Assessment of the impact of noise magnitude and bandwidth variations on a probabilistic inversion of reflection seismic data

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 use an estimated seismic wavelet to capture the correlated noise model (coloured noise) for the processed reflection seismic data. We assess the proposed method through a direct inversion of post-stack seismic data associated with a carbonate reservoir of an oil field in southwest Iran to porosity, using a probabilistic sampling-based inversion algorithm. In the probabilistic formulation of the inverse problem, we assume eight different noise models with varying bandwidth and magnitude and investigate the corresponding posterior statistics. The results indicate that if the correlated nature of the noise samples is ignored in the noise covariance matrix, some unrealistic features are generated in porosity realizations. In addition, if the noise magnitude is underestimated, the inversion algorithm overfits the data and generates a biased model with low uncertainty. Furthermore, by considering an imperfect bandwidth for the noise model, the error is propagated to the posterior realizations. Assuming the correlated noise in a probabilistic inversion resolves these issues significantly. Therefore, for inverting real seismic data where the estimation of the magnitude and correlations of the noise is not straightforward, the wavelet, which is estimated from the real seismic data, 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.