Chapter 11 Applications to Marine Geophysics

C H A P T E R

11 Applications to Marine Geophysics A N N Y CAZENAVE* and JEAN YVES ROYER t *Laboratoire d'Etudes en Geophysique et Oceanographie Spatiales Centre National d'Etudes Spatiales 18, Av. Edouard Belin 31401 Toulouse Cedex 4 France t UBO-IUEM Domaines Oc#aniques Place Nicolas Copernic--29280 Plouzane France

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

pensation. In addition to the well-known geoid anomalies associated with seamounts, volcanic chains, fracture zones and deep-sea trenches, the map reveals details of the midocean ridge segmentation, off-axis V-shaped structures and many other features such as microplates, lineated patterns, in particular in the Pacific ocean, or fossil plate boundaries (extinct spreading ridges, extinct triple junctions, etc.). The altimetry-derived geoid data have been widely used since 2 decades to model the thermal and mechanical structure of the oceanic lithosphere, to study the interaction between the convecting upper mantle with the lithosphere, spreading ridges, hotspots and in some off-ridge regions to study plate kinematics and reconstruct past motions of tectonic plates. These observations have no doubt greatly improved our knowledge of the dynamics of the lithosphere and upper mantle. In this chapter, we first discuss classical compensation models usually considered in order to interpret geoid anomalies over marine features and then we review the various areas which have benefited over the past 2 decades of highaccuracy and high-resolution altimeter geoid data. Topics discussed here concern: seamount loading and the mechanical structure of oceanic plates, thermal evolution of the oceanic lithosphere, hotspot swells, geoid lineation patterns, plate kinematics, seamount production, and mid-ocean ridge segmentation.

In the mid 1970s, the Geos3 and Seasat missions successfully demonstrated the interest of radar altimeter measurements for mapping undulations of the sea surface. Recovery of the time variable ocean surface signal of interest for oceanography, began only a decade later with the Geosat mission and especially since the early 1990s with the ERS and TOPEX-POSEIDON missions. Thus during nearly 15 years altimetry missions have mostly served marine geophysicists who abundantly used altimetry-derived geoid observations over the oceanic domain to study the oceanic lithosphere and the mantle-lithosphere interactions. The high-density data set acquired by the ERS-1 satellite altimeter during its geodetic mission (April 1994 to March 1995) let to a new step in the use of geoid data for marine geophysics. Indeed together with the dense Geosat altimeter data collected ten years earlier but classified for a decade, this new data set provided a detailed view of the marine gravity field with a resolution better than 5 km everywhere, opening new perspectives for global studies in marine geophysics. Figure 1 (see color insert) presents a map of the marine geoid based on the dense Geosat and ERS-1 altimeter data. This map shows in great details the gravitational signature of submarine tectonic features and their isostatic corn-

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2. FILTERING THE LONG.WAVELENGTH GEOID SIGNAL Geoid anomalies associated with most submarine tectonic features have wavelengths typically shorter than 3000 km. To extract the geoid signal from altimetry data, it is first necessary to remove the long-wavelength geoid associated with density variations occurring in the deep mantle (Hager and Richards, 1989; Hager and Clayton, 1989). A widely applied approach consists of subtracting from the altimeter geoid, a reference long-wavelength geoid N based on geopotential solutions given by:

(equivalent wavelength of ~4000 km), the cumulative error on the geoid is ~ 10 cm. The higher the degree, the larger the error. Besides geoid anomalies, other gravitational informations may be used for geophysical interpretation such as altimetryderived gravity anomalies (e.g., Sandwell and Smith, 1997; Hwang et al., 1998) or deflection of the vertical. These observations enhance short wavelength gravitational signal, hence may be preferred in a number of studies. However, since they poorly reproduce the medium-wavelength (10002000 km) gravity signal, they are not very useful for studies related to hotspot swells or upper mantle convection. In the latter case, geoid data may be preferred.

{[Clm c o s m)~ + Slm sin m~.]

N ( R , q), )~) -- R

3. GEOID ANOMALIES A N D I S O S T A T I C COMPENSATION

/=2 m=0

x Plm(sin qO)}]

(1)

qS, )~ are latitude and longitude, R is earth's mean radius. Clm, Slm are the Stokes' coefficients related to the integrated mass distribution inside the earth (Heiskanen and Moritz, 1967). Current geopotential models give sets of Clm, Slm coefficients up to a maximum degree and order. Recent models such as JGM-3 or GRIM4-C4, are complete to degree 70 (e.g., Tapley et al., 1996; Schwintzer et al., 1997). The associated geographical wavelength A of a geoid undulation is related to the maximum degree 1 through A = 27rR/(l(1 + 1)) 1/2. Many studies have provided medium-wavelength geoid maps based on satellite altimetry after removing the long wavelength signal using Eq. (1) developed up to a given degree expansion. However, abrupt truncation of Eq. (1) introduces Gibbs oscillations in the residual geoid [observed geoid minus truncated geoid given by Eq. (1)]. Sandwell and Renkin (1988)proposed minimizing these artifacts by tapering the higher degrees of the spherical harmonics in Eq. (1), prior to summation. The Ctm, Stm coefficients are the multiplied by a weighting function such as a Gaussian or a cosine function. Applied to harmonics between degrees l l and 12, this approach leaves in principle unattenuated geoid anomalies of wavelength shorter than A -- 2a" R / (12(12 + 1)) 1/2. Another approach consists of applying a 2-D high-pass filter to gridded geoid data. Several kinds of 2-D filters may be implemented. A 2-D filter based on inverse methods (Tarantola, 1987) in which the long-wavelength geoid is modelled as a sum of Gaussian functions centered at the data points proved to be a useful approach (e.g., Cazenave et al., 1992, 1996). 2-D filtering is by far a better method than subtracting a reference geopotential model. This is so because except for the very low degree harmonics which are accurately determined, large errors still affect geopotential solutions beyond degrees 10-20. For example, at degree 10

The geoid represents the integrated mass distribution over the volume of the earth. For this reason, geoid data alone cannot inform on the lateral density structure. In most instances, however, geoid anomalies are associated with other geophysical anomalies, in particular topography. Used together, these observations are able to constrain plausible models of earth's internal structure. In the framework of the classical concept of isostasy, geophysical applications of satellite altimetry simultaneously use geoid and topography information. Isostasy assumes that loads on (or inside) the earth are compensated by internal density variations such that, at depth, pressure is hydrostatic. The depth above which density variations are confined is sometimes called the compensation depth although its definition is not unique. Isostasy may be understood in terms of mass conservation, minimization of strain energy, and mechanical equilibrium (Dahlen, 1982). Various mechanisms are able to insure isostatic equilibrium: crustal thickening, thermal expansion or contraction of mantle rocks, thermal thinning, plate flexure, etc. Dynamic compensation is often opposed to static compensation and assigned to convection. Convective stresses produce deformation of mantle interfaces, in particular of the earth surface, giving rise to geoid anomalies. Internal density variations associated with thermal anomalies produce geoid anomalies of opposite sign and of magnitude which depends in a complex manner on the mantle stratification and viscosity structure. As for static compensation, observed geoid is the net effect between these opposing effects. Geoid anomalies over marine tectonic structures have been classically interpreted through simple isostatic models. Most topographic loads of wavelengths <50 km are supported by the strength of the lithosphere and are uncompensated. At wavelengths longer than "-~500 km, topography is in general locally compensated. At intermediate wavelengths (50-500 km) most loads are compensated by elastic flexure of the upper lithosphere.

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3.1. Local Compensation in the Long-Wavelength Approximation Ockendon and Turcotte (1977), and Haxby and Turcotte (1978) derived useful expressions for geoid anomalies caused by two-dimensional density variations within a layer of horizontal scale large compared to its thickness. Under the assumption of isostatic compensation (i.e., local density variations are in hydrostatic equilibrium), the geoid anomaly is given by:

N

H N --

27rG f z A p ( x , z ) d z g 0

surface topography is compensated by a density contrast at the base of the crust (thickened crust). For a Pratt compensation, the surface topography overlays a layer of constant thickness but of variable density. Compensation occurs at the Moho in the Airy model and at the base of the lithosphere in the Pratt model (Figures 2a and 2b). Application of Eq. (2) in these two situations gives: Airy model:

rca

---

(2)

where N is geoid height, z is depth positive downward, A p ( x , z) is the 2-D density variation occurring between the surface z = 0 and the base of the layer at z = H. G is the gravitational constant, and g is the mean surface gravity. Eq. (2) assumes that A p ( x , z), integrated between z = 0 and z = H, is equal to zero. The above relation may be applied to the classical Airy and Pratt isostasy models. For an Airy compensation, the

[

(Pc - Pw) 2h(zc - zw) + (Pro - Pw) h Z l (Pro -- Pc)

J

(3)

Pratt model: rcG N = -~(Pm

-

-

pw)Hh

(4)

where p~, pc, Pm are, respectively, seawater, crust, and mantle densities, h is the height of the topography (above the surrounding seafloor), zw and Zc are the seafloor and Moho

FIGURE 2 Schematicdiagrams of isostatic compensation models: (a) Airy compensation; (b) Pratt compensation; (c) Lithospheric thinning compensation; (d) Regional compensation by plate flexure.

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depth below sea level, and H is the layer (lithosphere) thickness. The Airy model has been extended to a two-layer model (Marks and Sandwell, 1991). In the latter model, the base of the crust is underlain by a thin layer of depleted mantle (of density Pe, slightly lower than the normal mantle density Pm). This model was developed to explain the topography and geoid anomalies over oceanic plateaus not associated with hotspots. The corresponding geoid anomaly is: N =

2zrG g

For the half-space model, it becomes: 2zrG

N ( t ) -- - - ~ O e p m K T m [ 1 g

(8) where tc is the thermal diffusitivity and t is plate age. For the plate model, the expression for T (t, z) is more complicated (Parsons and Sclater, 1977). The corresponding geoid anomaly is given by (e.g., Cazenave, 1984): 2 r r G H 2 1 1-~(Pm - pw)d2(t) g

N ( t ) --

[

(Pc - pw)h Zc - zoo

+ ~Pm rm

h [1 + 2/3 - f12] (Pc - Pw) -Jr- -~ (Pm --Pc) + (1

f12) (Pc -- Pw) ]

Q,

(9)

with: (5)

1

d(t) - - - ~ P m rm(Pm -- p~)--I

13 is a parameter ranging from 0-1 expressing the fraction of topography compensated by the one layer Airy expression. Eq. (5) reduces to Eq. (2) for fl = 1. Eq. (2) can also be applied for modeling cooling of the oceanic lithosphere. The temperature structure T ( x , z) inside the oceanic lithosphere is well described by conductive heat transfer models (see Section V). The inferred density structure p ( x , z) is related to T ( x , z) through the equation of state: (6)

where Tm is the average temperature of the underlying mantle and ot is the volume coefficient of thermal expansion. The topography of the seafloor is directly related to Eq. (6) if isostatic equilibrium (mass conservation) is assumed. The conductive half-space model (Turcotte and Oxburgh, 1967) predicts a subsidence of the seafloor, proportional to the square root of the distance to mid ocean ridge (or to the square root of seafloor age if the plate is assumed to move at a constant velocity) whereas in the plate model (McKenzie, 1967), the seafloor depth asymptotically approaches a constant value at large age. The latter model assumes that the lithosphere has a constant thickness H unlike the half space model which predicts that the lithosphere continues to thicken at all ages. The geoid anomaly [Eq. (2)] caused by the temperature distribution inside the cooling plate (assuming the ridge crest as a reference and d being the seafloor depth, positive downwards) is: N(t) = _27rG I

