Application of the Post-Widder Laplace inversion algorithm to postseismic rebound models

The postseismic response of a viscoelastic Earth can be computed analytically with a normal-mode approach, based on the application of propagator methods. This framework suffers from many limitations, mostly connected with the solution of the secular equation, whose degree scales with the number of viscoelastic layers so that only low-resolution models can be practically solved. Recently, a viable alternative to the normal-mode approach has been proposed, based on the Post-Widder inversion formula. This method allows to overcome some of the intrinsic limitations of the normal-mode approach, so that Earth models with arbitrary radial resolution can be employed and general linear non-Maxwell rheologies can be implemented. In this work, we test the robustness of the method against a standard normal-mode approach in order to optimize computation performance while ensuring the solution stability. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the postseismic relaxation of a realistic Earth model.