stochastic inversion

Reservoir modeling is the process of creating a three-dimensional numerical model to show the spatial distribution of geological or petrophysical properties of the reservoir. The process of obtaining elastic properties from seismic data is called seismic inversion. There are different methods for seismic inversion, which are classified into two main groups:deterministic methods and stochastic methods. Understanding the differences between these two methods and their restrictions is important for their correct application and interpretation. Due to the band-limited nature of the seismic data, the results of deterministic methods are smooth maps of acoustic impedance and may be far from the reservoir facts. In contrast, stochastic inversion produces high-resolution maps of the acoustic impedance because the spatial continuity models (variograms) control the frequency content of stochastic inversion results. A well-known challenge of stochastic inversion is that it is often extremely expensive from computational point of view. In this study, a stochastic method has been used to obtain the facies and other properties of the reservoir.

In this study, to show the ability of the introduced method in modeling reservoir facies, a two-dimensional artificial model has been used. The formation in the reference model of this study consists of sandstone facies with high porosity (reservoir interval) and dense shale facies (non-reservoir interval). The formation is located at a depth of 2000 to 2200 m. At the top and bottom of the formation, a 50-m layer of shale with constant properties is considered. In order to model the facies of the reservoir, variogram parameters for different facies have been calculated from the well logs of the reference model. In the next step, the conditional probability of occurrence of the facies in each cell has been calculated using the sequential indicator simulation method with different random seeds. Then, the probability perturbation optimization algorithm has been applied to update each facies model until the model become consistent with the seismic data. At each step, a geophysical forward model is constructed and compared with seismic data.

After implementing the stochastic inversion method to the seismic data with a signal-to-noise ratio of 9 in the reference model, it was found that the optimized facies had an 81.83% correlation with the reference facies and was improved the initial facies model by 19.97%. The correlation values decreased to 77.67% and 72.38% when the seismic data with the signal-to-noise ratios of 4 and 2 were respectively used. When the seismic data with the signal-to-noise ratio of 4 was used, the initial model was improved by 15.81%, and when the seismic data with the signal-to-noise ratio of 2 was used, the correlation decreased to 10.52%.