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.