  Iterative geostatistical seismic inversion integrates seismic and well data
to infer the spatial distribution of subsurface elastic properties. These
methods provide limited assessment to the spatial uncertainty of the inverted
elastic properties, overlooking alternative sources of uncertainty such as
those associated with poor well-log data, upscaling and noise within the
seismic data. We express uncertain well-log samples, due to bad logging reads
and upscaling, in terms of local probability distribution functions (PDFs).
Local PDFs are used as conditioning data to a stochastic sequential simulation
algorithm, included as the model perturbation within the inversion. The problem
of noisy seismic and narrow exploration of the model parameter space,
particularly at early steps of the inversion, is tackled by the introduction of
a cap on local correlation coefficients responsible for the generation of the
new set of models during the next iteration. A single geostatistical framework
is proposed and illustrated with its application to a real case study. When
compared against a conventional iterative geostatistical seismic inversion, the
integration of additional sources of uncertainty increases the match between
real and inverted seismic traces and the variability within the ensemble of
models inverted at the last iteration. The selection of the local PDFs plays a
central role in the reliability of the inverted elastic models. Avoiding high
local correlation coefficients at early stages of the inversion increases
convergence in terms of global correlation between synthetic and real seismic
reflection data at the end of the inversion.
