Inverting Glacial Isostatic Adjustment signal using Bayesian framework and two linearly relaxing rheologies

Glacial Isostatic Adjustment (GIA) models commonly assume a mantle with a viscoelastic Maxwell rheology and a fixed ice history model. Here, we use a Bayesian Monte Carlo approach with a Markov chain formalism to invert the global GIA signal simultaneously for the mechanical properties of the mantle and the volumes of the ice sheets, using as starting ice models two previously published ice histories. Two stress relaxing rheologies are considered: Burgers and Maxwell linear viscoelasticities. A total of 5720 global palaeo sea level records are used, covering the last 35 kyr. Our goal is not only to seek the model best fitting this data set, but also to determine and display the range of possible solutions with their respective probability of explaining the data. In all cases, our a posteriori probability maps exhibit the classic character of solutions for GIA-determined mantle viscosity with two distinct peaks. What is new in our treatment is the presence of the bi-viscous Burgers rheology and the fact that we invert rheology jointly with ice history, in combination with the greatly expanded palaeo sea level records. The solutions tend to be characterized by an upper-mantle viscosity of around 5 x 10(20) Pa s with one preferred lower-mantle viscosities at 3 x 10(21) Pa s and the other more than 2x10(22) Pa s, a rather classical pairing. Best-fitting models depend upon the starting ice history and the stress relaxing law. A first peak (P1) has the highest probability only in the case with a Maxwell rheology and ice history based on ICE-5G, while the second peak (P2) is favoured for ANU-based ice history or Burgers stress relaxation. The latter solution also may satisfy lower-mantle viscosity inferences from long-term geodynamics and gravity gradient anomalies over Laurentia. P2 is also consistent with large Laurentian and Fennoscandian ice-sheet volumes at the Last Glacial Maximum (LGM) and smaller LGM Antarctic ice volume than in either ICE-5G or ANU. Exploration of a bi-viscous linear relaxing rheology in GIA now seems logical due to a new set of requirements to satisfy observations of transient post-seismic flow seen so ubiquitously in space gravimetry and other global geodetic data.