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Mathematical modeling of bodily tides can be carried out in various ways.Most straightforward is the method of complex amplitudes, which is often usedin the planetary science. Another method, employed both in planetary scienceand astrophysics, is based on decomposition of each harmonic of the tide intotwo bulges oriented orthogonally to one another.  We prove that the two methods are equivalent. Specifically, we demonstratethat the two-bulge method is not a separate approximation, but ensues directlyfrom the Fourier expansion of a linear tidal theory equipped with an arbitraryrheological model involving a departure from elasticity. To this end, we usethe most general mathematical formalism applicable to linear bodily tides. Toexpress the tidal amendment to the potential of the perturbed primary, we acton the tide-raising potential of the perturbing secondary with a convolutionoperator. This enables us to interconnect a complex Fourier component of thetidally generated potential of the perturbed primary with the appropriatecomplex Fourier component of the tide-raising potential of the secondary. Thenwe demonstrate how this interrelation entails the two-bulge description.  While less economical mathematically, the two-bulge approach has a goodillustrative power, and may be employed on a par with a more concise method ofcomplex amplitudes. At the same time, there exist situations where thetwo-bulge method becomes more practical for technical calculations.

Justification of the two-bulge method in the theory of bodily tides