We use a sampling-based Markov chain Monte Carlo method to invert seismic data directly for porosity and quantify its uncertainty distribution in a hard-rock carbonate reservoir in Southwest Iran. The noise that remains on seismic data after the processing flow is correlated with the bandwidth in the range of the seismic wavelet. Hence, to account for the inherent correlated nature of the band-limited seismic noise in the probabilistic inversion of real seismic data, we assume the estimated seismic wavelet as a suitable proxy for capturing the coupling of noise samples. In contrast to the common approach of inserting a delta function on the main diagonal of the covariance matrix, we insert the seismic wavelet on its main diagonal. We also calibrate an empirical and a semi-empirical inclusion-based rock-physics model to characterize the rock-frame elastic moduli via a lithology constrained fitting of the 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 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.

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.

No abstract

No abstract