+ ~ n=l

(Pm -- Pc) 3

p ( x , z) -- pm[1 -+- ot(Tm - T ( x , z))]

+ 2otpmTm(Pm - p w ) - l ( r c ) - l ] t

x

E

t u,)

exp --fi2n-1 --~ (2n - 1)-2

1 - ~-g n=l

Qn__(-1)n(ut) n2

exp --fin -h--

]

(10)

fin -- ( - R 2 -+-n27t'2)1/2 -- R R=

uH

(2K)

u is the half-spreading velocity assumed constant. According to Eq. (9), N ( t ) tends asymptotically toward a constant value at large age. Another isostatic model has been considered in the literature: the thinning lithosphere model (Figure 2c). This model was first proposed by Crough (1978) to explain the broad topography and geoid swell observed over mid-plate hotspots. In the thinning model, the swell topography is assumed to be compensated by hot, low density asthenospheric material placed in the lower part of the lithosphere: the heat associated with mantle plumes drives the lithospheric isotherms upwards, thins the lithosphere, and produces an uplift of the surface. The geoid anomaly (Sandwell and McKenzie, 1989) is: 27rG N - -~h[Zw(pc g

- Pw) + Zc(Pm - Pc) - Zm(Pm - Pro)]

(11) where h is the height of the swell above the surrounding seafloor of depth Zw below sea level, Zc is the average Moho depth, and Zm the average depth of the low density anomaly; Zm is sometimes referred to as the compensation depth.

(Dm --2Pw) d2(t) 3.2. Regional Compensation

oo

--Olpm f (d(t)-+- g)(Tm 0

r(t, z))dz].(7)

Expressions given above are valid in the long wavelength approximation of isostatically compensated topography, i.e.,

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11. APPLICATIONSTO MARINE GEOPHYSICS

if the wavelength of the topography is much larger than the compensation depth. At wavelengths _<500 km, compensation of the topography is better explained by regional rather than local isostasy, assuming elastic flexure of the lithosphere under the surface load (Veining Meinenz, 1964). This model successfully explains medium wavelength (< 500 km) geoid anomalies associated with intraplate volcanoes (Watts, 1978). A seamount load causes the upper elastic layer of the lithosphere to flex (see Figure 2d). The downward deflection w(x, y) is given by the solution of the equilibrium equation of a continuous elastic plate overlying a fluid medium subject to normal load P (x, y)" D V 4 w + (Pm - pc)gW -- P

3.3. Admittance Approach The expressions of geoid anomalies described in the previous sections are used in analyses conducted in the spatial domain. However, compensation mechanisms eventually produce responses at different wavelengths that may not be easily separated from observed geoid anomalies. Hence, a number of investigators have preferred to work in the spectral domain to avoid assumptions on the characteristic wavelengths of signals. This approach initially developed by Dorman and Lewis (1970) assumes that geoid and topography are linearly related in the spectral domain: Z(kn)H(kn)

(13)

where kn is wavenumber, G(kn) and H(kn) are Fourier transforms of geoid and topography. Z(kn) is the transfer function or admittance.

(14)

Z(kn) = [G(kn)I2I(kn)]/[H(kn)tl(kn)]

where bars indicate complex conjugate. Observed admittance computed as a function of wavenumber with Eq. (14) can be compared to various theoretical admittances derived from models of isostatic compensation. We list below the most widely used theoretical admittances. The Airy, Pratt, and flexure admittance can be written as:

(12)

where D is the flexural rigidity related to the elastic thickness Te of the plate through D -- ETe3/12(1 - v2), with E and v being the Young modulus and the Poisson ratio. The load P is related to the topography height h above the unloaded lithosphere through P ,~ (Pt - Pw)gh (Pt is the load density). For simple axisymmetric loads analytical solutions of Eq. (12) exist. However, for 3-D seamounts of arbitrary shape, it is necessary to integrate Eq. (12) numerically over the volume of the load, knowing the topography h. The geoid anomaly observed at the surface results from several contribution: (1) the positive density contrast of the topographic load, (2) the negative density contrast due to deflection of the Moho and fill-in of the deflection, and (3) the positive density contrast due to the deflection of the base of the elastic plate. The latter effect is generally considered negligible and omitted. As for the deflection w(x, y), the total geoid anomaly has to be computed numerically. The theoretical geoid anomaly is derived for various values of the flexural rigidity D. Comparison with the observed anomaly allows to estimate D, hence the elastic thickness Te. The schematic diagrams in Figure 2 illustrate the above discussed isostatic compensation models.

G(kn)-

Eq. (13) is valid in the absence of noise (noise in the data or geological noise due to unrelated features). A better estimate of Z(kn) is given by McKenzie and Bowin (1976) in the presence of noise:

Z(k.)-

Z~c(k,)[1 -

(15)

g,(k,)]

where Znc (kn) is admittance for uncompensated topography equal to: 2rcG(gkn) -1 (Pc - Pw) e x p ( - k n z w )

and 7r (kn) is a function ranging from 0 to 1 representing the part of the geoid anomaly due to the topography compensated at depth. It comes (under the approximation that the wavelength is long compared to the layer thickness): Airy model: (16)

qJ(kn) - e x p [ - k n ( z c - zw)].

Pratt model: qJ(kn) =

1 - exp(-kn H) KnH

.

(17)

Flexure model: ~(kn)

--

[

1 +

g(Pm

-

Pc)

ll

exp[-kn(zc

-

z~)].

(18)

Notations are the same as above. A number of other theoretical admittances have been derived, for example for subsurface loading models of an elastic plate (Forsyth, 1985) and for thermal cooling models (Black and McAdoo, 1988). Admittance models have been also computed for convection in the upper mantle (e.g., Parsons and Daly, 1983; McKenzie, 1977). In these models, analytical expressions have been derived for simple temperature structure using a Green's function approach to solve motion equations. Other approaches solve numerically full convection equations, derive surface topography and geoid due to the convective flow, and deduce the admittance.

4. MECHANICAL BEHAVIOR OF OCEANIC PLATES: FLEXURE UNDER SEAMOUNT LOADING Altimetry-derived geoid anomalies constitute a basic data set for flexure studies. Indeed 2-D high-resolution geoid

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(or gravity) grids allow precise computation of the flexural rigidity of the lithosphere under topographic loads of arbitrary shapes. Because of the characteristic wavelengths of flexured geoid anomalies (300-500 km), it is clear that geopotential models are inappropriate, as are ship-board gravity surveys which give only 1-D gravitational information. The flexure model has been widely applied to seamount loading and trench bending to determine the elastic thickness of the lithosphere using geoid and topography anomalies. This approach not only informs on the present mechanical behavior of oceanic plates but also on its evolution. Since the early work of Watts (1978), it is widely accepted that the upper layer of the lithosphere is well described by an elastic rheology over geological time scales and that the elastic thickness increases with the square root of plate age at the time of loading. The base of the elastic layer coincides with an isotherm of the conductive lithosphere (400-700~ This temperature range corresponds to the transition between the rigid-elastic to ductile behavior of mantle rocks and is in general agreement with predictions based on rock mechanics experiments (Goetze and Evans, 1979). Flexure studies suggest that the measured elastic thickness is that acquired at the time of loading, an indication that isostatic compensation of the load is not significantly altered by continuing cooling of the plate and that viscous relaxation is either unimportant or occurs on a time scale much shorter than the cooling process. The relationship between the elastic thickness Te and the age of a plate at the time of loading was first derived by Watts (1978) over the Hawaiian volcanoes and proved to be valid on a worldwide scale by numerous subsequent studies. It has been very useful to get information on the tectonic setting of volcanoes at the time of formation (Watts et al., 1980; Smith et al., 1989): low Te indicates that seamounts formed on very young lithosphere, while large Te indicates that they formed on old lithosphere. Detailed elastic thickness estimates at different locations of individual features have also revealed local variation, hence a composite origin for these features. The Te vs. (age) 1/2 relationship has also been used to infer the age of the plate knowing the age of the volcanoes and inversely (Calmant et al., 1990). Figures 3a and 3b present a summary of the available estimates of Te as a function of age of plate (at the time of loading in the case of seamounts). Depth of isotherms of the half-space conductive cooling model are superimposed. The Te values at seamounts presented in Figure 3a are based on the compilation of Wessel (1992) to which we have added or replaced Te values based on subsequent studies (Goodwillie and Watts, 1995 for some of the Polynesian volcanoes; Wessel and Keating, 1994 for the Hawaiian volcanoes; Kruse et al., 1997 for the Easter seamount chain; Watts et al., 1997, and Canales and Dafiobetia, 1998 for the Canary Islands; Goodwillie, 1993 for the Puka Puka ridge in the central Pacific). Te values at trenches presented in Figure 3b are from

Levitt and Sandwell (1995). Although there is much scatter, it is clear from Figures 3a and 3b that the oceanic lithosphere becomes more rigid as age increases. Moreover, comparing Figure 3a and Figure 3b indicates that elastic thickness deduced from studies at seamounts is significantly lower that estimated at trenches. The base of the elastic layer beneath seamounts follows roughly the 400~ isotherm while in the case of trenches, it follows the 500-700~ isotherm (e.g., Judge and McNutt, 1991). This difference was first interpreted by McNutt (1984) as the result of an upward migration of the plate isotherms due to reheating associated with the emplacement of seamounts. Subsequent observations however made this explanation difficult to support. Indeed, heat flow measurements along the Hawaiian volcanoes (Von Herzen et al., 1989) as well as in the Polynesian region (Stein and Abott, 1991) do not show the extra heat predicted by the reheating hypothesis and rather indicate a normal seafloor heat flow. Wessel (1992) proposed that while the lithospheric reheating during a seamount emplacement may contribute to an apparent low Te at seamounts, other phenomena generally neglected in flexure studies, such as thermal stresses, may play a significant role. Neglect of thermal stress systematically underestimates the strength of the plate, hence the elastic thickness. Account of it would reconcile Te estimates at seamounts and at trenches and lead to a more likely temperature range of 500-700~ for the elasticductile transition inside oceanic plates, whatever the tectoning setting. We note that the Te estimates reported in Figures 3a and 3b fall within three distinct populations. From high to low Te values, these populations correspond to (1) trenches, (2) world seamounts, (3) some seamounts of the central Pacific and western Pacific. A number of past studies have reported that the elastic thickness under some volcanoes of the Polynesian province is thinner than elsewhere in the world (e.g., Calmant, 1987; Calmant and Cazenave, 1987). A similar observation has been made for some seamounts in the western Pacific, a region characterized by a high seamount concentration and known as the Darwin rise (Smith et al., 1989; Wolfe and McNutt, 1991). The Polynesian province is known as the South Pacific Superswell and is characterized by anomalously shallow seafloor, higher than normal volcanoes concentration, low subsidence rate, enriched volcanism and negative geoid anomaly (McNutt and Fischer, 1987; McNutt and Judge, 1990; McNutt, 1998). Early explanation for the apparent low elastic thickness in the south central Pacific suggested a thinned thermal lithosphere, a result of hotter than normal upper mantle under the South Pacific Superswell. This explanation appears however in conflict with the absence of regional heatflow anomaly over the superswell. Indeed,the thermal hypothesis should be accompanied by elevated temperature in the upper layers of the lithosphere, which is not observed.

