Abstract:
The asthenosphere can be considered as a layer of incompressible Newtonian fluid much thinner than its horizontal extent. Consequently a kinematic model has been developed from two-dimensional lubrication theory that will describe the flow averaged over the depth in the asthenosphere. The fixity of "hotspots" leads us to assume a rigid layer under the asthenosphere. The model assumes a subduction boundary as a thin, straight, subducting slab moving normal to its major axis in a Hele-Shaw cell. In addition, mass transfer between the mid-ocean ridge and trench has been incorporated in the theory. The value of the angle of the dip of a subducting slab is irrelevant to our model despite its physical importance.
This model is applied to simulate flow contributed by the Tonga-Kermadec-Hikurangi subduction zone. A relationship between the velocity of the moving slab and the horizontal force it exerts perpendicular to the subduction zone on the asthenosphere is found. This permits estimation of back-arc spreading rates behind subduction zones of the world. Estimated rates appear to agree with the tectonic features behind some subduction zones reasonably well. Nevertheless, it fails to provide results compatible with some presently available observed rates. The theory is also a first step towards explaining why some subduction zones have back-arc spreading and others do not.
