On the application of adjoint methods to the GIA inverse problem

We consider the application of adjoint methods to the glacial isostatic adjustment (GIA) inverse problem. In this problem, the given data comprise observations of GIA such as records of past sea level change, and the aim is to make robust inferences about both the viscosity of the Earth's mantle and ice sheet history. Adjoint methods - which have been successfully applied in a number of other areas of geophysics - allow for the efficient calculation of sensitivity kernels expressing the linearized dependence of a given set of GIA observations to both mantle viscosity and ice sheet history. These sensitivity kernels may be employed in the iterative solution of the GIA inverse problem using gradient-based optimization methods, and also provide important information on the likely model resolution obtainable from a given set of observations. The theoretical basis for this adjoint method is described in terms of a new time-domain formulation of the GIA forward problem which circumvents the need for the iterative solution of the sea level equation and is also well suited for application to laterally heterogeneous earth models.