  Context. Spectroscopic analyses to interpret the spectra of the brightest
supernovae from the UV to the near-IR provide a powerful tool with great
astrophysical potential for the determination of the physical state of the
ejecta, their chemical composition, and the SNe distances even at significant
redshifts.
  Methods. We report on improvements of computing synthetic spectra for SNIa
with respect to i) an improved and sophisticated treatment of thousands of
strong lines that interact intricately with the "pseudo-continuum" formed
entirely by Doppler- shifted spectral lines, ii) an improved and expanded
atomic database, and iii) the inclusion of energy deposition within the ejecta.
  Results. We show that an accelerated lambda iteration procedure we have
developed for the mutual interaction of strong spectral lines appearing in the
atmospheres of SNeIa solves the longstanding problem of transferring the
radiative energy from the UV into the optical regime. In detail we discuss
applications of the diagnostic technique by example of a standard SNIa, where
the comparison of calculated and observed spectra revealed that in the early
phases the consideration of the energy deposition within the spectrum-forming
regions of the ejecta does not qualitatively alter the shape of the spectra.
  Conclusions. The results of our investigation lead to an improved
understanding of how the shape of the spectrum changes radically as function of
depth in the ejecta, and show how different emergent spectra are formed as a
result of the particular physical properties of SNe Ia ejecta and the resulting
peculiarities in the radiative transfer. This provides an important insight
into the process of extracting information from observed SNIa spectra, since
these spectra are a complex product of numerous unobservable SNIa spectral
features which are thus analyzed in parallel to the observable spectral
features.
