  Mathematical modeling of bodily tides can be carried out in various ways.
Most straightforward is the method of complex amplitudes, which is often used
in the planetary science. Another method, employed both in planetary science
and astrophysics, is based on decomposition of each harmonic of the tide into
two bulges oriented orthogonally to one another.
  We prove that the two methods are equivalent. Specifically, we demonstrate
that the two-bulge method is not a separate approximation, but ensues directly
from the Fourier expansion of a linear tidal theory equipped with an arbitrary
rheological model involving a departure from elasticity. To this end, we use
the most general mathematical formalism applicable to linear bodily tides. To
express the tidal amendment to the potential of the perturbed primary, we act
on the tide-raising potential of the perturbing secondary with a convolution
operator. This enables us to interconnect a complex Fourier component of the
tidally generated potential of the perturbed primary with the appropriate
complex Fourier component of the tide-raising potential of the secondary. Then
we demonstrate how this interrelation entails the two-bulge description.
  While less economical mathematically, the two-bulge approach has a good
illustrative power, and may be employed on a par with a more concise method of
complex amplitudes. At the same time, there exist situations where the
two-bulge method becomes more practical for technical calculations.
