age from about

Table 1. Ages, flexural rigidity D, effective elastic thickness H , maximum deformation wmax and maximum stress difference.

Region Sea-floor age (Myr)

Crozet - 80 Ob , Lena, - 80 Marion Dufresnes

Marquesas - 44-46 Society - 70 Manihiki - 110

Age of loads (Myr)

- 5 ?

- 1 - 4 -0.5-4 - 100

D ( 10 30 dyne cm)

1 .o 1 .o

0.4 0.8 0.8

22.5 10.4 6.5 22.5 7.4 7 .O

16.5 6.8 3.8 20.9 6.0 2.5 20.9 7.1 2.2

4.0 to 0.3 Myr (Duncan & McDougall 1976) and sit on a lithosphere of about 7 0 f 8 Myr old. The island ages are based on rock samples collected from sea-mounts that rise above sea level and the actual ages of the formation may be somewhat older. The sea-mounts are all associated with unambiguous geoid anomalies similar to those found over the Indian Ocean sea-mounts. To the north-west of these areas the altimeter passes show distinct geoid anomalies over the Manihiki plateau and Tongareva. The age of this plateau appears to be at least 106 Myr (Schlanger et al. 1976), similar to that of the surrounding lithosphere. The age of Tongareva is unknown. Table 1 summarizes the various features and their ages. Numerous other sea-mounts in this area are not associated with clear geoid anomalies but this is more a consequence of the limited spatial distribution of the altimeter data than of the geophysics. Like the Indian Ocean geoid the Pacific geoid is dominated by long-wavelength anomalies that are mainly of upper mantle origin and Fig. 6 illustrates the residual geoid upon removal of the harmonics of degree G 10.

242 A. Cazenave et al. 4 The elastic plate model

The theory of the deformation of loaded elastic plates overlying a weaker or fluid medium is well developed in the engineering mechanics literature (e.g. Reisner 1946; Frederick 1956; Timoshenko & Woinowsky-Kreiger 1959) and has been reviewed in the recent geo- physical literature by Brotchie & Silvester (1969) and Brotchie (1971). The basic equation expressing the deformation w ( x , y ) of the elastic plate of flexural rigidity D due to a normal load P(x, y ) is

D V 4 w + p m g w = P. (1)

Pm is the density of the underlying fluid-like medium. The deformation is positive down- ward. D is the flexural rigidity defined as

H 3 - P A + P

1 2 ( 1 - 2 ) 3 x + 2 p -- - EH3

D =

where E = Young’s modulus, u = Poisson’s ratio, g = rigidity, A = second Lami parameter, H = plate thickness.

In the sea-mount problem there is usually little bathymetric evidence for large deflections of the sea-floor in the vicinity of the load and this has been attributed to a filing-in of the depression with the same basalts that formed the volcanic load and with consolidated sedi- ments (Fig. 7). With this assumption of an extra load pcgw on the upper surface, equation (1) becomes

D V 4 w + ( p m - p c ) g w = P . (3 1 If loading occurs under water of density p o then P = ( p , - po)gh where h is the height of the load, also of density p c , above the fill-in layer. The solution to equation ( 3 ) for a point load was discussed by Hertz (1895) and is conveniently expressed in terms of Bessel-Kelvin functions. That is, the deformation w at a distance r from the point load is

where I = [D/(pm - p,)g] ‘’4 is the ‘radius of relative stiffness’. I-’ is also referred to as the flexural parameter. w and dw/dr are taken to be zero at infmity. Analytical solutions of equation (3) exist for simple axisymmetric loads but for most geophysical problems it will be necessary to integrate equation ( 3 ) numerically over the volume of the load so as to obtain the total deformation w ( x , y).

sea surface sea water ( geoid 1 p = 1.03

Figure 7. Geometry of the elastic flexure model for a loaded unfractured lithosphere.

Response of ocean lithosphere to sea-mount loads 243 A number of simplifying assumptions made in these models need further investigation.

