We use a sampling-based Markov chain Monte Carlo method to invert seismic data directly to porosity and quantify its uncertainty distribution in a hard-rock carbonate reservoir in Southwest Iran. Due to the processing of the seismic data, the remainder noise is correlated with the bandwidth in the range of the seismic wavelet. Hence, we assume the estimated seismic wavelet as a suitable proxy for capturing the coupling of noise samples and we propose a simple and pragmatic approach to account for the correlated (colored) noise in the probabilistic inversion of real seismic data. We also calibrate an empirical and a semi-empirical inclusion-based rock-physics model to characterize the rock-frame elastic moduli via lithology constrained fitting parameters of these models, i.e. the critical porosity and the pore aspect ratio. These calibrated rock-physics models are embedded in the inversion procedure to link petrophysical and elastic properties. In addition, we obtain the pointwise critical porosity and pore aspect ratio, which can potentially facilitate the interpretation of the reservoir for further studies. The inversion results are evaluated by comparing with porosity logs and an existing geological model (porosity model) constructed through a geostatistical simulation approach. We assess the consistency of the geological model through a geomodel-to-seismic modeling approach. The results confirm the performance of the probabilistic inversion in resolving some thin layers and reconstructing the observed seismic data. We also present the applicability of the proposed sampling-based approach to invert 3D seismic data for estimating the porosity distribution and its associated uncertainty for four subzones of the reservoir. The porosity time maps and the facies probabilities obtained via porosity cut-offs indicate the relative quality of the reservoir’s subzones over each other.

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.