  High spectral resolution studies of cool Ap stars reveal conspicuous
anomalies of the shape and strength of many absorption lines. This is a
signature of large atmospheric chemical gradients produced by the selective
radiative levitation and gravitational settling of chemical species. Here we
present a new approach to mapping the vertical chemical structures in stellar
atmospheres. We have developed a regularized chemical inversion procedure that
uses all information available in high-resolution stellar spectra. The new
technique for the first time allowed us to recover chemical profiles without
making a priori assumptions about the shape of chemical distributions. We have
derived average abundances and applied the vertical inversion procedure to the
high-resolution VLT UVES spectra of the weakly magnetic, cool Ap star HD
133792. Our analysis yielded improved estimates of the atmospheric parameters
of HD 133792. We show that this star has negligible vsini and the mean magnetic
field modulus <B>=1.1+/-0.1 kG. We have derived average abundances for 43 ions
and obtained vertical distributions of Ca, Si, Mg, Fe, Cr, and Sr. All these
elements except Mg show high overabundance in the deep layers and solar or
sub-solar composition in the upper atmosphere of HD 133792. In contrast, the Mg
abundance increases with height. We find that transition from the
metal-enhanced to metal-depleted zones typically occurs in a rather narrow
range of depths in the atmosphere of HD 133792. Based on the derived
photospheric abundances, we conclude that HD 133792 belongs to the rare group
of evolved cool Ap stars, which possesses very large Fe-peak enhancement, but
lacks a prominent overabundance of the rare-earth elements.