These include (i) the neglect of the effects of bending of shear stresses and normal pressures in planes parallel to the surface of the plate, (ii) the requirement that deflections are small compared with plate thickness, (iii) the neglect of any pre-stress in the plate, and (iv) the choice of boundary conditions. The effect of any depth dependence of the elastic para- meters should also be investigated as should any non-elastic response of part or all of the plate (Walcott 1970; Liu & Kosloff 1978).

Once the deflection w is known the stress in the x - y plane follows from (e.g. Timo- shenko & Woinowsky-Krieger 1959)

1 (5a)

1 where z is measured downwards from the x y plane lying in the middle of the plate. The upper surface of the plate is at z = - H / 2 , the lower surface at z = H / 2 . u,, and Uee reach absolute maxima when z = f H / 2 . The vertical stress is (see, e.g. Frederick 1956)

where q 1 is the load at z = - H / 2 , equal to P(x, y ) and q 2 = pmgw is the load at z = + H / 2 . The maximum value for uzz is p,gh at z = - H / 2 . The remaining stress-tensor elements urz, Ore and Goz are generally small compared with the maximum values attained by u,,, 000 and uzz and these last three components can be considered as the principal stresses on the surfaces of the plate. For axisymmetric loads of small areal extent, the maximum stresses occur below the centre of the load. Here, at z = - H / 2 , urr = 000, uzz = - P and all three stresses are compressive. The maximum stress-difference T,, will be la,, - uzzl. At z = + H / 2 , u, and Dee are tensile, uzz = - pmgw is compressive and T,,, = I u, t uzzl. For simple load geometries, analytical solutions for the stresses can be found but in most geological solutions equations ( 5 ) will have to be evaluated numerically.

5 Results

The estimation of the effective flexural rigidity and related parameters involves several successive steps in the data analysis:

(i) Estimation of the vertical deflection of the lithosphere by numerically integrating the point load response ( 4 ) over the load using the actual bathymetry. In the case of the south Indian Ocean the bathymetric maps of Schlich (1975) were used while for the equatorial Pacific we used the maps of Monti & Pautot (1975). These maps were digitized and mean values estimated for a 10' x 10' grid size. Table 1 summarizes the maximum deformation occurring below the load.

(ii) Computation of the gravity anomalies over the sea-mount. Gravity perturbations result from, (a) the topographic load, of effective density pc-po, (b) the fill-in of the de- flection of effective density pc - p s where ps is the density of the fa-in, (c) the density contrast pm - pc at the deformed crust-mantle interface, (d) the displacement of other equal density surfaces within a plate with a density gradient and (e) any effect of com- pression. As the base of the elastic plate will usually be defined by a specific geotherm there

244 A. Cazenave et al.

will be no density contrast here, and as density gradients in the upper lithosphere are generally small, the main contributions to the gravity perturbations come from (a), (b) and (c). Adopting the usual assumption that p, = ps only the contribution: (a) and (c) contribute to the gravity anomaly. Gravity is computed numerically on the ocean surface, following the method given by Talwani (1973) for isolated bodies of arbitrary shape on a spherical earth.

(iii) Computation of the geoid heights from the gravity anomalies using the Stokes integral (see Heiskanen & Moritz 1967). The area over which the gravity anomalies have been computed is taken to be sufficiently large so that at the limits the contribution of the deflection model to gravity is zero. In order to compute the geoid over the same area, the grid of gravity anomalies has been artificially extended by zero values. The geoid deflections for each area have been computed for different values of flexural rigidity D and compared with the observed residual geoid. If h, is the computed geoid height and ho is the observed residual height (the observed less the contributions from the long wavelengths), then that value of D is selected that minimizes the sum of the residuals

for the n grid areas. With this test, both amplitude and wavelength contribute to the estimate of the rigidity. Fig. 8 illustrates the computed geoid over the Crozet plateau for several values of D. A comparison between model geoids and observed residual geoid is also given in

11) u LmOm

L8 BATHYMETRY

-68

OBSERVED GEOlD 53 La

Figure 8. Bathymetry, observed geoid and computed geoid heights for different flexural rigidities, for a o z e t plateau. Geoids contours are at 1 m intervals.

