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 viscoelas-
tic 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 intrin-
sic 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 stan-
dard 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.