Critical behavior in buoyant melting instabilities beneath extending lithosphere

Abstract: Upwelling mantle beneath extending lithosphere typically undergoes decompression partial melting and is the ultimate source of volcanism in most extensional provinces on Earth. Decompression melting of the upper mantle is associated with a decreased density due to the presence of a small fraction of melt and changes in composition and phase abundance in the rock. Thus if one portion of a partially melting layer ascends at a slightly faster rate, it will produce and retain more melt and as a consequence become less dense than adjacent portions of the layer. This in turn gives rise to a buoyancy surplus in faster upwellings that causes them to ascend even more quickly and produce more melt, thus setting the stage for what we call a "buoyant melting instability," or unstable buoyant overturn within the partially melting region. Using numerical convection models that include thermal expansion, melt retention, and melt depletion buoyancy as well as melt percolation effects, we have studied the occurrence of buoyant melting instabilities in a plane layer of partially melting mantle accompanying diffuse extension of the lithosphere. We find that buoyant melting instabilities do not always occur during extension, and in some cases only develop after extension has slowed or stopped, producing two pulses of melt generation. The occurrence of this "post-extensional" variety of instability depends on the rate of extension, melt percolation, and mantle viscosity as well as the depth-distribution of melt depletion density changes. Using a linear stability analysis, we have derived a "Rayleigh number" for this process with a critical value that accurately describes the occurrence of post-extensional instabilities in the models, and also compares reasonably well with previous studies on the occurrence of buoyant melting instabilities beneath slow-spreading mid-ocean ridges. These results have potentially interesting applications for the observed increase in localized volcanism following Miocene extension in the western United States Basin and Bange province as well as the occurrence of spreading-rate dependence in three-dimensional structure along mid-ocean ridges.