Figure 9. rigidities.

Response of ocean lithosphere to sea-mount loads 245

c

0 200

DISTANCE (Km) Crozet plateau: observed and computed geoid heights in profile form, for different flexural

The profiles’ direction coincides with the maximal longitudinal extension of the plateau.

-=-

COMPUTED GEOlD

D=L1OZ9dyn.cm

145W 135W

MARQUESAS ISLANDS Figure 10. Bathymetry, observed geoid and best fitting geoid for the Marquesas Islands.

246 A. Cazenave et al.

profile form (Fig. 9). The model geoids are quite sensitive to the choice of D and the optimum value of D is 1.0~ 10mdyne cm. Smaller values, implying a more localized compensation, result in shorter geoid anomaly wavelengths while larger values, implying that the load is carried over a much larger area of the plate, results in an overly smooth geoid. The Ob, Lena, Marion Dufresnes chain also gives D = 1 .O x low dyne cm for the best fitting geoid. In both c a m the regional compensation model is consistent with the observed geoid.

Figs 10, 11 and 12 show the results from the equatorial Pacific; the Marquesas, Society and the Manihiki and Tongareva Islands. The flexural rigidity for the Marquesas Islands, D = 4.0 x 1029dyne cm, is somewhat lower than that for the other areas for which the best fitting flexural rigidity is D = 8.0 x 1029dyne cm. The uncertainty estimates in D are of the order of 25 per cent.

(iv) Estimation of the elastic plate thickness. Table 1 summarizes the thickness H of the plate as inferred from D using the definition ( 2 ) and the elastic parameters appropriate for low frequency deformation (see below). With the above uncertainty estimate in D, H is determined to within about 10 per cent.

(v) Estimation of the maximum stress-differences in the deformed plate. For the loads considered here we have simply taken

TmaX = urr(x = 0 ; y = 0)

as an estimate of the maximum stress-difference occurring anywhere in the plate. In order to evaluate urr we require the elastic parameters p, X, E, v of the lithosphere. The thickness of the elastic layer is of the order of 20 km (see below) and appropriate average seismic values

OBSERVED RESIDUAL

GEOlO

156W 148W

-15

COMPUTED GEOID

0. 8.10 29 dyn

156w 148W

-cm

SOCIETY ISLAND Figure 11. Same as Fig. 8 but for the Society Islands.

Response of ocean lithosphere to sea-mount loads 247 - 1 5

- 20

156W 148 W

-15

- 20

1 4 8 W 756W

OBSERVED RESIDUAL

GEOlD

BATHYMETRY

COMPUTED GEOID

, 8 10*8dm-cm)

156w 148 W

MANlHlKl plateau and TANGAREVA Island

Figure 12. Same as Fig. 8 but for the Manihiki plateau and Tongareva Island.

for the ocean crust and uppermost lithosphere are p = h = 0.7 x 10'2cgs, v = 0.25. For the long-term response, lower values for p are appropriate and we adopt p = 0.35 x 10L2cgs. The bulk modulus remains essentially constant with age so that h = 0.93 x 10l2cgs, E = 0.95 x 10l2 cgs and u = 0.36; Poisson's ratio increasing since the layer responds more like a fluid with increasing age. Table 1 summarizes the results for T,, for the previously discussed loads. Whether or not these stress-differences can be supported over millions of years in the uppermost 20 or so kilometres of the Earth is discussed further below.

6 Discussion

The lithospheric thickness H deduced from the flexural rigidity is the equivalent elastic thickness of a plate with uniform properties, responding to an applied load in the same way as does the actual ocean lithosphere. Other definitions of the lithospheric thickness include the thermal lithosphere and the seismic lithosphere. The first, involving parameters such as thermal conductivity, thermal expansion coefficient and subcrustal heat flow, separates the region where conductive heat transport dominates from the lower regions where con- vection is the principal mechanism of heat transport. The seismic lithosphere is defined as

248 A. Cazenate et al.

the layer of high velocities and low attenuation of the seismic waves. Alternatively, the base of the thermal lithosphere may be defined, in terms of the response to loads on a geological time-scale, as the depth which differentiates plastic from fluid-like behaviour. Likewise the base of the elastic lithosphere can be considered as the transition from elastic to plastic behaviour (Haxby, Turcotte & Bird 1976).

