Sensitivity of glacial isostatic adjustment observations on 3D Earths with lateral viscosity variations: A perspective from the Forward problem

Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment (GIA). However, depending on whether sensitivity is used for the Inverse Problem or the Forward Problem, the final formulation and display of the sensitivity kernel will be different. Unfortunately, in the past, both perspectives give the same name to their quantity computed/displayed, and that has caused some confusion. To distinguish between the two, their perspective should be added to the names. This paper focuses only on the perspective of the Forward Problem where the input parameters are known. The Perturbation method has been successfully used in the computation of the sensitivity kernels of observations on 1D and 3D viscosity variations from the Forward perspective. One aim of this paper is to review and clarify the physics of the Perturbation method and bring out some important aspects of this method that have been misunderstood or neglected. Another aim is to present sensitivity kernels from the Perturbation method using 3D (both radially and laterally heterogeneous) Earth models with realistic ice history. These new results are now suitable for future comparison with those from new methods using the Forward perspective. Finally, the sensitivity computations for realistic ice histories on a 3D Earth is reviewed and used to search for optimal locations of new GIA observations.