On computing viscoelastic Love numbers for general planetary models: the ALMA3 code

The computation of the Love numbers (LNs) for a spherically symmetric self-gravitating viscoelastic Earth is a classical problem in global geodynamics. Here we revisit the problem of the numerical evaluation of loading and tidal LNs in the static limit for an incompressible planetary body, adopting a Laplace inversion scheme based upon the Post-Widder formula as an alternative to the traditional viscoelastic normal modes method. We also consider, within the same framework, complex-valued, frequency-dependent LNs that describe the response to a periodic forcing, which are paramount in the study of the tidal deformation of planets. Furthermore, we numerically obtain the time-derivatives of LNs, suitable for modelling geodetic signals in response to surface loads variations. A number of examples are shown, in which time and frequency-dependent LNs are evaluated for the Earth and planets adopting realistic rheological profiles. The numerical solution scheme is implemented in ALMA³ (the plAnetary Love nuMbers cAlculator, version 3), an upgraded open-source Fortran 90 program that computes the LNs for radially layered planetary bodies with a wide range of rheologies, including transient laws like Andrade or Burgers.