The estimates of D in Table 1 lead to an elastic thickness that is considerably less than the seismic estimates of about 60-80 km for ocean lithosphere older than about 40 Myr (beds, Knopoff & Kausl 1974; Forsyth 1975; Asada & Shimamura 1976). A comparison of the elastic and seismic thickness suggests a ratio of about 3, somewhat greater than the model proposed by Anderson & Minster (1979). Thermal considerations usually lead to even thicker estimates for the lithosphere. Parsons & Sclater (1977), by matching the thermal models to observed sea-floor bathymetry and heat flow obtained Hthemal = 125 km with a basal isotherm of about 1350°C. With the usual thermal models for the lithosphere (e.g. Forsyth 1977) this suggests that the base of the elastic plate corresponds to about the 400" isotherm where the temperature is about a third of the solidus temperature. That is, these results suggest that creep in the lithosphere may become significant when the temperatures T exceed about '/3 T,. Laboratory measurements indicate that TIT, must generally exceed about 0.5 for steady-state flow to take place but for geological strain-rates this ratio is almost certainly lower (Carter 1976; Paterson 1976). Hence the above result is not incom- patible with what is known about the ductile behaviour of the lithosphere.

The maximum-stress difference, evaluated numerically with equations (S), range from 7.0 kbars for the Ob-Lena-Marion Dufresnes chain to 2.5 kbars for the Society Islands. These maxima occur at z = - H/2 and z = +H/2 and, while the upper and cold part of the lithosphere may be able to support such stress differences over geological time, the existence of such high tensile stress-differences in the lower and warmer part of the plate are problemati- cal. A simple way around these high deviatoric stresses is to consider a plate whose elastic parameters are depth-dependent. The flexural rigidity D as defined by equation (2) assumes an elastic lithosphere of constant elastic properties but this is at variance with the increasing temperature at depth. More reasonable is a model in which the rheology varies with depth and while there is little seismic evidence for this, such a behaviour could be anticipated for the response of the plate to toads on a geological time-scale due to the pressure and temperature dependence of the brittle failure and ductile flow mechanisms. This can result in a reduction of stress differences by a factor of 2 to 4 near the base of the plate compared with the corresponding value of the purely elastic theory (Lambeck & Nakiboglu 1979; see also Lago & Cazenave 1980). With such models the stress at the lower reaches of the plate, some 20 km depth, beneath the above discussed sea-mounts, range from about 1.7 kbar in the case of Crozet to Zbout 500 bars below the Society Islands and present less severe tests of our concepts of the strength of crustal and upper mantle materials.

Both the thermal and seismic thickness of the lithosphere appear to increase with the square root of age (e.g. Yoshii, Kono & Ito 1976; Forsyth 1977) and the elastic lithosphere can be expected to exhibit a similar behaviour since this thickness will be a function of the thermal state of the crust and upper mantle and indeed this appears to be so from the results in Table 1. Such an age dependence of H or of the flexural rigidity D has already been suggested by Watts (1978) amongst others. Several ages must be considered. (i) The age of the lithosphere, as this determines its thermal history; the plate cooling and thickening with increasing age. (ii) The age of the load as this determines the duration of the loading and any subsequent relaxation of the lithosphere. (iii) The age of the lithosphere at the time of loading at this determines the initial response of the layer to the load. All three can be expected to contribute to various degrees to an eventual age dependence of D or H .

