A comparison of methods for the inversion of viscoelastic relaxation spectra

The majority of investigations of the glacial isostatic adjustment problem have proceeded by invoking the correspondence principle and solving for the (Laplace) transformed impulse response of the viscoelastic Earth model that is represented in terms of Love number spectra (Peltier 1974). This formulation requires a final inversion of the solution into the time domain, and the present paper is concerned with a comparison and assessment of the three techniques (pure collocation, full normal mode analysis using residue theory, and a hybrid technique which we term mixed collocation) that have been developed to perform it. On the basis of the analysis presented here we conclude that both the full normal mode analysis and mixed collocation can generate accurate inversions of the Love number spectra. We also derive clear guidelines on the choice of collocation points that ensure that the same accuracy is achieved using pure collocation. As a final point we stress anew that, regardless of the technique employed, the accuracy of the inversions can and should be checked by comparing the predicted infinite time-scale response for a Heaviside loading history with an independent calculation of the response for an inviscid Earth with a lithosphere of appropriate thickness.