Feasibility study of probabilistic seismic inversion to porosity for a carbonate reservoir

The goal of this study is to invert the seismic data directly to porosity as well as to quantify the associated uncertainty in one of the carbonate reservoirs located in southwestern Iran. Probabilistic inverse methods are able to present the model parameters as a posterior probability distribution function by combining the probability density function of the model prior information and the likelihood model. The likelihood density function is defined based on the noise model. The answer to the probabilistic inverse problem is a posterior distribution function that is not only consistent with the prior model but also is constrained to the seismic data. In this study, one of the sampling methods based on Markov chain Monte Carlo is used, which is able to generate realizations of the desired model parameter by sampling from the posterior distribution function. Unlike deterministic inverse methods, which provide only one answer for the model parameters, in probabilistic inverse methods the realizations generated from the posterior distribution function allow statistical analysis and model uncertainty quantification. The results of the implementation of the proposed method on synthetic seismic data showed that the estimation of noise variance has a significant effect on the results of probabilistic inversion and the uncertainty of the model realizations. The underestimation of the noise variance leads to fitting the noise on the data and subsequently generates artifacts on the output realizations. The overestimation of the noise variance provides smooth realizations with higher uncertainty. In the latter case, the reference porosity model is in the 95% confidence interval in contrast to the former case. Therefore, care should be taken in estimating the noise variance in probabilistic inverse methods. Considering a calibrated rock physics model for the carbonate reservoir under study, which is the main core in a direct inversion approach, the proposed algorithm was applied to the seismic traces adjacent to the four well logs. The uncertainty of the porosity was quantified in each well location. The correlation coefficient of the mean of the porosity realizations and the true porosity in four well locations were approximated about 79%, 63%, 51% and 67%. The consistency of the results obtained from the inversion with the observed porosity at the well locations indicates the good performance of the algorithm in estimating the porosity and its associated uncertainty. Due to the ability of the probabilistic inverse methods in a direct inverse of seismic data to the petrophysical properties, and their applicability in being performed in a parallel structure in processing clusters, these algorithms can be used in reservoir characterization of 2D and 3D data.