Two models, a simple cooling model and the plate model, have been advanced to account for the variation in depth and heat flow with increasing age of the ocean floor. The simple cooling model predicts a linear relation between depth and t½, and heat flow and 1/t½, where t is the age of the ocean floor. We show that the same t½ dependence is implicit in the solutions for the plate model for sufficiently young ocean floor. For larger ages these relations break down, and depth and heat flow decay exponentially to constant values. The two forms of the solution are developed to provide a simple method of inverting the data to give the model parameters. The empirical depth versus age relation for the North Pacific and North Atlantic has been extended out to 160 m.y. B.P. The depth initially increases as t½, but between 60 and 80 m.y. B.P. the variation of depth with age departs from this simple relation. For older ocean floor the depth decays exponentially with age toward a constant asymptotic value. Such characteristics would be produced by a thermal structure close to that of the plate model. Inverting the data gives a plate thickness of 125±10 km, a bottom boundary temperature of 1350°±275°C, and a thermal expansion coefficient of (3.2±1.1) × 10−5°C−1. Between 0 and 70 m.y. B.P. the depth can be represented by the relation d(t) = 2500 + 350t½ m, with t in m.y. B.P., and for regions older than 20 m.y. B.P. by the relation d(t) = 6400 - 3200 exp (−t/62.8) m. The heat flow data were treated in a similar, but less extensive manner. Although the data are compatible with the same model that accounts for the topography, their scatter prevents their use in the same quantitative fashion. Our analysis shows that the heat flow only responds to the bottom boundary at approximately twice the age at which the depth does. Within the scatter of the data, from 0 to 120 m.y. B.P., the heat flow pan be represented by the relation q(t) = 11.3/t½ μcal cm−2s−1. The previously accepted view that the heat flow observations approach a constant asymptotic value in the old ocean basins needs to be tested more stringently. The above results imply that a mechanism is required to supply heat at the base of the plate.

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An analysis of the variation of ocean floor bathymetry and heat flow with age

THE concept of crustal plate motion over mantle hotspots has been advanced1 to explain the origin of the Hawaiian and other island chains and the origin of the Walvis, Iceland-Farroe and other aseismic ridges. More recently the pattern of the aseismic ridges has been used in formulating continental reconstructions2. I have shown3 that the Hawaiian-Emperor, Tuamotu-Line and Austral-Gilbert-Marshall island chains can be generated by the motion of a rigid Pacific plate rotating over three fixed hotspots. The motion deduced for the Pacific plate agrees with the palaeomagnetic studies of seamounts4. It has also been found that the relative plate motions deduced from fault strikes and spreading rates agree with the concept of rigid plates moving over fixed hotspots. Fig. 1 shows the absolute motion of the plates over the mantle, a synthesis which satisfies the relative motion data and quite accurately predicts the trends of the island chains and aseismic ridges away from hotspots.

Convection Plumes in the Lower Mantle

Summary A number of possible mechanisms have recently been proposed for driving the motions of the lithospheric plates, such as pushing from mid-ocean ridges, pulling by downgoing slabs, suction toward trenches, and coupling of the plates to flow in the mantle. We advance a new observational method of testing these theories of the driving mechanism. Our basic approach is to solve the inverse problem of determining the relative strength of the plausible driving forces, given the observed motions and geometries of the lithospheric plates. Since the inertia of the plates is negligible, each plate must be in dynamic equilibrium, so that the sum of the torques acting on a plate must be zero. Thus, our problem is to determine the relative sizes of the forces that minimize the components of net torque on each plate. The results indicate that the forces acting on the downgoing slab control the velocity of the oceanic plates and are an order of magnitude stronger than any other force. Namely, all the oceanic plates attached to substantial amounts of downgoing slabs move with a ' terminal velocity ' at which the gravitational body force pulling the slabs downward is nearly balanced with the resistance acting on the slab; regardless of the other features of the trailing horizontal part of the plates. The drag on the bottom of the plates which resist motion is stronger under the continents than under the oceans.

