A nonlinear rheology model for mid‐ocean ridge axis topography
Authors: Chen Yongshun , Morgan W. Jason 
Published: February 2008

This paper describes a mechanical model of the mid‐ocean ridge axis based on a nonlinear rheology. The oceanic lithosphere is modeled as a strongly temperature‐dependent “power law” material with the Byerlee's friction law describing the brittle behavior of the upper oceanic lithosphere. We examined two simple models. A mantle‐only model predicted an axial rift valley 1–2 km deep and 10–15 km wide at slow half‐rates of 5–25 mm/yr which is in fair agreement with observations. However, the rift valley did not completely vanish at fast spreading rates even though its width and relief became much smaller. Thus, the mantle‐only model failed to explain the observed transition in axial topography with spreading rate. By including a uniform thickness oceanic crust with theological properties different from the mantle, our second model produced the first order variation of axial topography with spreading rate: a pronounced rift valley with 1–2 km relief at slow rates, a smaller relief (<500 m) rift valley at intermediate rates, and no rift valley at fast rates. There are two additional results of the nonlinear rheology model which are distinctively different from the previous uniform viscosity mantle models. First, horizontal velocity at the seafloor changes sharply in a very narrow zone at the ridge axis, i.e., the stresses are concentrated in a very narrow zone for the nonlinear rheology. This conclusion is remarkably independent of the boundary conditions at the seafloor. Second, the computed width of the axial plastic failure zone decreases with spreading rate, a result very different from that of a uniform viscosity model. This is caused by the strong temperature dependence of the power law rheology and the fact that the temperature of the oceanic lithosphere depends greatly on the spreading rate. Beyond some distance from the ridge axis, the brittle plate (roughly the region above the 750°C isotherm) deforms very little; both the horizontal strain rate ė11 and the maximum shear strain rate ėmax are less than 10−17 s−1 which is in good agreement with the 10−18 s−1 average for oceanic brittle plate deformation inferred from seismic moment data. Within the ductile region (area beneath the 750°C isotherm) the strain rates are in the range of 10−14–10−16 s−1, except within a narrow band near the ridge axis where higher strain rates are located. We found that the thermal structure of the oceanic lithosphere is not very sensitive to the details of the mantle flow pattern (or the rheology) but is very sensitive to the cooling by hydrothermal circulation near the ridge axis. Axial structure is also influenced by factors other than the spreading rate. Within the range of slow and intermediate rates, our calculations show that the size of an axial rift valley decreases with an increase in either the thickness of the oceanic crust or the mantle temperature; in other words, a thinner crust or a cooler mantle temperature will produce a more pronounced rift valley. In the vicinity of hotspots, the absence of an axial rift valley even at slow spreading rates, such as the Reykjanes Ridge, can be well explained by the anomalously thicker crust and higher mantle temperatures. In contrast, at the Australian‐Antarctic Discordance a deeper than normal section of an intermediate spreading ridge has very rough topography not present on the adjacent sections of the ridge; this can be explained by our model as due to an anomalously low mantle temperature as has been suggested or perhaps also due to a thinner oceanic crust