This paper presents a practical approach for the application of real seismic amplitude data in the context of reflection seismic tomography. The estimation of recorded seismic amplitudes from reflection seismic gathers is performed with the aid of pre-stack time migration, which enhances continuity and reflection strength and reduces reflection point dispersal and diffraction effects. Moreover, contraction of the Fresnel zone by migration brings the amplitudes closer to the ray amplitudes assumed in the inversion. De-migration of the amplitudes follows, so that we recover a set of 'true' observations for input to inversion. To make the amplitude inversion robust, the effect of noise in the amplitude data is mitigated by applying iteratively a locally reweighted regression, which can efficiently reject amplitude outliers. This approach is applied to a reflection seismic profile from the North Sea to constrain the geometry of a stack of interfaces by using both the amplitude inversion and a joint inversion with traveltime data. The application example represents a valuable contribution to the discussion of how the combined effort of imaging and inversion of seismic data should be organized when we are dealing with field data.