  We present a detailed spectral analysis of Type Iax SN 2011ay. Our spectra
cover epochs between -3 and +19 days with respect to the maximum light in
B-band. This time range allows us to employ a so-called abundance tomography
technique. The synthetic spectral fitting was made with the 1D Monte Carlo
radiative transfer code TARDIS. In this paper, we describe our method to fit
multiple epochs with a self-consistent, stratified atmospheric model. We
compare our results to previously published SYN++ models and the predictions of
different explosion scenarios. Using a fixed density profile (exponential fit
of W7), we find that a uniform abundance model cannot reproduce the spectral
features before maximum light because of the emergence of excessively strong Fe
lines. In our best-fit TARDIS model, we find an abundance profile that
separated into two different regimes: a well-mixed region under 10,000 km
s$^{-1}$ and a stratified region with decreasing IGE abundances above 10,000 km
s$^{-1}$. Based on a detailed comparative analysis, our conclusion is that the
available pure deflagration models cannot fully explain either the observed
properties of SN 2011ay or the results of our TARDIS modeling. Further
examinations are necessary to find an adequate explanation for the origin of
this object.