On the Relative Importance of the Driving Forces of Plate Motion

We present a new estimate of the Earth's heat loss based on a new global compilation of heat flow measurements comprising 24,774 observations at 20,201 sites. On a 5 o x 5 o grid, the observations cover 62% of the Earth's surface. Empirical estimators, ref- erenced to geological map units and derived from the observations, enable heat flow to be estimated in areas without measurements. Corrections for the effects of hydrothermal circulation in the oceanic crest compen- sate for the advected heat undetected in measurements of the conductive heat flux. The mean heat flows of continents and oceans are 65 and 101 mW m -2, re- spectively, which when areally weighted yield a global mean of 87 mW m -2 and a global heat loss of 44.2 x 10 2 W, an increase of some 4-8% over earlier esti- mates. More than half of the Earth's heat loss comes from Cenozoic oceanic lithosphere. A spherical hat- monic analysis of the global heat flow field reveals strong sectoral components and lesser zonal strength. The spectrum principally reflects the geographic dis- tribution of the ocean ridge system. The rate at which the heat flow spectrum loses strength with increasing harmonic degree is similar to the decline in spectral strength exhibited by the Earth's topography. The spectra of the gravitational and magnetic fields fall off much more steeply, consistent with field sources in the lower mantle and core, respectively. Families of con- tinental and oceanic conductive geotherms indicate the range of temperatures existing in the lithosphere under various surface heat flow conditions. The heat flow field is very well correlated with the seismic shear wave velocity distribution near the top of the upper mantle.

Heat flow from the Earth's interior: Analysis of the global data set

Variations in sea-floor depth and heat flow with age provide the main constraints on the thermal structure and evolution of the oceanic lithosphere. Joint fitting of heat flow and bathymetry yields a model with a hotter, thinner lithosphere than in previous models. The new model provides a significantly better fit to the data, including those from older lithosphere previously treated as anomalous. This will facilitate the analysis of lithospheric processes, including the effects of mid-plate volcanism and swells, regional subsidence, and hydrothermal circulation near spreading centers.

A model for the global variation in oceanic depth and heat flow with lithospheric age

Summary The average heat flow through continental orogenic belts decreases with the age of the orogeny to an approximately constant value for the Precambrian shields and platforms. The average heat flow for provinces of the North Pacific decreases with the age of the province. The mean heat flow through the province younger than 10 million years is 2.82 p cal cm-2 -1 whereas the mean heat flow through provinces older than the middle Cretaceous is 1.15~ cal cm-2 s-'. The contrast in the chemical composition of continental and oceanic crustal rocks and the disparity in time scale for the decay of heat flow suggest a different explanation for the heat flow through oceans and continents. The observed equality of the mean oceanic and continental heat flows may not be relevant to evaluating the thermal contribution of the upper mantle. Two geophysical and geochemical models of the oceanic and continental crust and upper mantle are presented. Both can explain the near equality of heat flow through the Precambrian shields and the old ocean basins when plates of continental and oceanic lithosphere are allowed to move. The oceanic lithosphere is approximately 100 km thick and the mantle is assumed to be the same under both the continents and oceans. The models differ principally in the condition assigned to their lower boundary. These conditions result in two different geochemical compositions for the oceanic lithosphere. Both oceanic models can explain the flow of heat through the North Pacific and the topography of the East Pacific Rise. If the effects of water in the mantle and subsolidus phase changes are considered, the lithosphere could be as thin as 75 km and still consistent with the heat flow and topographic anomalies. The models also account for the elevation of the mid-Atlantic ridge and the gross structure of the heat flow through the South Atlantic. The loss of heat in creating oceanic lithosphere may be as much as 45 per cent of the total average heat flow of the Earth. Heat lost by this process can no longer be ignored in models of the thermal history of the Earth. s

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The Implications of Terrestrial Heat Flow Observations on Current Tectonic and Geochemical Models of the Crust and Upper Mantle of the Earth