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11. APPLICATIONS TO MARINE GEOPHYSICS

Age at time of loading ( m.y. ) 0

20

40

60

~,A

100

80

120

LT

-10 r~

140

200~C

-20

r.~

-3O

~-40 9~

-50 t Seamounts

r

-60 t

Seamounts (Central Pacific)

-70 (a)

Age ( m.y. ) 0

,•

-10

'~

-20

20

40

60

80

100

120

140

@

200 C

-30

;~-40 9~

-50

A A AA

-60 A Trenches -70

(b) F I G U R E 3 (a) Elastic thickness at seamounts versus age of plate at the time of loading (triangles indicate seamounts from the central Pacific while open circles correspond to other seamounts). (b) Elastic thickness versus age of plate at trenches.

Revisited estimates of Te under the Superswell volcanoes (e.g., Marquesas and Society Islands; Filmer et al., 1993) with more precise bathymetry and geoid data led to normal Te values in a number of cases. It remains however that even with refined geophysical data, a number of Te values at seamounts in the central and northwestern Pacific are lower than normal at the time of volcanism. Recent investigations of the origin of the Superswell (McNutt and Judge, 1990; Cazenave and Thoraval, 1994; McNutt, 1998) conclude to a dynamic support through upwelling in a convective mantle. These models suggest that Superswell hotspots may not have a deep, lower mantle origin but rather may originate at the base of the upper mantle. The volcanic chains associated with these hotspots do not show the clear linear age progression seen elsewhere in the world, an indication of

intermittent activity possibly biasing elastic thickness estimates (McNutt et al., 1997; McNutt, 1998). A similar explanation may hold for Te values at seamounts of the Darwin Rise region. The Darwin Rise presents many characteristics in common to the Polynesian province and may have been an active superswell in Cretaceous time, as is the south Pacific Superswell today (McNutt, 1998).

5. THERMAL EVOLUTION OF THE OCEANIC LITHOSPHERE Cooling and contraction of oceanic plates has long been considered as a reasonably well understood phenomenon. The problem is classically treated as a purely conductive

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process and described by simple models (half-space and plate models) giving the temperature distribution inside the plate as solution of the heat transport equation. In the halfspace model, the lithosphere is the boundary layer of a large convection cell through which cooling is purely conductive (Turcotte and Oxburgh, 1967). The plate thickens with (age) 1/2 and its base coincides with an isotherm. A variant of the half-space model is the plate model which assumes a slab of constant thickness with a fixed basal temperature. This model had been originally proposed by McKenzie (1967) to account for nearly constant heatflow observed in old basins. Both models predict that seafloor depth increases with (age) 1/2 up to ~80 Ma. Beyond, depth tends toward a constant value in the plate model. The plate model has been often preferred to the half-space model because in some regions, in particular in the western Pacific and north western Atlantic, depth data are suggestive of seafloor flattening (Parsons and Sclater, 1977; Stein and Stein, 1992). The plate model assumes a constant temperature at a fixed depth which corresponds to the bottom of the plate. The GDH1 cooling plate model proposed by Stein and Stein (1992) is based on simultaneous inversion of depth and heat flow data. It predicts a depth-age curve which flattens beyond 70 Ma and a mean plate thickness of 95 km. Unlike the halfspace model for which the lithosphere coincides with the thermal boundary of large-scale convective cells, the plate model has no physical meaning but provides a mathematical basis for a system in which additional bottom heatflux balances heat lost by conduction. Several mechanisms have been invoked to explain seafloor flattening observed in some regions, such as reheating (and subsequent uplift of the lithosphere) by hotspots (Heestand and Crough, 1981), radiogenic heating (Jarvis and Peltier, 1980), asthenospheric return flow (Phipps Morgan and Smith, 1992), supply of heat by small-scale convection (e.g., Parsons and McKenzie, 1978; Buck, 1987), convective destabilization at the base of the cooling plate (Yuen and Fleitout, 1985; Davaille and Jaupart, 1994; Eberle and Forsyth, 1995). In the latter studies, small-scale convection occurs through instabilities growing at the base of the cooling plate and become effective below old plates. An alternative model has been proposed by Doin and Fleitout (1996), considering that convection provides heat at the base of the lithosphere whatever plate age. It should be noted however that seafloor flattening is principally observed in the western Pacific and north western Atlantic. Maps of the so-called "dynamic topography," (i.e., the observed topography corrected for shallow density contrasts due to crustal thickening and seafloor subsidence) which should reflect dynamic deformation of the Earth surface by large scale convection, presents two antipodal maximas which, in fact, coincide with the regions of observed elevated seafloor (e.g., Cazenave et al., 1989). Such an observation still holds when subsidence effects are removed us-

ing GDH 1 plate model which empirically fits observations of elevated seafloor topography in the western Pacific. Thus it cannot be ruled out that seafloor flattening, or at least part of it, is not caused by additional heat at the base of the cooling plate but results from dynamic uplift of the earth's surface by large scale convective stresses. The above discussion concerns mean subsidence estimates. Several observations however suggest significant deviations with respect to the mean, in particular areas still subsiding with (age) 1/2 at very old ages (Marty and Cazenave, 1989; Calcagno and Cazenave, 1994; Hohertz and Carlson, 1998). This is to be compared with the analysis of surface wave data (Tanimoto and Zhang, 1990) which reports continuous thickening (up to 150 Ma) of oceanic plates. Besides, the seismic data show significant differences from one ocean to another which are not predicted by the standard cooling models. Depth data also show important regional variations in lithospheric subsidence (Hayes, 1988; Kane and Hayes, 1994; Calcagno and Cazenave, 1994; Perrot et al., 1998). These studies indicate seafloor subsidence variations up to 100%, not accounted for by the cooling models unless implausible variations in asthenospheric temperature as high as several hundreds degrees are invoked. In some of these studies, other features such as asymmetrical subsidence or sudden deepening of the topography before flattening are also reported. It is thus quite clear that neither half-space nor plate models are able to account for the complexity of the observations. With the availability of geoid data from satellite altimetry, geoid anomalies at fracture zones have been much used in the past 15 years for constraining the thermal models. Cooling of the lithosphere causes the geoid height to decrease regularly from mid-ocean ridges with increasing plate age [see Eqs. (8), (9), and (10)]. This behavior is mostly at longwavelength and is almost impossible to isolate from other long-wavelength geoid components due to mantle convection. The variation in geoid height with age is in turn responsible for the geoid offset observed across fracture zones (FZ), a result of the difference in plate thermal structure and of the isostatically compensated seafloor depth step (see Figure 4). From Eqs. (7) and (8), the geoid step AN divided by the age offset At across the FZ approximates the first order derivative of N(t). In the half-space model, A N ~ A t is a constant which depends on the thermal parameters of the model (thermal diffusivity, mantle temperature, thermal expansion), whereas in the plate model, A N ~ A t decreases with age as shown in Figure 5. Availability of geoid profiles along altimeter tracks roughly perpendicular to the FZ trend has given rise to numerous determinations of A N / A t variations with age (Detrick, 1981; Sandwell and Schubert, 1982; Cazenave, 1984; Marty and Cazenave, 1988; Driscoll and Parsons, 1988; Gibert et al., 1987; Freedman and Parsons, 1990). A difficulty in determining the geoid step AN arises because other factors acting at the FZ obscure the

11. APPLICATIONS TO MARINE GEOPHYSICS

415

8

7

6 --

0 Z 4--

0 0

3--

1 --

l

I

I

38

1

39

I 40

I

t

I

41

l 42

LATITUDE FIGURE 4

Geoid anomaly across the Mendocino fracture zone (Northeast Pacific).

A

E v

u.

14. O U,I

-,

20 125 km

(5

~ -r

10

w D LLI (.'3

0

,

I 10

I 20

I' 30

I 40

I 50

I 60

1 70

I 80

I 90

AGE (my)

FIGURE 5 Variationof the geoid slope versus age for three values of the plate thickness (65, 95, and 125 km).

pure thermal effect: lateral heat conduction, (Louden and Forsyth, 1976), plate flexure due to differential subsidence and thermal bending stresses (Sandwell, 1984a; Parmentier and Haxby, 1986), and small scale convection developing beneath the FZ (Craig and McKenzie, 1986; Robinson et al., 1988).

There is a considerable disagreement among the various results so far obtained. Early studies based on geoid data at the Mendocino FZ concluded in favor of the plate model, but subsequent studies found that neither plate nor half-space model could fit the data and some of them concluded that the behavior of the geoid step with age is consistent with small scale convection occurring beneath the FZ as predicted by Craig and McKenzie (1986) and Robinson and Parsons (1988). This view was further questioned by Sandwell (1984a) and Wessel and Haxby (1990) who reanalyzed geoid profiles along 4 Pacific FZ (Clarion, Clipperton, Murray and Udintsev), with modeling of lateral heat flux, and flexural response due to differential subsidence and thermal stresses. Putting all together A N ~ A t results obtained for all four FZ, they conclude that data are compatible with simple conductive models and that previous results were systematically biased. Richardson et al. (1995) compiled a large number of published geoid slopes estimated from satellite altimetry. Their study concludes that the data can fit plate model predictions as well, such as those of the GDH1 model. In Figure 6, we have reported geoid slopes with age from 4 Pacific FZ (data are from Marty and Cazenave, 1988). Inspection of this figure which contains essentially the same data set as in Richardson et al. (1995) suggests indeed that

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SATELLITE ALTIMETRYAND EARTH SCIENCES

of the medium wavelength geoid as revealed by satellite altimetry maps. Figure 7 shows, as an example, the geoid and topography across the Bermuda swell. It is an axisymmetric feature of 1000-km radius showing a perfect correlation between geoid and topography. In general, other swells do not display such a radial symmetry and are either elongated (Hawaiian or Polynesian swells) or completely irregular (Cape Verde swell). Over the past two decades, many studies have been devoted to measure the geophysical characteristics of oceanic swells, in particular depth and geoid anomalies. The general correlation observed between depth and geoid anomalies over swells has often been used to infer an apparent compensation depth of the topography through simple isostatic models (Crough, 1983; McNutt and Shure, 1986; Fischer et al.,

on the average the observed trend can be explained by purely conductive models (but cannot univoquely discriminate between them) but that additional physical phenomena such as those previously mentionned to explain regional subsidence variations, need to be invoked to explain the scatter of the results.

6. OCEANIC H O T S P O T SWELLS Most oceanic hotspots are associated with broad topographic and geoid anomalies (swells) of ~ 1000-2000 km width and amplitude in the range 0.5-1.5 km and ~ 1-10 m respectively. Hotspot swells represent the dominant signal

50-

E E

40-

0 ~176 0

30-

o

Z

0 o

20-

I=

o ~ ..........................

