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\begin{document}

\title{Assessment of the impact of noise magnitude and bandwidth variations on
a probabilistic inversion of seismic data}



\author[1]{Hamed Heidari}%
\author[2]{Rasmus Bødker Madsen}%
\author[3]{Hamed Amini}%
\author[4]{Thomas Mejer Hansen}%
\author[5]{Mohammad Emami Niri}%
\author[6]{Navid Amini}%
\affil[1]{University of Tehran}%
\affil[2]{Geological Survey of Denmark and Greenland}%
\affil[3]{AkerBP}%
\affil[4]{Aarhus University,University of Aarhus}%
\affil[5]{Institute of Petroleum Engineering, College of Engineering, University of Tehran}%
\affil[6]{CoCoLink, subsidiary of Seoul National University, Republic of Korea}%


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  \date{June 16, 2024}


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\begin{abstract}
Accounting for an accurate noise model is essential when dealing with
real data which are noisy due to the effect of environmental noise,
failures and limitations in data acquisition and processing. Quantifying
the noise model is a challenge for practitioners in formulating an
inverse problem and usually, a simple Gaussian noise model is assumed as
a white noise model. Here we propose a pragmatic approach to using an
estimated seismic wavelet to capture the correlated noise model
(coloured noise) for the processed reflection seismic data. We test the
method for a probabilistic sampling-based inversion where post-stack
seismic data, associated with a hard carbonate reservoir in southwest
Iran, is inverted directly to porosity. We assume eight different
scenarios for the bandwidth and the magnitude of the noise. The
investigation of the corresponding posterior statistics shows that
ignoring the correlation of the noise samples in the noise covariance
matrix generates unrealistic features in porosity realisations while
underestimating the noise magnitude leads to overfitting the data and
generating a biased model with low uncertainty. Furthermore, by
considering an imperfect bandwidth for the noise model, the error is
propagated to the posterior realisations. These issues are resolved
considerably when the correlated noise is considered in the inversion.
Therefore, in real data applications where the estimation of the
magnitude and correlations of the noise is not trivial, the estimated
seismic wavelet provides a good proxy for describing the correlation of
the noise samples or equivalently the bandwidth of the noise model. In
addition, it might be better to overestimate the noise magnitude than to
underestimate it. This is true especially for an uncorrelated noise
model and to a lesser degree also for the correlated noise model.%
\end{abstract}%



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