The Effect of a Shallow Low Viscosity Zone

Many features of the oceanic plates cannot be explained by conductive cooling with age. A number of these anomalies require additional convective thermal sources at depths below the plate: mid-plate swells, the evolution of fracture zones, the mean depth and heat flow relationships with age and the observation of small scale (150-250 km) geoid and topography anomalies in the Central Pacific and Indian oceans. Convective models are presented of the formation and evolution of these features. In particular, the effect of a shallow low viscosity layer in the uppermost mantle on mantle flow and its geoid, topography, gravity and heat flow expression is explored. A simple numerical model is employed of convection in a fluid which has a low viscosity layer lying between a rigid bed and a constant viscosity region. Finite element calculations have been used to determine the effects of (1) the viscosity contrast between the two fluid layers, (2) the thickness of the low viscosity zone, (3) the thickness of the conducting lid, and (4) the Rayleigh number of the fluid based on the viscosity of the lower layer. A model simple for mid-plate swells is that they are the surface expression of a convection cell driven by a heat flux from below. The low viscosity zone causes the top boundary layer of the convection cell to thin and, at high viscosity contrasts and Rayleigh numbers, it can cause the boundary layer to go unstable. The low viscosity zone also mitigates the transmission of normal stress to the conducting lid so that the topography and geoid anomalies decrease. The geoid anomaly decreases faster than the topography anomaly, however, so that the depth of compensation can appear to be well within the conducting lid. Because the boundary layer is thinned, the elastic plate thickness also decreases and, since the low viscosity allows the fluid to flow faster in the top layer, the uplift time decreases as well. We have compared the results of this modeling to data at the Hawaii, Bermuda, Cape Verde and Marquesas swells, and have found that it can reproduce their observed anomalies. The viscosity contrasts that are required range from 0.2-0.01, which are in agreement with other estimates of shallow viscosity variation in the upper mantle. Also, the estimated viscosity contrast decreases as the age of the swell increases. This trend is consistent with theoretical estimates of the variation of such a low viscosity zone with age. Fracture zones juxtapose segments of the oceanic plates of different ages and thermal structures. The flow induced by the horizontal temperature gradient at the fracture zone initially downwells immediately adjacent to the fracture zone on the older side, generating cells on either side of the plume. The time scale and characteristic wavelength of this flow depends initially on the viscosity near the largest temperature gradient in the fluid which, in our model, is the viscosity of the low viscosity layer. They therefore depend on both the Rayleigh number and the viscosity contrast between the layers. Eventually the flow extends throughout the box, and the time scales and the characteristic wavelengths of the flow depend on the thickness and viscosity of both layers. When the Rayleigh number based on the viscosity of the top la er, and the depth of both fluid layers, is less than 10 , the geoid anomalies of these flows are dominated by the convective signal. When this Rayleigh number exceeds 106, the geoid anomalies retain a step across the fracture zone out to large ages. We have compared our results to geoid anomalies over the Udintsev fracture zone, and have found that the predicted geoid anomalies, with high effective Rayleigh numbers, agree at longer wavelengths with the observed anomalies and can produce the observed geoid slope-age behaviour. We have also compared the calculated topographic steps to those predicted by the average depth-age relationships observed in the oceans. We have found that only with a low viscosity zone will the flow due to fracture zones not disturb the average depth versus age relationships. We have also applied the model to a numerical study of the effect of a low viscosity zone in the uppermost mantle on the onset and surface expression of convective instabilities in the cooling oceanic plates. We find that the onset and magnitude of the geoid, topography and heat flow anomalies produced by these instabilities are very sensitive to the viscosity contrast and the Rayleigh number, and that the thickness of the low viscosity zone is constrained by the wavelength of the observables. If the Rayleigh number of the low viscosity zone exceeds a critical value then the convection will be confined to the low viscosity zone for a period which depends on the viscosity contrast and the Rayleigh number. The small scale convection will eventually decay into longer wavelength convection which extends throughout the upper mantle, so that the small scale convective signal will eventually be succeeded by a longer wavelength signal. We compare our model to the small scale geoid and topography anomalies observed in the Southeast Pacific. The magnitude (0.50-0.80 m in geoid and 250 m in topography), early onset time (5-10 m.y.) and lifetime (over 40 m.y.) of these anomalies suggest a large viscosity contrast of greater than two orders of magnitude. The trend to longer wavelengths also suggests a high Rayleigh number of near or over 10 and their original 150-250 km wavelength indicates a low viscosity zone of 75125 km thickness. We have found that the presence of such small scale convection does not disturb the slope of the depth-age curve but elevates it by up to 250 m, and it is not until the onset of long wavelength convection that the depth-age curves radically depart from a cooling halfspace model. In the Pacific, the depth-age curve is slightly elevated in the region where small scale convection is observed and it does not depart from a halfspace cooling model until an age of 70 m.y.. Models that produce the small scale anomalies predict a departure time between 55 and 65 m.y.. These calculations also predict an asymptotic heat flow on old ocean floor which is higher than the plate model and between 50 and 55 mW/m2 . This value agrees with measurements of heat flow on old seafloor in the Atlantic. In conclusion, we prefer an approximate model for the viscosity structure of the upper mantle which initially has a 125 km thick low viscosity zone that represents a viscosity contrast of two orders of magnitude. The viscosity contrast decreases as the plate ages to one order of magnitude or less by 130 m.y., and the low viscosity zone may also thicken with age. Finally, the Rayleigh number of the upper mantle is at least 105 and may be as large as 107 . With this model, the evolution of the surface plates would initially involve small scale convection which is driven by shear coupling to instabilities downstream and to small scale convection associated with fracture zones. This convective flow would begin at close to 5 m.y. and remain confined to the low viscosity zone until nearly 40 m.y.. As this convective flow cools the upper mantle beneath the low viscosity zone, longer wavelength convection begins throughout the upper (or whole) mantle, and the heat transport from the longer wavelength convection flattens the depth-age curve and may form swells. Thesis Supervisor: Barry Parsons Reader of Geodesy, Oxford University UK