Data on ridges with slow spreading rates (1–3 cm/yr), obtained through detailed studies with Deep-Tow instruments and manned submersibles (French-American Mid-Ocean Undersea Study), or where the active structures are not submarine (Afar triangle) yield a precise picture of the axial region. There is evidence for a thinned lithosphere to be present at the axis with a thickness of 4–5 km. The thermal structure and composition of this solid layer can be estimated from seismic data and thermal and petrologic models. Extensional tectonics prevails in a belt some 10 km wide and is expressed at the surface by normal faults and fissures. In most previous mechanical models the existence of the lithosphere at the axis is neglected, and the rise of viscous asthenospheric material in a narrow vertical cleft beneath the axis is considered the main cause for the steady state presence of an axial valley and the development of normal faults. In contrast with these models we suggest here that these features depend on the rheological behavior of the lithosphere at the axis: the lithosphere is continually thinned by tectonic strain but also thickened by cooling at the base and by volcanism at the surface. In the steady state this process can be viewed as a succession of tectonic ‘neckings’ in the central active part of the axial valley (10 km) followed by doming of the lithosphere over the whole width of the axial valley (30 km), in response to isostatic disequilibrium. Creep is likely to control the process at depth and because of the high temperature and large strains will be of the steady state type. The application of experimental flow laws for material constituting layer 3 and the uppermost mantle to this problem, where both temperature profile and strain rate can be estimated, allows an order of magnitude of the ‘strength’ of the lithosphere at a given strain rate to be calculated. With this strength, isostatic recovery in response to vertical shear stresses will occur at a distance of about 8–15 km from the axis. The resulting ‘simple shear’ strain progressively ‘levels off’ the mean topographic slope until it becomes horizontal in the rift mountains. Whereas for rifted ridges or slowly accreting plate boundaries the behavior of the lithosphere controls the mechanics of the axial region, where only small discontinuous transient magma chambers exist, we suggest that in the case of nonrifted ridges the behavior of the asthenosphere is more important, with axial crust in isostatic equilibrium over a large continuous permanent magma chamber.

Necking of the lithosphere and the mechanics of slowly accreting plate boundaries

The East Pacific Rise near 21°N, 13°N and 20°S: inferences for along-strike variability of axial processes of the Mid-Ocean Ridge

The direction and intensity of magnetization of a uniformly magnetized seamount can be computed if its shape and associated magnetic anomaly are known. This technique has been applied to nine seamounts close to Hawaii, twelve seamounts close to the tip of Baja California, and twenty-eight seamounts surveyed during the Pioneer survey. All available paleomagnetic results from the Pacific basin have been used to establish a preliminary polar curve relative to the northeastern Pacific. This polar curve is weighted in favor of the Cretaceous point. This point at 61°N, 16°E is the mean pole position of seventeen seamounts and has an α95 of only 8°. The curve confirms earlier results indicating a 30° northward movement of the Northeastern Pacific since the Cretaceous. Paleomagnetic results obtained from seamounts near Japan suggest that, since the Cretaceous, the northwestern and northeastern Pacific have not always been rigidly connected. The pattern of long linear fracture zones in the South Pacific can be used to determine the motion of the Pacific plate relative to Antarctica since the Upper Cretaceous. Paleomagnetic data show that Antarctica has remained stationary in latitude over the same time span. A comparison of the paleomagnetic data obtained on the northeastern Pacific and on Antarctica yields a relative motion in conflict with that predicted by the South Pacific fracture zones. This conflict can be resolved if these two areas of the Pacific were decoupled some time between the Cretaceous and the present. Thus, it appears likely that the present Pacific plate is a composite of at least three distinct plates. Volcanic aseismic ridges within the Pacific Ocean may be the fossil boundaries of these plates now coalesced into a single plate.

Magnetization of Pacific Seamounts: A preliminary polar curve for the northeastern Pacific

THE concepts of sea floor spreading and plate tectonics provide a useful framework within which to examine the tectonic history of oceans and continents1–4. In these new theories, the Earth is envisaged as a complex mosaic of rigid plates in constant interaction and the instantaneous relative motion between any two of these plates can be represented by a rotation about a pole. Morgan3 pointed out that sections of fracture zones should follow small circles centred about such poles. This generalization is useful in deriving the path of continents which have been separated by continental drift, for the fracture zones mark the lines of movement.

Jean Francheteau

Papers

The Implications of Terrestrial Heat Flow Observations on Current Tectonic and Geochemical Models of the Crust and Upper Mantle of the Earth

Necking of the lithosphere and the mechanics of slowly accreting plate boundaries

The East Pacific Rise near 21°N, 13°N and 20°S: inferences for along-strike variability of axial processes of the Mid-Ocean Ridge

Magnetization of Pacific Seamounts: A preliminary polar curve for the northeastern Pacific

Pattern of Relative Motion from Fracture Zone and Spreading Rate Data in the North-eastern Pacific