10"

x

=I

x

El

n Ito I x ......% X x'~ x O ~-=t =

x

x

x~

x

0

0 x =~= AA~A~&--O---'q'~ . . . . . . . . . . . . . . . . . . . . mm

ox u-- x

c==

~= ~ = o

"

I

I 30

.... /'

10

20

I 40

= &&

o

I 50

=

=

It

I 60

=

I 14 (cm I my)

I

A

"'1 70

I 80

I .... 90

I 100

I 110

AGE (my)

FIGURE 6

Ratios of geoid anomaly to age offset at fracture zones as a function of mean plate age. The data are from four fracture zones (FZ) of the Pacific ocean: Mendocino FZ (dark squares), Clarion FZ (open squares), Murray FZ (triangles), West Udintsev FZ (crosses) and East Udintsev FZ (open circles). The horizontal line corresponds to a constant ratio of 14 cm/my predicted by the half-space cooling model.

-

RESIDUAL

DEPTH

----

RESIDUAL

GEOID

T l

T

4rn

1 km

J_

I

-1000

!

1

1

!

!

-500

1

!

!

l

!

0

!

!

.

t

!

!

500

!

1000 KM

FIGURE 7 Geoid and topography anomalies across the Bermuda swell.

....

11. APPLICATIONS TO MARINE GEOPHYSICS

1986; McNutt, 1988; Monnereau and Cazenave, 1988, 1990; Sheehan and McNutt, 1989; Wessel and Keating, 1994; Cafiales and Dafiobetia, 1998; Moore et al., 1998). If it is assumed that the topography is locally compensated at long wavelength (> 500 kin), then to a first approximation, geoid and depth anomalies are linearly related [see Eq. (3)] and their ratio depends on the average depth of the compensating density contrast, a parameter which may eventually inform on the mode of compensation of the swell. Although estimates of the depth and geoid anomalies over swells are subject to some uncertainties due to subsidence effect correction for the topography and removal of the long wavelength geoid components, there is a certain agreement between the various results which show a rough linear relationship between geoid and topography and give geoid to depth anomaly ratios in general less than 5-6 m km -1 (see for example Monnereau and Cazenave, 1990). Interpreted in terms of compensation depth [Eqs. (2), (3), and (10)], such values indicate that the compensating density contrast is located inside the lithosphere at depths ranging between 50 and 100 km. Such apparent shallow depths led Crough (1983) and Menard and McNutt (1982) to propose that the lithosphere is reheated as it passes over hotspots. In this model, referred as to thermal rejunvenation model, elevated mantle temperature is accompanied by thinning of the rigid plate up to a given depth and the thinned lithosphere is replaced by hot low-density asthenospheric material causing uplift of the surface and explaining the resulting geoid anomaly. Several observations argue however against a pure lithospheric cause of swells. One of them is the short uplift time (< 10 myr) of the Hawaiian swell that heat conduction alone is unable to produce unless the asthenospheric heat flux is excessively large. Another observation concerns surface heat flow around the Hawaiian swell which shows no heat flow anomaly, a result in contradiction with a significantly thinned lithosphere by reheating processes (Von Herzen et al., 1989). Other results indicate that the lithosphere may not be thinned at hotspot swells. Woods et al. (1991) and Woods and Okal (1996) measured plate thickness beneath the Hawaiian swell using dispersion of Rayleigh waves between Midway and Oahu and found that the lithosphere has a normal thickness of ~ 100 km for its age. A similar conclusion was derived by Tarits (1986) from conductivity measurements at several sites in the Pacific. Discontinuities of the mantle conductivity with depth are indeed indicative of partial melting. Such discontinuities are found at depths of 90-100 km around the Hawaiian and Society swells, i.e., at depths expected for the base of a normal lithosphere. Thus, heat flow, seismic, and electric measurements over hotspot swells strongly argue against extensive thinning of the lithosphere. A recent tomographic investigation of the seismic structure of the mantle along the Hawaiian swell by Katzman et al. (1998) has reported a fast region beneath the en-

417

tire Hawaiian swell located in the uppermost 200-300 km of the mantle which is obviously in conflict with the hypothesis that the uppermost mantle beneath the Hawaiian swell is anomalously hot. Although this result remains controversial, the reheating model leading to a substantially thinned lithosphere beneath hotspot swells is not widely accepted. A number of authors have proposed that topographic swells result from surface uplift by convective stresses (e.g., Fischer et al., 1986; McNutt, 1988). However, numerical calculations based on constant viscosity convection in the upper mantle give a geoid to depth anomaly ratio in the range 6-10 mkm -1 (Parsons and Daly, 1983), i.e., a factor ~2 larger than observed. On the other hand, convective calculations by Robinson et al. (1987) assuming a low viscosity zone (LVZ) beneath the lithosphere, showed that the geoid to depth anomaly ratio can be much lower than in the constant viscosity convection case. To infer the apparent compensation depth de corresponding to their convective calculations, Robinson et al. used the Pratt model [see Eq. (3)] to relate the computed geoid to the computed topography and found that de can vary from ~20-100 km depending upon the viscosity contrast between the LVZ and underlying upper mantle. Their analysis showed that the LVZ damps the surface uplift while it causes the geoid response to surface and deep density contrasts to change sign inside the LVZ in such a way that the net response is dominated by the shallow contribution. These results may explain why surface observables, when interpreted in terms of simple compensation mechanisms (Airy, Pratt, plate-thinning models), suggest shallow compensation depths whereas the real compensating density distribution may depend in a complex manner on the viscosity structure of the mantle. Dynamic support of hotspot swells in the presence of a LVZ is also able to explain the linear increase of the geoid to depth anomaly ratio with (age) 1/2 observed over oceanic swells (Monnereau and Cazenave, 1990). According to Ceuleneer et al. (1988), the presence of a LVZ extending to ~200 km depth, of thickness decreasing with plate age at the expense of the growing lithosphere, is able to explain the observed trend providing that the viscosity drops in the LVZ by a factor ~50. Convective calculations by Moriceau et al. (1991), Monnereau et al. (1993) and Ribe and Christensen (1994) with pressure and temperature dependent rheology have indicated that, unlike in stratifiedviscosity models of convection, the deep contribution to the geoid response is negligible, compensating masses being concentrated at a depth corresponding to the base of the thermal plate. These numerical calculations of mantle flow do not produce any lithospheric thinning below hotspot swells, the plume-lithosphere interaction being limited to the base of the lithosphere. Mechanical erosion at the base of the plate may also explain the rapid uplift of swells, as shown by other models of dynamical plume-lithosphere interactions (Sleep,

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SATELLITEALTIMETRYAND EARTH SCIENCES

1990, 1992; Moore et al., 1998). While dynamical support of swells are certainly indicated, other effects may also contribute, such as chemical-differentiation mechanism (Phipps Morgan et al., 1995; Katzman et al., 1998). According to these authors, the swell may be partly supported by chemical buoyancy caused by depletion of the source region from its incompatible elements and extraction of volatiles, as a result of basaltic-differentiation mechanism.

7. SHORT A N D MEDIUM WAVELENGTH LINEATIONS IN THE MARINE GEOID One of the most exciting results based on satellite altimetry was the discovery by Haxby and Weissel (1986) of shortwavelength (200-250 km) geoid undulations of 10-20 cm amplitude elongated in the NW-SE direction over the central Pacific. Other short-wavelength lineations have also been detected in the Indian Ocean and in the south Atlantic (Haxby and Weissel, 1986; Cazenave et al., 1987; Fleitout et al., 1989; Gibert et al., 1989), but it is in the Pacific that the geoid lineations are the most visible, west of the East Pacific Rise between 10~ and 30~ (Figure 8 [see color insert]). They appear oblique with respect to the large Pacific FZ and their orientation coincides with the present motion direction of the Pacific plate in the hotspot reference frame. Some lineations are remarkably continuous over several thousands kilometers. The geoid lineations coincide with topography lineations of ~200 m amplitude. Closely associated with one of the lineation of the south central Pacific is an elongated topographic ridge, called the Puka Puka ridge, discovered by Sandwell et al. (1995) during a research cruise. This volcanic ridge extends over 3000 km and consists of en-echelon individual ridge segments of ~300 km long. A remarkable feature of the Puka Puka ridge is that it is located in a trough of a gravity lineation, while adjacent lineation troughs may be devoid of such volcanic ridges. Although the short-wavelength lineations have been the object of many studies, their origin remains controversial. A variety of mechanisms has been invoked: 1. Small-scale convection developing in a low viscosity layer below the lithosphere (Haxby and Weissel, 1986; Buck and Parmentier, 1986). 2. Magmatism resulting from lithospheric fracturing under the effects of tensile stresses (Winterer and Sandwell, 1987; Sandwell et al., 1995). 3. Off-ridge origin: magmatic traces left into the plate as it moves over fixed convective plumes more numerous than the classical hotspots (Moriceau and Fleitout, 1989). 4. On-ridge origin: magmatic traces or variations in crustal thickness caused by long-lived, along-strike variations

in melt production between transform faults and overlapping spreading centers (Macdonald et al., 1986; Shen et al., 1993, 1995). In the small-scale convection hypothesis, the direction of the lineations should coincide with the direction of present absolute motion of the plate. This is obviously the case in the south central Pacific where the lineations are parallel to the present motion of the Pacific plate and are oblique to the direction of fossil fracture zones. To explain the nonobserved increase in wavelength with plate age predicted by small-scale convection models, it has been proposed that the lineations are produced by seafloor topography undulations frozen into the plate of young age (when the elastic layer is thin enough) and transported by the motion of the plate (Buck and Parmentier, 1986). The second model put forward by Winterer and Sandwell (1987) and Sandwell et al. (1995) hypotheses that the lineations are surface expressions of tensional cracks filled by magmatic intrusions. In this model, the cause of lithospheric stretching are plate boundary stresses. According to Sandwell et al. (1995), three observations argue in favor of the lithospheric stretching model: (1) the very low admittance (geoid to depth ratio) of "~ 1 m km -1 associated with the lineations and (2) the presence of a volcanic ridge, the Puka Puka ridge, located in the trough of a geoid lineation and (3) the absence of clear age progression of the Puka Puka ridge volcanism, inconsistent with a hotspot origin. The very low admittance of the geoid lineations is suggestive of a compensation at Moho depths. In the stretching model, tensional stress field produces deformations of the lithosphere in form of boudins with strain being maximum in the topographic troughs. It is thus in lineation troughs that magmatic intrusion may preferentially occur. This is unlike the small-scale convection model, where volcanism is expected at the crest of the geoid lineations, above the upwelling convective instabilities (see Figure 9).

LITHOSPHERE v

v

ASTHENOSPHERE ASTHENOSPHERE

EXTENSION

SMALL-SCALE CONVECTION

F I G U R E 9 Schematic representation of lithospheric stretching (left) and small-scale convection (right). (Redrawn from Sandwell et al., 1995.)

