The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast

Abstract

We derive the expressions for computing the ice density contrast stripping
corrections to the topography corrected gravity field quantities by means of the spherical
harmonics. The expressions in the spectral representation utilize two types of the spherical
functions, namely the spherical height functions and the newly introduced lower-bound
ice functions. The spherical height functions describe the global geometry of the upper
topographic bound. The spherical lower-bound ice functions combined with the spherical
height functions describe the global thickness of the continental ice sheet. The newly
derived formulas are utilized in the forward modelling of the gravitational field quantities
generated by the ice density contrast. The 30×30 arc-sec global elevation data from
GTOPO30 are used to generate the global elevation model (GEM) coefficients. The
spatially averaged global elevation data from GTOPO30 and the 2×2 arc-deg ice-thickness
data from the CRUST 2.0 global crustal model are used to generate the global lower-bound
ice model (GIM) coefficients. The mean value of the ice density contrast 1753 kg/m3 (i.e.,
difference of the reference constant density of the continental upper crust 2670 kg/m3and
the density of glacial ice 917 kg/m3) is adopted. The numerical examples are given for
the gravitational potential and attraction generated by the ice density contrast computed
globally with a low-degree spectral resolution complete to degree and order 90 of the GEM
and GIM coefficients.