On computing viscoelastic Love numbers for general planetary models: the ALMA(3) 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 ALMA(3) (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.