The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed\udanalytically within the framework of normal-modes, based on the application of propagator\udmethods. This technique, widely documented in the literature, suffers from several shortcomings;\udthe main drawback is related to the numerical solution of the secular equation, whose\uddegree increases linearly with the number of viscoelastic layers so that only coarse-layered\udmodels are practically solvable. Recently, a viable alternative to the standard normal-mode\udapproach, based on the Post–Widder Laplace inversion formula, has been proposed in the\udrealm of postglacial rebound models. The main advantage of this method is to bypass the\udexplicit solution of the secular equation, while retaining the analytical structure of the propagator\udformalism. At the same time, the numerical computation is much simplified so that\udadditional features such as linear non-Maxwell rheologies can be simply implemented. In this\udwork, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic\udrebound model. We test the method against the standard normal-mode solution and we perform\udvarious benchmarks aimed to tune the algorithm and to optimize computation performance\udwhile ensuring the stability of the solution. As an application, we address the issue of finding\udthe minimum number of layers with distinct elastic properties needed to accurately describe\udthe post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities\udof our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman\udearthquake comparing results based upon Maxwell and Burgers rheologies
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