Response of ocean lithosphere to sea-mount loads 249

Watts & Cochran (1 974), investigating the lithospheric deflection under the Hawaiian- Emperor sea-mount chain, did not find a dependence of D on the age of the load despite the increase in this age from about 3 Myr near Hawaii to 70 Myr at the northern end of the Emperor chain. The age of the underlying lithosphere ranges from 80 Myr at Hawaii to an oldest age of 11 5 Myr near the Hawaiian-Emperor bend. These results do suggest that the important time factor may not be the age of the lithosphere not the age of the load, but the age of the lithosphere at the time of loading; that the effective flexural rigidity reflects conditions at the time of loading and that this response does not subsequently evolve in an appreciable manner with time (Watts 1978). This interpretation is also borne out by the recent theoretical considerations of Anderson & Minster (1979) who computed H as a function of load duration, on the assumption that the flow properties of the lithosphere can be explained by dislocations motions. Taking account of the thermal cooling of the plate, Lago & Cazenave (1980) show that the observed elastic thickness is in fact that acquired at a date of stabilization of the lithospheric response. The time required for stabilization after loading is found to be at most 6 per cent of the age of the lithosphere at time of loading. Thus, the date of stabilization cannot be distinguished from the latter, in support to Watts’ interpretation.

The Indian Ocean and equatorial Pacific results also appear to support this observation; the Marquesas, Society and Crozet Islands are associated with an effective elastic thickness H that increases with the age of the lithosphere at the time of loading. The Manihiki Plateau does not follow this trend but then it is nearly as old as the surrounding lithosphere and its geological history is quite complex and distinctly different from that of the more typical sea-mounts. The Ob-Lena-Marion Dufresnes chain also can not be used because their age is unknown. Hence the only useful results for testing the age dependence hypothesis are those for Crozet, Society and Marquesas and the observation that for the on-the-ridge islands of St Paul and Amsterdam, the flexural rigidity is very low. These results are also limited by the remaining uncertainties in the age of the lithosphere and of the loads. The loaded plate ranges in age from about 80-45 Myr and while this is not sufficient to establish the nature of this age dependence (Fig. 13) the results are compatible with the

- E Y

4 Y E

2 a

AGE OF LITHOSPHERE (My)

Figure 13. Effective elastic lithospheric thickness for Crozet, Society and Marquesas Islands. The 6 is shown by the solid line.

250 A. Gzzenave et al.

square root of age model. Specifically, the effective elastic thickness follows an approximate rule of

H(km) = 2.5 d w ) . The thermal models for the oceanic lithosphere (e.g. Forsyth 1977) indicate an age dependence of the order

H(km) = (10-12)4*)

or about four times greater than the elastic thickness. That is, the effective elastic plate comprises that part of the lithosphere where temperatures T are below about 400°C, or where T/T, < Y3. In so far as the transition from the elastic response to ductile response will be gradual, this thickness must be considered only as an effective thickness, the actual value may be greater if the finite strength of the lithospheric material is depth dependent.

The three loads comidered in Fig. 13 are all relatively young so that the age of the litho- sphere is nearly equal to the age of the layer at the time of loading and no distinction between the two ages is possible. A further complication is any eventual stress dependence of the response; small loads will result in a thicker apparent lithosphere than will large loads, all other factors being equal. Thus the estimates of H for Crozet and Marquesas may be low compared with those of the Society Islands for which the deviatoric stresses are least. With the limited data presently available, a separation of these various factors contributing to the lithospheric response is not yet possible and more sea-mounts need to be analysed.

References Anderson, D. L. & Minster, J. B., 1979. Seismic velocity, attenuation and rheology of the upper mantle,

in Magnitude of Deviatoric Stresses in the Earth's Crust and Upper Mantle, ed. Evernden, J., US Geol. Surv., Menlo Park.

Assada, T. & Shimamura, H., 1976. Observation of earthquakes and explosions at the bottom of the Western Pacific: Structure of oceanic lithosphere revealed by longshot experiment, in The Geo- physics of the Pacific Ocean Basin and its Margin, eds Sutton, G . H., Manghnani, M. H. & Moberly, R., Am. geophys. Un., Monogr. 19, 135-153, Washington D.C.

Balmino, G., Reigber, Ch. & Moynot, B., 1978. Le Modhle de potentialgravitationnel terrestre Grim 2 - DBtermination, &valuation, Ann. Gkophys,, 34,55-78.

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