Sea-Floor Depth and the Lake Wobegon Effect

Seth Stein, Carol A. Stein

S. Stein is in the Department of Geological Sciences, Northwestern University, Evanston, Il 60208, USA. E-mail: seth@earth.nwu.edu. C. Stein is in the Department of Geological Sciences, University of Illinois, Chicago, Il 60607, USA. E-mail: carol@ocean.geol.uic.edu

Although sea-floor topography is complicated, three primary effects were identified after the recognition of plate tectonics in the late 1960s. Plates of oceanic lithosphere form at mid-ocean ridges, move away from those ridges, and eventually subduct into the deep Earth. It was recognized that seafloor depth increases approximately as the square root of lithospheric age and that the flow of heat through the sea floor decreases similarly. Because square-root-of-time behavior characterizes diffusion processes, depth and heat flow can be described by treating the lithosphere as the upper layer of a half space that cools, thickens, and contracts as it ages (1). The oceanic lithosphere thus forms the cold, strong outer boundary layer of the convection system removing heat from Earth's interior.

A great deal of old sea floor is, however, shallower than predicted by a simple model of half-space cooling. This shallowing is typically treated in terms of two processes thought to jointly describe heat addition to the lithosphere from below. In one, diffuse heating below most old lithosphere balances heat lost at the sea floor, causing old lithosphere to approach equilibrium thermal structure, depth, and heat flow (2). In addition to the general "flattening" due to diffuse heating, some localized shallowing appears to reflect concentrated plumes of upwelling mantle material. Plumes move slowly relative to plates moving over them, causing linear shallow hotspot swells often marked by volcanic islands such as Hawaii (3).

In this view, the terrestrial heat engine is characterized by the balance between three modes of heat transfer from Earth's interior: (i) the overall plate tectonic cycle (evidenced by half-space cooling and flattening), (ii) mantle plumes (evidenced by swells), which are another feature of the convective system, and (iii) heat conduction through continents (which do not participate directly in the convective system owing to their low density relative to oceanic lithosphere). Hence, seafloor topography provides the primary evidence for present estimates that about 70% of terrestrial heat loss occurs by means of plate tectonics and 5% by means of plumes (4, 5). In contrast, although direct measurements are not available, Mars and Venus seem to function quite differently, because large-scale plate tectonics is presumed absent (6). The question of how and why mantle convection takes place differently on the three planets is thus a "hot" (as it were) topic.

Considerable effort has thus been directed toward estimation of the relative thermal effects of plate tectonics, mantle plumes, and other local phenomena. The challenge is that the primary observables, depth and heat flow, reflect combinations of possible effects. The approach taken is to develop reference models predicting depth and heat flow for normal oceanic lithosphere as functions of age, and then identify anomalous areas where predictions misfit data, presumably because processes not depending on age (such as plumes) operate. The simplest model, a cooling half-space, is reasonably successful for lithosphere younger than 70 million years age but overpredicts depths and underpredicts heat flow for older areas. Alternatively, a model of a cooling plate with an isothermal lower boundary accounts for heat addition from below the lithosphere and thus better fits data. However, a commonly used plate model with parameters given by Parsons and Sclater (PSM) (7) still results in a systematic misfit of depths and heat flow for most old lithosphere, implying widespread depth and heat-flow anomalies. Hence, regions were considered anomalous despite not differing from others of similar age.

This situation prompted a recent joint inversion of depth and heat-flow data, which found that these anomalies can be reduced significantly by a reference model, termed GDH1, with a thinner thermal plate than previously assumed (8). Depth, heat flow, and satellite gravity data not inverted in deriving GDH1 are also better fit by the thin-lithosphere model (9). As a result, possible depth and heat-flow anomalies have come under renewed scrutiny.

Of special interest have been possible anomalies over hotspot swells. The GDH1 model reduced inferred anomalies at swells like Hawaii, implying that reheating of the lithosphere was less than previously thought (10). This reduction leads naturally to the consideration of "superswells", such as the Darwin Rise region (see figure), where multiple hotspot tracks may indicate that in the Cretaceous (before 65 million years ago), an unusual outpouring of mantle heat produced a broad upwelling. Depth anomalies relative to different reference models yield quite different maps and hence tectonic inferences (see figure). The entire Darwin Rise is shallow relative to a half-space model (11). Relative to PSM, much of the area is also shallow, suggesting a remnant regional thermal signature of the volcanism that formed the swells (12). However, because almost all lithosphere of this age is shallower than these models predict, the anomalies need not indicate that the Rise currently differs from lithosphere of this age elsewhere. In contrast, relative to GDH1, swells associated with volcanic chains are shallow, whereas depths between them are within a standard deviation of that predicted. Because of the three models GDH1 best describes average old lithosphere, it indicates that much of the Darwin Rise is not significantly deeper than lithosphere of the same age elsewhere, implying that the region between the swells retains no significant large-scale thermal signature of the Cretaceous events (10).

The superswell region near Polynesia, considered a possible present analog to the Darwin Rise, is also receiving new scrutiny. Although the extent of the depth anomaly is under debate (13), the region is shallow relative to all three reference models, which make similar predictions because the lithosphere is relatively young. The suggestion that the depth anomaly and weakening of the lithosphere inferred from satellite gravity observations reflected regional thermal thinning of the lithosphere (14) now seems precluded by heat-flow data (10, 15). Hence, the weakening seems likely to be mechanical, with the plate acting as though it were broken (10). The extent and cause of the depth anomaly remains an active research area, because of the challenge of separating any regional shallowing due to large-scale mantle upwelling from the effects of localized volcanism.

The revived interest in depth and heat flow anomalies seems likely to continue. New thermal models are being proposed (16), and new analysis techniques are being developed. The growing availability of data on the World Wide Web--including depths from combined shipboard and satellite observations (17), sea-floor ages (18), sediment thickness (19), and heat flow (5)--provides useful tools. Geophysicists will thus be inverting data, improving models, reducing misfits, pondering alternative depth anomaly maps, and debating their implications for years to come.

References and Notes

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8. C. Stein and S. Stein, Nature 359, 123 (1992). (http://www.earth.nwu.edu/research/stein)
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17. W. Smith and D. Sandwell, Eos 77, F315 (1996). (http://topex.ucsd.edu)
18. R. Muller et al., J. Geophys. Res., in press. (http://omphacite.es.su.oz.au/StaffProfiles/dietmar/Agegrid/agegrid.html)
19. See http://www.ngdc.noaa.gov/mgg/sedthick/sedthick.html