11. APPLICATIONS TO MARINE GEOPHYSICS

The third and fourth hypotheses are related to a hotspottype origin for the lineations. The directional analysis performed by Moriceau and Fleitout over the Pacific lineations showed that these tend to be aligned with present and fossil directions of the absolute motion of the Pacific plate. They suggested that the lineations reveal the presence of mini hotspot plumes much more numerous than the classical hotspots, leaving magmatic traces in the lithosphere elongated in the direction of motion. Another suggestion has been proposed which relates the wavelength of the lineations with that of typical axial depth undulations of the East Pacific Rise (Macdonald et al., 1986; Shen et al., 1993, 1995). The lineations could represent topographic traces left by near-axis seamount volcanism in response to long-lived changes in along-strike melt production. If the magmatic source is fixed with respect to the mantle, the traces will be aligned with the absolute plate motion direction. If the source is fixed with respect to the spreading axis, the traces will coincide with the spreading direction. Numerous linear chains of small seamounts originating at mid-ocean ridges appear parallel to either absolute or relative plate motions. Some of them (those aligning with absolute plate motion) may result from mini hotspots trapped by the spreading center. The hotspot hypothesis appears however inconsistent with the radiogenic dating of the Puka Puka ridge. Over a distance of 1800 km, the Puka Puka volcanoes erupted within less than 5 myr, thus cannot have been formed by a single or even two or three hotspots. While an hotspot origin should most likely be discarded, it is not yet possible to discriminate between lithospheric stretching or small scale convection as the source of the geoid lineations. It is worth mentioning that the two mechanisms are not mutually exclusive and perhaps both may be invoked to explain the observations. Longer wavelength geoid lineations have been also identified in the Pacific (Figure 8). Maia and Diament (1991) as well as Baudry and Kroenke (1991) found evidence of 400-600 km wavelength geoid lineations in the south central Pacific. In addition, Cazenave et al. (1992, 1995), reported longer wavelength (1000-1200 km) lineations parallel to the short-wavelength lineations discovered by Haxby and Weissel, hence trending in the direction of absolute plate motion. Inspection of Figure 8 shows clearly that the geoid in the south central Pacific exhibits a superposition of parallel lineations of preferential wavebands (150-250 km), (400-600 km), (1000-1200 km). Although not stricly continuous, the 1000-1200 km wavelength lineations extend over several thousands of kilometers. The Polynesian volcanic chains appear trapped in these 1000 km-wavelength lineations. However, the latter extend farther eastward and clearly preceed the active hotspots. On the other hand, north of the Polynesiam province, well-developed geoid lineations do not coincide with known topographic features. The analysis by Cazenave et al. (1995) showed that the geoid lin-

419

eation amplitude, as well as geoid to depth ratio, increases from young to old plate, from 15 to ~45 cm, and from 1.5 to 3 m km -1, respectively, over a plate age range of 1060 Ma. Wessel et al. (1994, 1996) quantitatively demonstrated the three types (200 km, 400-600 km and 1000 km wavelength) of geoid lineations are oriented in the direction of absolute Pacific plate motion in a hotspot reference frame, and that the highest correlations in direction as a function of wavelength are seen for the 200-250 km and 10001200 km wavebands, which corresponds to the most visible geoid lineations (see Figure 8). Wessel et al. (1994, 1996) incidently noted that the discrete wavebands of maximum correlation have values coinciding with the depth of major mantle discontinuities and inferred that the observed lineations are influenced by mantle dynamics. In fact, a number of phenomena may be able to produce the geoid lineations" crustal thickness variations, lithospheric thickness and density variations, and upper mantle convection. Although the observed low admittance (geoid to depth ratio) is suggestive of a shallow origin, it is not possible to discriminate between a lithospheric or sublithospheric origin with this parameter alone. For instance Robinson et al. (1987) showed that convection in the upper mantle within a low viscosity asthenosphere would produce very low admittance values of <2 m km -1 . The orientation of the geoid lineations is of greater help for discriminating between lithospheric or convective processes. Indeed, if the source of the lineations is inside the crust or the lithosphere, their orientation should coincide with the direction of spreading, which is obviously not the case. The orientation and average wavelength (10001200 km) of the geoid lineations is suggestive of the roll-like upper mantle convection pattern observed in experiments conducted by Richter and Parsons (1975). These authors predicted that beneath fast moving plates (as it is the case for the Pacific plate), convective instabilities will align along rolls oriented in the absolute plate motion direction, although this alignement should occur above some critical plate velocity (Rabinowicz et al., 1990). Richter (1973) first noticed that in the Pacific ocean, hotspot chains are ~ 1000 km apart and proposed that the associated swells are the surface expression of convective rolls. This was further confirmed by the statistical analysis of Yamaji (1992) which showed that the hotspot distribution is periodic, with a typical spacing of 1000 km. The Polynesian hotspot swells are indeed clearly part of the medium-wavelength lineations and very likely share with them a common origin. The experiments of Richter and Parsons (1975) assumed constant upper mantle viscosity and low Rayleigh number. In this case, the depth of the convective layer should equal the half-wavelength of the lineations. In the mantle, where the viscosity varies with depth and the appropriate Rayleigh number is probably much higher, the length-scale of boundary layer instabilities may become much smaller than the depth. If the medium-wavelength geoid lineations are indeed related to

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SATELLITE ALTIMETRY AND EARTH SCIENCES

mantle convection, we can just say that the observed horizontal length-scale appears to be compatible with a depth of convection of ~600-700 km. Whatever, it is very likely that the ~ 1000 km geoid lineations are related to mantle convection. The 200 km undulations, on the other hand, may result either from small-scale convection or lithospheric streching, or a combination of both mechanisms. More theoretical and experimental work is indicated to clarify the origin of these curious features.

8. MAPPING THE SEAFLOOR TECTONIC FABRIC Because of the close correlation between the 20-200 km wavelengths of the geoid height or gravity and the uncompensated seafloor topography (McKenzie and Bowin, 1976), the dense and uniform coverage of the satellite-altimeter measurements reveal in detail the seafloor tectonic fabric in most of the world's ocean, and particularly in the poorly charted southern oceans (Figure 1). Tectonic fabric charts of the ocean floor were initially derived from interpreting altimeter data plotted along satellite tracks (e.g., Vogt et al., 1984; Cande et al., 1988; Gahagan et al., 1988; Royer et al., 1989; Royer et al., 1990; Mtiller and Roest, 1992). Global geoid or gravity images constructed from gridding satellitealtimeter data progressively unveiled with finer details the topography of the seafloor. The "blurred" images based on Geos-3 and Seasat data (Haxby et al., 1983; Sandwell, 1984b; Haxby, 1987) focused as the dense Geosat Geodetic Mission (GM) data were released (McAdoo and Marks, 1992) and TOPEX and ERS-1 data became available (Laxon and McAdoo, 1994; Cazenave et al., 1996; McAdoo and Laxon, 1997; Sandwell and Smith, 1997). These data now permit an accurate mapping of almost any relief of the seafloor wider than 10 km and higher than about 1 km, such as fracture zones, seamounts and mid-oceanic spreading ridges. This detailed information leads to many improvements in determining the relative and absolute plate motions of the lithospheric plates, and in characterizing in a global perspective the processes that shape the oceanic crust (spreading ridge morphology, ridge segmentation, intraplate deformation, hotspots ...).

8.1. Fracture Zones Oceanic fracture zones are perhaps the most striking features visible in a set of parallel satellite-altimeter profiles or in satellite-derived gravity grids (see Figure 1). Fracture zones form long, continuous and linear bathymetric structures reflecting the past relative motions between plates (Wilson, 1965a; Morgan, 1968). Mapping the full extent of fracture zones over 90% of the world's ocean basins proved

very useful for testing and refining plate reconstruction models. Satellite-derived gravity also helped identifying other linear conjugate structures of the ocean floor that rifted and spread apart, adding new constraints on plate reconstructions. 8.1.1. Geoid/gravity Signatures o f Fracture Z o n e s

The topography of fracture zones is characterized by very long ridges, troughs or escarpments that delineate corridors of ocean crust of different age. These general characteristics are also observed in the satellite-altimeter data and vary with the spreading rates. In a fast-spreading regime, such as in the Pacific ocean (Figures 10a and 10b [see color insert]), the fracture zone morphology is dominated by a step reflecting the age difference between adjacent corridors, resulting in a geoid step in the order of 1-2 m (see Figure 4) or 20-60 mGal gravity anomalies, for a topographic step of about 1 km (-~ 10 Ma offset; e.g., Sandwell, 1984a). In a slow spreading regime, such as in the Atlantic and western Indian oceans (Figures 10c and 10d), this age step is dominated by a complex topography expressed by deep valleys bounded by elevated and steep walls (e.g., Colette, 1986; Fox and Gallo, 1986), producing up to 1.5 m peak-to-trough geoid anomalies for a ~ 1.4 km ridge-to-trough height difference (5-10 Ma offset; e.g., MUller et al., 1991). Hence, global tectonic fabric charts of the ocean crust were easily produced by correlating the geoid height anomalies (Vogt et al., 1984; Cande et al., 1988), deflection of the vertical anomalies (Gahagan et al., 1988; Royer et al., 1989; Royer et al., 1990) or vertical gravity anomalies (Mtiller and Roest, 1992) over a series of satellite passes intersecting fracture zones. Automatic searches either fitting a Gaussian shape to geoid troughs (Shaw and Cande, 1990) or detecting minima in the geoid heights or gravity (Gibert et al., 1989; Royer et al., 1997) were also applied to individual satellite passes in order to accurately map the fracture zone valleys in the South Atlantic and western Indian oceans. The dense spatial resolution of the global gravity images based on the Geosat and ERS-1 geodetic missions would now be suitable for applying terrain analysis or image processing techniques in order to extract all the continuous highs and lows (Figure 11). Despite the improvements in the spatial resolution of satellite altimeter data, mapping precisely the actual location of fracture zones is generally difficult. Firstly, fracture zones often exhibit a complex topography over a 10-30 km width, particularly along large offset fracture zones (Tasman FZ in Figure 10b) or in areas where a change in the direction of motion occurred (Heezen and Eltanin FZ in Figure 10a). Thus locating precisely the depth/age step between adjacent corridors may be uncertain. Note that the same limitation applies to high-resolution wide-beam bathymetric data (e.g., Caress et al., 1988; Kuykendall et al., 1994). Secondly, since geoid or gravity anomalies are actually caused by density contrasts (mainly between the oceanic crust and sea water),

421

11. APPLICATIONS TO MARINE GEOPHYSICS

30"S

40~

50"S 50~

60~

70~

F I G U R E 11 Gravity lows extracted in the south-western Indian Ocean from the global gravity anomaly grid of Sandwell and Smith (1997): (A) Ultra-slow (10-20 mm year -1) Southwest Indian Ridge characterized by a series of deep north-south fracture zones and deep east-west spreading ridge axes, (B) SW-NE fracture zones in the Southern Crozet Basin created at ultra-fast to fast spreading rates (100-220 mmyear-1), (C) Eastern Crozet Basin created at intermediate spreading rates (60-100 mm year-1 ). (CP) Crozet Plateau, (KP) Kerguelen Plateau. After Munschy (1997).

they may also reflect density variations within the oceanic crust and upper mantle, which are common in the vicinity of fracture zones (e.g., Detrick et al., 1993). A comparison of the geoid signature and the basement topography along the Kane fracture zone in the Central Atlantic shows that the mismatch in the location of the fracture-zone valley may be as large as 15 km, although the average phase shift between geoid and topography is about 5 km (MfiIler et al., 1991). Thus satellite-derived gravity can be used to locate a fracture zone axis within i 5 kin. These studies also empha-

size that satellite-derived (or shipborne) gravity reveal the actual basement topography, which in some cases is burried by thick sediments. In this respect, the satellite altimeter data helped tracing the fracture zones up to the continental margins (see the Equatorial Atlantic Ocean in Figure 1). Another difficulty when mapping fracture zones, is that there are other look-alike features which are not representative of relative plate motions. In Figure 10d, the Northern FZ follows a flowline parallel to the Kane FZ and progressively departs from it towards the ridge axis to form

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a low-angle V-shaped trough. Such V-shaped structure reflects the migration of the mid-Atlantic Ridge relative to an underlying mesospheric framework (hotspot reference frame; Schouten et al., 1987; Mtiller and Roest, 1992). Some small- to medium-offset fracture zones appear to be meandering on either side of the spreading axis, like the fracture zones immediately south of the Atlantis FZ and of the Kane FZ (Figure 10d); they reflect back and forth migrations of non-transform discontinuities along the spreading ridge and thus record the evolution of the small-scale ridge segmentation through time. Note that the symmetry of these meanders puts tight constraints on plate reconstructions, although they do not follow flowlines. High-angle V-shaped structures are also observed, for instance south of Australia, east of Australian-Antarctic Discordance (Phipps-Morgan and Sandwell, 1994), or along the Pacific-Antarctic Ridge (Figure 1); they result from a fast migration of spreading centers, known as propagating rifts, leaving pseudo-faults in their wake (Hey et al., 1989).

