Uniform spectral representation of the Earth’s inner density structures and their gravitational field

Abstract

We introduce the generic expressions for computing the gravitational field
(potential and its radial derivative) generated by an arbitrary density (contrast) layer
with a variable depth and thickness having a laterally-distributed radial density variation.
The information on the geometry and density distribution of a volumetric mass layer is
described by means of spherical harmonics. These generic expressions can uniformly be
applied to model all major known density structures within the Earth’s interior using
methods for a spherical harmonic analysis and synthesis of the gravitational field. This
is demonstrated on specific examples given for various density models commonly adopted
for the approximation of crust density structures.