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.