8.1.2. Application to Plate Tectonic Reconstructions Active transform faults record the instantaneous direction of motion between two plates, and thus follow small circles about the pole of rotation describing these motions (Morgan, 1968). Fracture zones form the fossil extension of these transform faults and hence provide a continuous record of the trajectories or flow-lines of each plate relative to the spreading ridge axis. Several techniques can be applied to take advantage of the satellite-altimeter data in order to better constrain plate motion models. Some methods use the property that fracture zones follow small circles about instantaneous poles of rotation. Transform azimuths measured from Seasat data in the southern ocean were inverted in order to better constrain the direction of the Pacific-Antarctic instantaneous motions (DeMets et al., 1990, 1994). Satellite-derived trends for all the fracture zones in the South Atlantic, south of the Equator, were simultaneously fitted using a single rotation between Africa and South America for the last 35 Ma (Gibert et al., 1989). A more detailed model was also achieved by adjusting several different small circles instead of a single one to these satellite-derived flowlines (Shaw and Cande, 1990). Other methods assume that the image of a mid-ocean ridge at a given time is identical on the two plates that shared this plate boundary. This image or isochron, whose shape may vary through time, is defined by a succession of magnetic lineations offset by transform fault segments. Superimposing two isochrons identified in conjugate basins yield the finite rotation describing the past position of one plate relative the other at the corresponding time. Isochrons are mapped from crossings of shipborne or airborne magnetic profiles with the magnetic lineations and from crossings of satellite altimeter profiles across fracture zones. If

the plate motion model is correct, and assuming symmetric seafloor spreading, flowlines derived from the combination of successive finite rotations should match the observed fracture zone trends. This test was for instance applied to compare satellite-derived flowlines with predicted flowlines in the Atlantic (Mtiller and Roest, 1992). It confirmed that the fracture zones trends in the Equatorial Atlantic, south of the Fifteen Twenty Fracture Zone, are better accounted for by the Africa/South America motion than by the Africa/North America motion. The southwest Indian Ocean is another example where the satellite altimeter data help constraining plate motion (Africa/Antarctica). Seasat data gave a hint that two consecutive major changes of motion occurred along the southwest Indian Ridge. A kinematic model combining satellite altimeter information with magnetic anomalies (Royer et al., 1988) predicted that a series of closely spaced fracture zones developed as the result of the first change of motion and coalesced together, during the second change of direction, into the very large offset fracture zones that now offset the Southwest Indian Ridge. This model was later confirmed when the Geosat GM data unveiled all the details of the Southwest Indian Ridge seafloor fabrics (Marks et al., 1993). Satellite altimeter data helped improve finite reconstruction models in many other areas such as the Atlantic (Cande et al., 1988; Nurnberg and MUller, 1991; Mtiller and Roest, 1992), the southwest Pacific (Mayes et al., 1990; Cande et al., 1995), the southeast Pacific (Tebbens and Cande, 1997), the Indian Ocean (Royer and Sandwell, 1989; Royer et al., 1997), or the Tasman Sea (Gaina et al., 1998). For the purpose of plate reconstructions, locating the symmetric traces of a fracture zone is critical, but generally difficult, since the expression of a fracture zone may be different on conjugate flanks. For instance, the fracture immediately west of Tasman FZ (bottom fracture zone in Figure 10b) is better expressed on the Antarctic plate than on the Australian plate; the same can be observed in Figure 10c (bottom fracture zone). Along large offset-fracture zones, any change in the spreading direction will reshape their topographic expression. Depending on the fault geometry and the direction of change, extensional or compressional features will develop as the new direction fabric overprints the former direction fabric, asymmetrically on the conjugate limbs of the fracture zone (Caress et al., 1988; Hey et al., 1988). For this reason, one should avoid using large-offset fracture zones for plate reconstructions. In slow spreading regimes, deep valleys seem representative of the actual fracture zone location; this signature appears to be symmetrical on the two limbs of a fracture zone, as for example along the Kane FZ (Figure 10d). Dispersion analysis of reconstructed fracture zone crossings extracted from satellite passes, along the slow spreading Central Indian and Carlsberg ridges, showed that the standard deviation was in the order of 4 km (Royer et al., 1997), slightly better than

11. APPLICATIONS TO MARINE GEOPHYSICS

the 5 km uncertainty inferred from geoid/topography comparison (Mtiller et al., 1991). This analysis combined leftlateral and right-lateral transform offsets, hence any systematic bias due to an anomalous density distribution along fracture zones should have canceled out. Along fast to medium spreading ridges, the signature is generally anti-symmetric (e.g., Figure 10a and 10b), with a ridge on the young side of the fracture zone and a trough on the old side; then the inflection points in the geoid or gravity signal would be more representative of the symmetric depth/age steps. Satellite-derived gravity data proved also very useful to identify and map conjugate features of the ocean floor, such as rifted margins, limits of the continental shelf, edges of submarine plateaus that rifted apart, or troughs left by major ridge jumps (e.g., Henry and Hudson troughs in Figure 10a). In some cases (Figure 12 [see color insert]), the remarkable symmetry of these tectonic scars provide a valuable constraint for paleogeographic reconstructions, particularly in the poorly charted southern oceans or near continental margins where sediments often hide the basement structures. Most recent models unraveling the plate tectonic history around Antarctica have taken advantage of this information (e.g., Royer and Sandwell, 1989; Lawver et al., 1991; Lawver and Gahagan, 1994; Sutherland, 1995; Marks and Stock, 1997; Tikku and Cande, 1998).

8.2. Seamounts Away from the trenches and mid-oceanic ridges, seamounts, and submarine plateaus are, together with fracture zones, the main type of relief of the ocean floor. Until the advent of satellite altimeters, most seamounts or undersea volcanoes remained uncharted because only a small fraction of the world's ocean has been mapped by surface ships. Since seamounts represent an excess of mass relative to the surrounding abyssal plains, they produce little bumps on the mean sea surface or geoid height. Thus satellite altimetry has proven a very powerful tool not only to systematically detect and locate seamounts, but also to infer, upon certain assumptions, their size and shape, as well as their ages. This information is important for understanding the processes that control their origin and evolution, for determining absolute plate motion, or measuring the mechanical properties of the lithosphere. Other applications include the detection of hazards for submarine navigation, the search for new fishing grounds or modeling the ocean circulation pattern. The main progresses in this field since the launch of GEOS-3 in 1975 come from the increasing coverage and improving quality of the satellite altimeter data.

8.2.1. Seamount Signature A typical signature of a seamount on the geoid (Figures 13 and 14) consists of a small geoid anomaly superimposed on a broad regional trend [curve (b) in Figure 14].

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After removing the long-wavelength component (> 200 km), the geoid signal correlates fairly well with the topography of undersea volcanoes [curve (a) in Figure 14]. The geoid anomaly is centered on the seamount and reaches 1-2 m for a 1-3 km high seamount with a typical base-diameter of 10-50 km. The horizontal derivative of this geoid anomaly along the satellite track, known as deflection of the vertical, will form a sharp dipolar anomaly easier to detect; peak-to-trough amplitudes range from 20-200 microradians and the inflection point is at the vertical of the seamount summit [curve (e) in Figure 14]. The geoid signature can also be converted into a sharper gravity anomaly [vertical derivative of the geoid; curve (d) in Figure 14]. Amplitudes of the seamount gravity anomaly typically range from 20200 mGal. Depending on the age, and therefore on the mechanical strength of the underlying lithosphere at the time when the seamount emplaced, the positive anomaly associated with the seamount will be surrounded by a ring-shaped negative anomaly, marking the deflection of the lithosphere caused by the seamount load (Figure 2d). This depression is unfortunately often indiscernible in the bathymetry due to sediment infill. If the topography of the seamount and associated depression is known, then the thickness of the elastic portion of the lithosphere can be inferred from the amplitude and diameter of this gravity low. The parameters used to characterize a seamount are generally the amplitude of the geoid or gravity anomaly and the distance between the center of the positive anomaly and the zero-crossing. The amplitude is not a good measure of the height of the seamount because of the flexural response of the lithosphere, which tends to reduce this amplitude. The zero-crossing is also often difficult to locate precisely. Peakto-trough amplitudes of the deflection of the vertical suffers the same limitation. However the peak-to-trough distance is equal to the characteristic diameter of the seamount and the difference between the deflection diameter (distance between the outer zero crossings) and the seamount diameter is equal to the flexural diameter (Craig and Sandwell, 1988). The amplitude of the vertical gravity gradient, which enhances the short-wavelength relative to the long flexural wavelength, is less sensitive to the loading effect; zerocrossings are also easier to detect as the anomaly is sharper (Wessel and Lyons, 1997). 8.2.2. S e a m o u n t Distribution

Techniques for detecting seamounts from the geoid height anomalies measured by satellite altimeters evolved as the satellite data coverage and data quality improved. GEOS-3 data coverage was not uniform, with best coverage occurring near tracking stations. Early failure of Seasat left losange-shaped gaps of about 100 km side between profiles; also, due to sea-ice, recovery of Seasat data south of 60~ was poor. However, these gaps are now filled by the Geosat and ERS-1 geodetic missions.

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FIGURE 13

Satellite-altimeter profiles along the Louisville Ridge: (A) TOPEX, (B) and (C) ERS-1, (D) Geosat ERM, (E) Seasat. (Bottom) Bathymetric chart based on the GEBCO chart 5-10 (Monahan et al., 1982). Band-path filtered (20-200 km) geoid heights are plotted along satellite tracks, positive to the west (4 m/degree of longitude). (Top) Gravity anomaly contours based on the grid of Sandwell and Smith (1997). Band-path filtered (20-200 km) satellite-derived gravity anomalies are plotted along satellite tracks, positive to the west (120 mgal/degree of longitude). Circle symbols and large circle indicate the location and radius of seamounts as predicted from the global gravity grid (Wessel and Lyons, 1997). Satellitederived gravity reveals many more seamounts than initially charted. Thick black lines outline the shipboard data shown in Figure 14.

