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

Abstract

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 × 10 20 Pa s with one preferred lower-mantle viscosities at 3 × 10 21 Pa s and the other more than 2 × 10 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 icesheet 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.

Glacial Isostatic Adjustment modelling: historical perspectives, recent advances, and future directions

“…Peltier et al, 2015). A number of studies have made use of a biviscous Burgers rheology within a radially-varying framework, in which mantle deformation is dominated by the behaviour of two viscosities linearly relaxing over different timescales (Yuen et al, 1986;Caron et al, 2017). However, an increasing number of studies are making use of a framework that can accommodate three-dimensional variations in mantle viscosity (e.g.…”

“…When determining the past evolution of the global ice sheets, a previously-used method involves 715 taking an existing global reconstruction and scaling the thickness of each ice sheet in turn (e.g. Caron et al, 2017). However, building on new understanding of the feedbacks between ice dynamics and GIA (Sect.…”

Observation‐Driven Estimation of the Spatial Variability of 20th Century Sea Level Rise

“…Trends associated with the inverted barometer (IB) effect using the mean of three 20 th century atmospheric pressure data sets are first removed from the set of 15 tide gauges, following the results and discussion from Piecuch et al (). To account for and remove the trends associated with GIA, we generate new solutions using the method from Caron et al (), a Bayesian approach that provides expected GIA estimates and uncertainties thereof. In our case, the solid Earth model features a mantle with Maxwell rheology, and the reference ice history model is the ANU (Lambeck et al, ) model in the Nothern Hemisphere, the Ivins et al () model in Patagonia, and the Ivins and James () model in Antarctica.…”

Constraints on Transient Viscoelastic Rheology of the Asthenosphere From Seasonal Deformation

“…We compute surface displacements induced by variations of surface loading using a numerical model based on a spherical harmonics and temporal frequencies decomposition of the GRACE‐derived loads that uses the Love number theory. Surface loads, , varying with time ( t ), longitude ( θ ), and latitude (ϕ), are decomposed into loads, , varying with temporal frequency ( ω ) and spherical harmonics of degree and order ( l , m ) (Caron et al, ; Craig et al, ). We compute surface displacements induced by a unit load for each spherical harmonic of the decomposition and each frequency of the load (Figure ) by a system of equations for the deformation of a self‐gravitational spherical body, similar to classical normal modes theory used in seismology.…”