Sensitivity of glacial isostatic adjustment to a partially molten layer at 410 km depth

We present a sensitivity analysis aimed at testing whether observables related to glacial isostatic adjustment can support or refute the occurrence of a low viscosity melt-rich layer (MRL) above the mantle transition zone, as required by the 'transition-zone water-filter' model (Bercovici & Karato 2003). In total, 1600 model runs were performed sampling a range of MRL thicknesses (1, 10 and 20 km) and viscosities (10 15 -10 19 Pa·s), plausible viscosity values in the upper and lower mantle regions and four distinct ice histories. To determine decay time constraints, we consider relative sea level (RSL) data from two sites [Angerman River (AR), Sweden and Richmond Gulf (RG), Canada] and use a new method of observational sea level data correction. Comparing model output of postglacial decay times and J 2 to observational constraints, we find numerous possible solutions, largely as a result of parameter trade-off. The investigated observables are sensitive to the existence of an MRL and reasonable variations in its thickness and viscosity. The magnitude and nature of this sensitivity varies between the two data types as well as the adopted background viscosity structure. Decay time results from either considered location do not strictly support or exclude MRL existence. However, both locations offer MRL viscosity requirements for given thicknesses, with AR being more restrictive. RG constraints allow MRL viscosities as low as 10 16 Pa·s (10 km) and 10 17 Pa·s (20 km). AR results narrow these permitted viscosity ranges to 10 18 Pa·s or greater for both 10 and 20 km MRL thicknesses. In the case of a 1 km thick MRL, AR constraints permit the viscosity to be as low as 10 17 Pa·s, whereas those of RG permit any MRL viscosity. The decay time observations are satisfied by only a small subset of 'background' mantle viscosities (regardless of the MRL properties), none of which support a spherically symmetric solution of Earth viscosity. Finally, comparing model output to the observed J 2 value did not provide any constraints on MRL properties. However, our results show that this observable has a strong preference for viscosity values in the lower mantle that are equal to or greater than 10 22 Pa·s.