Quantifying the sensitivity of post-glacial sea level change to laterally varying viscosity

Abstract

We present a method for calculating the derivatives of measurements of glacial isostatic adjustment (GIA) with respect to the viscosity structure of the Earth and the ice sheet history. These derivatives, or kernels, quantify the linearised sensitivity of measurements to the underlying model parameters. The adjoint method is used to enable efficient calculation of theoretically exact sensitivity kernels within laterally heterogeneous earth models that can have a range of linear or non-linear viscoelastic rheologies. We first present a new approach to calculate GIA in the time domain, which, in contrast to the more usual formulation in the Laplace domain, is well suited to continuously varying earth models and to the use of the adjoint method. Benchmarking results show excellent agreement between our formulation and previous methods. We illustrate the potential applications of the kernels calculated in this way through a range of numerical calculations relative to a spherically symmetric background model. The complex spatial patterns of the sensitivities are not intuitive, and this is the first time that such effects are quantified in an efficient and accurate manner.

Inferences of Mantle Viscosity Based on Ice Age Data Sets: The Bias in Radial Viscosity Profiles Due to the Neglect of Laterally Heterogeneous Viscosity Structure

“…A more rigorous understanding of these issues requires inversions of 3D viscosity analyzed through a 3D sensitivity (Fréchet kernel) analysis. In this regard, a series of theoretical studies that build toward the application of adjoint methods to the GIA problem (e.g., Al‐Attar & Tromp, ; Crawford et al, ; Crawford et al, ) provide a framework for tackling the 3D viscosity problem. The conclusions herein may be seen as a motivation for the continued development of such methods.…”

Sea-level responses to rapid sediment erosion and deposition in Taiwan

“…Lastly, we note that sea-level responses in our simulations are governed by a spherically symmetric Earth model, a characteristic shared by nearly all implementations of the sea-level theory due to the computational expense of computing sea-level responses with a laterally varying 3-D Earth model (e.g., Latychev et al, 2005;de Boer et al, 2017;Gomez et al, 2018;Crawford et al, 2018). This approach necessarily neglects several things that may affect sealevel changes in Taiwan, including lateral variations in mantle and lithospheric properties (viscosity, elasticity, density, thickness), brittle crustal deformation, and crustal underplating, and other tectonic processes (e.g., Suppe, 1984).…”

Advances in glacial isostatic adjustment modeling

“…The background viscosity structure is scaled from a tomographic model of seismic shear wave-speed variations using a simple empirical relation. Results for other depths and times, when combined, define sensitivity kernels that can be used to invert RSL data from Tahiti for an optimal 3D viscosity model with uncertainty estimates (Crawford et al 2018).…”