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Improvements in the satellite-borne altimeters and storage capabilities reduced the limit of along-track resolution of the altimeter measurements by a factor of three from 75 km for Geos-3, to 50 km for Seasat, to 22-30 km for stacked Geosat Exact Repeat Mission (ERM), TOPEX or ERS-1 profiles (these limits reflect the 50% level of coherence between repeating passes; Sandwell and Smith, 1997). The accuracy in locating a seamount for an individual profile is also a function of the sampling rate along track (e.g., 1 sec or 6.6 km for Seasat). Across track, the resolution limit varies according to the track spacing and thus improves from the Equator towards the latitude of culmination (+72 ~ for Seasat and Geosat, +81 o for ERS-1). Merging data from ascending and descending passes or from different satellites partly palliates this limitation. Different techniques for predicting the presence of seamounts have been developed. Lambeck and Coleman (1982) modeled seamount signatures on the geoid and searched visually Geos-3 and Seasat profiles. Lazarewicz and Schwank (1982) and White et al. (1983) applied a systematic search on Seasat profiles using matched filters. Gairola et al. (1992) applied the same type of filter to Geosat data. Sandwell (1984b) analyzed an image of the sea-surface constructed from deflection of the vertical profiles and detected 72 uncharted seamounts in the southwest Pacific. Baudry et al. (1987) used a least-square fit between modeled geoid anomalies and actual Seasat profiles. Ground-truthing the prediction from satellite altimeter profiles by surface-ship bathymetric survey was initially not very successful (e.g., Keating et al., 1984), casting some doubts about the reliability of this tool; this was mainly due to the across-track uncertainty and in some cases to high noise-to-signal ratios. Detection of seamounts based on at least two adjacent or intersecting profiles proved highly reliable and accurate within 15 km (e.g., Baudry and Diament, 1987). The resolution of the latest gravity grids (e.g., Sandwell and Smith, 1997), in the order of 10 km with an rms accuracy of 3-6 mGal, now enables the detection of all seamounts taller than 1 kin, of which 30-50% were not charted previously. Satellite data also demonstrated that some previously charted seamounts were clearly mislocated because of errors in the celestial navigation of the mapping vessels [e.g., Fabert Bank in the Austral-Cook area (4158.78W, 24~ as in Mammerickx and Smith, 1982) or the Islas Orcadas Seamounts in the Weddel Sea (as in LaBrecque and Rabinowitz, 1981; see also Figure 13) or even non-existent (e.g., Novarra Knoll southwest of St Paul and Amsterdam islands in the Indian Ocean, as in Fisher et al., 1982)]. Nonetheless, there are only few quantitative studies of seamount global distribution using altimetry data. Craig and Sandwell (1988) were the first to perform a global search for seamounts by analyzing the deflection of the vertical on Seasat profiles and detected as many as 8556 seamounts. Comparison between charted and predicted seamounts in

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a well-mapped area suggested that less than 25% of the seamount population could be detected by Seasat profiles, because of the track spacing. Another difficulty when analyzing sparse individual profiles was to decipher a seamount from lineated structures associated with fracture zones; both have the same along-track signature in the geoid. Using the gravity grid of Sandwell and Smith (1997), Wessel and Lyons (1997) performed a systematic search for seamounts in the Pacific plate (Figure 15). They actually used the vertical gravity gradient (vertical derivative of gravity) which better reflects the seamount characteristics. On the Pacific plate alone, they isolated and characterized ~8882 seamounts out of ~25,000 volcanic edifices visible in the satellite data, discarding all features detected within 25 km of a known fracture zone and missing all seamounts smaller than ~ 1.5 km, unresolvable by this technique. These few global studies generalized and confirmed findings from regional analyses, which are mainly available for the Pacific Ocean, based on bathymetric charts or wide-beam soundings (e.g., Menard, 1964; Litvin and Rudenko, 1973; Batiza, 1982; Jordan et al., 1983; Abers et al., 1988; Smith and Jordan, 1988). The seamount population is the largest in the western tropical Pacific, with more than 150 per million square kilometers in the Central Pacific and French Polynesia (Wessel and Lyons, 1997). The northeast Pacific shows only few and generally small seamounts (Figure 15). While there is a general trend showing an increasing seamount population as the crustal ages increase (Wessel and Lyons, 1997), eastern half of the Pacific plate commonly shows high seamount aboundance on the younger sides of large offset fracture zones (Craig and Sandwell, 1988). The largest population of seamounts as well as the largest seamounts are found on the old Pacific crust (mid-Cretaceous age, 90120 Ma). In the Atlantic Ocean, seamounts cluster around areas showing hotspot activity, whereas seamounts look evenly distributed in the Indian and Southern Oceans (Craig and Sandwell, 1988). 8.2.3. Seamount Characteristics

Deriving the shape and size of a seamount solely from its signature on the geoid is not straightforward, because the solution is non-unique. The signature combines the effects of the topography and of the mode of compensation (local, regional or thermal) of the underlying plate. Another limitation is that satellite altimeters cannot resolve wavelengths shorter than ~20 km and hence are unable to detect seamounts whose diameter is smaller than ~ 10 km or whose height is smaller than ~ 1 km. Seamounts are usually defined by a conical and steepsided geometry, with sometimes a truncated or flat top. In order to characterize seamount signatures in the geoid, gravity or vertical gravity gradient, this shape is generally approximated by a Gaussian bell (Sandwell, 1984b; Watts and Ribe, 1984; Baudry et al., 1987; Craig and Sandwell, 1988; Wessel

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FIGURE 14 Typical satellite-altimeter signatures of seamounts along the Louisville Ridge (see location in Figure 13): (a) band-path filtered (20-200 km) geoid height, (b) unfiltered geoid height, (c) filtered vertical gravity gradient (dashed line), (d) filtered geoid-derived gravity, (e) filtered deflection of the vertical (geoid slope along track), (f) shipborne gravity, (g) gravity predicted along ship-track from the global gravity grid of Sandwell and Smith (1997; line with dots), (h) bathymetric profile. (R) and (H) are the base-radius and height, respectively, predicted by Wessel and Lyons (1997) from inversion of the vertical gravity gradient. Dots along curves give the sampling rate. Shipboard gravity and bathymetric profiles are from the R/V Vema cruise 3602 (1979). TOPEX, ERS-1 (35 d. cycle) and Geosat (ERM) profiles are stacks of 38, 9, and 44 repeat passes, respectively. All data are projected along the direction (Az) of the satellite ground tracks. Note the close correspondence between shipboard and satellite-derived gravity (curves f and g). Location mismatches of the seamount tops between the satellite and shipboard observation are due to offsets between the satellite or ship tracks and the projection point. Disagreements between the predicted and observed sizes of seamounts reflect the non-uniqueness of gravity data inversions. Gravity anomalies emphasize a small deflection of the lithosphere for all seamounts.

11. APPLICATIONS TO MARINE GEOPHYSICS

FIGURE

14

(Continued).

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FIGURE 14 (Continued).

11. APPLICATIONS TO MARINE GEOPHYSICS

F I G U R E 14

(Continued).

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FIGURE 14 (Continued).

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431

FIGURE 15

Seamount population on the Pacific plate, after Wessel and Lyons (1997). Locations were extracted from the vertical gravity gradient of the global gravity anomaly grid of Sandwell and Smith (1997). The size of circle symbols varies with the amplitude of the vertical gravity gradient: small open-circles 30-60 Eotvos (typically 1-2 km tall), medium grey-circles 60-120 Eotvos (typically 1.5-4 kin), large black-circles > 120 Eotvos (>2.5 km). The number of seamounts in each category is 4423, 2167, and 895, respectively. Eckert equal-area projection.

and Lyons, 1997). The mean slope is a function of the height to width ratio; hence for a given mean slope, the seamount shape is only controlled by the seamount height. In order to model the flexure of the lithosphere due to the seamount load, the simplest model is to assume that the lithosphere behaves as a continuous and elastic layer, characterized by its elastic thickness Te (Watts and Ribe, 1984). Comparisons between observed and calculated geoid anomalies, for a known bathymetry, show that a precise knowledge of Te

is not critical and that it is easy to distinguish a seamount generated near a ridge axis (e.g., Te"~5 km) from a seamount emplaced on an old lithosphere (Te > 15 km; Watts and Ribe, 1984; Baudry et al., 1987). Then for a given value or set of elastic thickness, a series of models can be computed with varying heights and slopes, and compared to the observed anomalies (geoid, gravity, or vertical gravity gradient) in order to derive the height and width of a seamount. Predicted and observed seamount sizes for well-charted seamounts

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may differ by 15-30%; the underestimation of the height is likely due to the Gaussian shape approximation (Baudry and Diament, 1987; Wessel and Lyons, 1997). The satellitederived volumes are about 10-25% smaller than the volumes determined from bathymetric data sets. The number of seamounts decreases as their diameter increases (Craig and Sandwell, 1988). In the 2-8 km range height, the frequency for seamount height varies as a power law of the seamount predicted heights (Wessel and Lyons, 1997). Perhaps the most promising technique is to invert the satellitederived gravity grid in conjunction with available shipboard bathymetric data (see Chapter 12; e.g., Baudry and Calmant, 1991; Calmant, 1994; Ramillien and Cazenave, 1997; Smith and Sandwell, 1997). These new predicted topography grids awaits quantitative studies. The age of the seamount is another parameter that can tentatively be derived from the size of a seamount, its geoid signature and the age of the underlying seafloor. One way would be to compute the elastic thickness in order to infer the age of the lithosphere at the time of loading; knowing the age of the seafloor, an estimate of the seamount age can be deduced (Calmant et al., 1990). However, accurate estimates of Te require an accurate knowledge of the topography. From a limited number of seamounts, Epp (1984) noted a linear relationship between the seamount heights and the age of the seafloor at the time the seamounts built up. Following this observation and from their collection of seamounts, Wessel and Lyons (1997) determined an empirical relation yielding the pseudo age of a seamount from the age of the seafloor and the vertical gravity gradient amplitude. This empirical law, although highly speculative, suggests that, in the Pacific, intraplate volcanism had a peak activity during the mid-Cretaceous, not in the Paleocene, as found from a previous study (Batiza, 1982). 8.2.4. Hotspot Traces Perhaps one of the most intriguing question about the numerous observed submarine volcanoes is their origin. Linear chains of seamounts and of elongated narrow ridges such as the Hawaiian-Emperor and Louisville chains are interpreted as the surface expression of stationary deep mantle plumes or hotspots on the overriding plate (Wilson, 1965b; Morgan, 1971). The trajectory of a fixed hotspot on the overriding plate follows a small circle about the absolute pole of motion; if the direction of motion changed through time, the hotspot track will follow a succession of small circles. Thus fitting small circles to at least two congruent hotspot traces yield the location of the stage poles. The length of each small-circle fitted to the seamount locations yields the angle of each stage rotation. Finally, age determinations along the modeled hotspot tracks yields the rate of motion. Thus a correct model of absolute plate motion must both predict the hotspot tracks and the age progression along the tracks (e.g., Clague and Jarrard, 1973; Morgan, 1981).

The identification of many new uncharted seamounts from satellite-altimeter data allows further tests of the hotspot hypothesis. Craig and Sandwell (1988) and Wessel and Lyons (1997) identified many new lineated chains with trends parallel to the Hawaiian-Emperor and Louisville chains, such as the Mariana, Gilbert, Tuamotu and Austral island groups. Some of these chains intersect with one another and are difficult to sort out. In addition, the location of the hotspots from which these chains would have originated is not always known. Wessel and Kroenke (1997) presented a geometric relationship that links hotspots to the seamounts they produced. For a given kinematic model, they constructed the flowlines or trajectories of each seamount relative to the hotspots, instead of reconstructing the hotspot trajectory relative to the overriding plate, the latter requiring to know its present-day location. If the tested model is correct, all the flowlines originating from seamounts related to the same hotspot should intersect at its present-day location, even if extinct. Applied to the Pacific plate, this technique is particularly demonstrative because of the sharp change in the direction of absolute motion which occurred at about 43 Ma, as illustrated by the Hawaiian-Emperor "elbow". However, except for the Hawaiian and Louisville hotspots, which were used to constrain the rotation poles and angles, most flowlines do not converge, or if so, at points that do not coincide with known hotspots such as Macdonald, Society, or Pitcairn. The main implications are either that the kinematic model is incorrect or that hotspots move relative to one another. In addition, as mentioned in Section 7, there are many seamounts, either isolated or in linear chains that do not fit the hotspot hypothesis. Some originated at spreading ridge axes or near transform fracture zones, marking short or long-lived outbursts of magmatism; other may originate from mini-hotspots moving relative to the major ones (Fleitout and Moriceau, 1992) or may result from tensional cracks in the lithosphere (Sandwell et al., 1995). Conversely, some short-wavelength undulations of the geoid, topped by few seamounts or linear ridges, seem to coincide with absolute plate motions (see Section 7), but have not been used to constrain them. Hence, the satellite-altimeter data provide an almost exhaustive set of information to improve the geometry of absolute plate motion model; however, age determinations still remain the limiting factor to fully constrain them and so, to address quantitatively the question of hotspot fixity or of hotspot fluxes trough time.

8.3. Spreading Ridges Mid-oceanic spreading ridges, the longest mountain chain on Earth, are now almost entirely and accurately mapped from satellite-gravity, except in the Arctic region north of 81.58~ not covered by satellite altimeters. As discovered since the earliest observation of seafloor morphology

11. APPLICATIONS TO MARINE GEOPHYSICS

(Heezen, 1960" Menard, 1960; Macdonald, 1982), the topographic expression of spreading ridges varies between two end-members: fast-spreading ridges such as the East Pacific Rise (130-160 mm year- 1) are characterized by a small axial rise and smooth flanks whereas slow-spreading ridges such as the mid-Atlantic Ridge (11-25 mm year -1) are characterized by a deep axial valley and rugged flanks. As shown in Figure 10, satellite-derived gravity reflects these characteristics and displays a linear axial positive anomaly and smooth flanks along fast-spreading ridges and a linear negative anomaly flanked by positive anomalies and rough flanks along slow-spreading ridges. Since the intermediate-spreading ridges (Southeast Indian Ridge and Pacific-Antarctic Ridge) are located in the remote southern oceans, the transition between this two end-member configurations used to be poorly ascertained. The uniform coverage of the satellite-derived gravity data now allows one to locate precisely the ridge axes and to compare the gravity signal along most of the world ocean spreading ridge system, and also to characterize the structural gravity grain, also called gravity roughness. 8.3.1. Gravity

Signature of Mid-oceanic Ridges

Along slow-spreading ridges, the peak-to-trough amplitude of the gravity anomaly at ridge axes decreases with increasing spreading rates, from - 1 2 0 - 0 mGal, whereas the amplitude remains relatively constant on fast spreading ridges, about ~10 mGal (Owens and Parsons, 1994; Small and Sandwell, 1994). The transition from the slow- to fastspreading structure occurs along the Southeast Indian and Pacific-Antarctic ridges within a narrow range of spreading rates, between 60 and 80 mm year -1 (Figure 16; Small and Sandwell, 1989; Small and Sandwell, 1992; Owens and Parsons, 1994; Small and Sandwell, 1994). In some instances, the transition occurs abruptly across a single transform fault, like at 171 ~ along the Pacific-Antarctic Ridge (60 mmyear -1" Sandwell, 1992) or at 78.5~ 41~ along the Southeast Indian Ridge (68 mm year-1. Owens and Parsons, 1994). In other instances, the transition is more gradual like along the Reykjanes Ridge (19 mm year- j" Hwang et al., 1994) or along the Australian-Antarctic Discordance (74 mm year -l" Palmer et al., 1993). The latter two areas are however notable exceptions in the observed patterns along slow- and fast-spreading ridges, respectively. The range of spreading rates at which the transitions from slow- to fastspreading structure occur, thus indicates that the spreading rate is not the only controlling factor. The crustal genesis model of Phipps Morgan and Chert (1993a; 1993b) suggests that the axial morphology is ultimately controlled by the thermal structure of the ridge axis, which is a function of the spreading rate and the magma supply. The transition in axial morphology would then occur above a threshold sensitive to small thermal perturbations (Marks and Stock, 1994; Small, 1994; Small and Sandwell, 1994; Sahabi et al., 1996), either

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local, or related to a hotspot (Iceland hotspot for the Reykjanes Ridge, Bouvet hotspot for the South Atlantic Ridge; Amsterdam-St. Paul hotspot for the Southeast Indian Ridge) or to asthenospheric flows (Pacific-Antarctic Ridge; Marks and Stock, 1994; Sahabi et al., 1996).

8.3.2. Geoid/gravity Roughness The previous sections have mainly used the 20-200 km wavelength in the satellite altimeter data for mapping the major structures of the seafloor. This bandwidth is also informative about the structural characteristics of large oceanic areas. Figures 10a and 10d show clearly that the amplitudes of the gravity anomalies are larger and vary over a wider range in the slow-spreading Atlantic Ocean than in the fastspreading Pacific Ocean. A quantitative comparison between a series of satellite passes in the Atlantic and Pacific oceans show that the gravity field in the Atlantic has more power than in the Pacific for all wavelengths larger than 20 km (Small and Sandwell, 1992). Variations in the amplitude of the small-wavelength (20200 km) geoid or gravity field, also called geoid or gravity roughness, can thus be used to characterize on a regional scale these spreading rate dependent processes. Geoid roughness has been estimated along satellite tracks by the envelope of band-path filtered Seasat geoid profiles (Gibert et al., 1989; Goslin and Gibert, 1990) or by a weighted average of least square (rms) of deflection of the vertical in a moving window along band-path filtered and stacked Geosat ERM profiles (Small and Sandwell, 1992). Global roughness map obtained from gridding these data emphasizes the variations of roughness along the spreading ridges. Slowspreading ridges (Atlantic and western Indian Ocean) display high roughness (> 13 cm) on the axis and lower roughness (5-6 cm) on the flanks; fast spreading ridges (East Pacific Rise, northern Pacific-Antarctic Ridge) present a low roughness (<3 cm) both on the axis and the flanks. Gravity roughness at spreading ridge crossings decrease by a factor 10 between 16 and 80 mm year -1, beyond which it remains uniformly low (Small and Sandwell, 1992). The abrupt transition between 60 and 80 mm year -1 is consistent with that found in the gravity amplitude or in the topography of spreading axes (Small, 1994, 1998). The roughness of the ridge flanks also increase as the spreading rates decrease, consistent with analyses of the ridge flank topography roughness (Goff, 1991; Hayes and Kane, 1991; Malinverno, 1991). However, except along some portions of the Carslberg and Southeast Indian ridges, the satellite passes are generally not parallel to the fracture pattern (i.e., flowlines), thus making difficult any quantitative comparison between geoid and topography roughness. Geoid roughness also reveals intermediate (90-400 km) wavelength patterns, reflecting the ridge large-scale segmentation (Gibert et al., 1989), small-scale convection pattern (Fleitout and Moriceau, 1992), compensation pro-

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F I G U R E 16 Variation of ridge-axis morphology and gravity anomaly with spreading rate, after Small (1998): (a) Amplitude of axial topographic relief measured from bathymetric profiles, (b) Amplitude of axial gravity-anomaly derived from the global gravity grid (Sandwell and Smith, 1997). Note the coincident change in polarity between 60 and 80 mm year-1. The axial rise along the slow-spreading Reykjanes Ridge and the axial valley at the Australian-Antarctic Discordance (AAD) along the intermediatespreading Southeast Indian Ridge are two notable exceptions in the general pattern.

cesses (Goslin and Gibert, 1990), or lithospheric deformation (McAdoo and Sandwell, 1985; Fleitout et al., 1989) (see also Section 7).

9. C O N C L U S I O N Satellite altimeters have provided a wealth of information about the structure of the seafloor and about the man-

tle processes that generate them. Perhaps one of the most important result is the confirmation of plate tectonics. The satellite-derived gravity data reveal the whole extension of the active oceanic plate boundaries, transform faults, spreading ridges and trenches, and their triple junctions. These data also outline the complexity of fracture zones which not only reflect the past and present direction of plate motion, but also the large- and fine-scale segmentation of the spreading ridges, and the common occurrence of propagating rifts. The

11. APPLICATIONS TO MARINE GEOPHYSICS

very large number of seamounts that these data unveiled, along with all the small seamounts (< 1 km) not resolved by these measurements, indicate that they contribute significantly to the oceanic volcanic layer. The complete mapping of seamount chains confirms and helps improving hotspot models; however, the occurrence of many linear chains that do not fit this model helped formulating alternative explanations, such as small-scale convection or tensional cracks. The satellite-altimeter data also lead to a better knowledge of the mechanical properties of the oceanic lithosphere and its behavior at fracture zones, under vertical stresses such as seamount loads and under horizontal stresses during intraplate deformation. Finally, these data are extremely valuable to plan and design ship cruises for investigating features of the ocean floor at a finer scale.

ACKNOWLEDGMENTS The authors are grateful to David Sandwell for his review of this chapter.

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CHAPTER 11, FIGURE 10 Satellite-derived gravity anomalies along oceanic fracture zones in different spreading contexts: (a) PacificAntarctic Ridge; (b) easternmost termination of Southeast Indian Ridge between Tasmania (TAS) and Australia; (c) westernmost termination of Southeast Indian Ridge just south of the Rodrigues Triple Junction; (d) Central mid-Atlantic Ridge. Spreading rates correspond to presentday full rates at the center of each plot (after NUVEL-1A model : DeMets et al., 1994). All plots are in oblique Mercator projections about chron 5 (11 Ma) Euler poles for the relevant plates. In such projection, the young parts (last 11 Ma) of fracture zones follow small circles (horizontal lines) about the Euler pole. Fracture zones along fast spreading ridges (a, b) are marked by a step in the gravity. This signature is asymmetric relative to the ridge axis; arrows in (b) show the change in polarity at the exact mid-point of the active transform fault along the Tasman FZ, where the age offset is equal to zero. Fracture zones in slower regimes (c, d) are outlined by a continuous gravity trough. Note the contrast in the gravity roughness of the oceanic crust between (a, b) and (c, d), and particularly the differernt gravity signatures of the spreading axes: axial rises in (a, b) vs. deep valley in (c, d). Same color scale as in Fig. 12 (Chapter 11).

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