Projection of 4D Seismic Onto the Ensemble Observation Subspace for Data Assimilation

Time-lapse (4D) seismic data offer valuable insights into fluid movements and pressure changes within reservoirs, thus aiding the updating of numerical models used in hydrocarbon recovery and geological CO2 storage. However, it is essential to characterize both the uncertainties in the data and the limitations in the forward model to effectively utilize this information. In the context of ensemble-based data assimilation methods, this objective is accomplished through the utilization of the data-error covariance matrix, denoted as Ce. The selection of an appropriate Ce is of paramount importance, as it determines the level of accuracy required to match the data and influences the relative weight assigned to various data sources and prior information during the computation of model updates.Despite significant efforts, the practical estimation of Ce, accounting for both data and model errors, remains a challenging task. This paper presents a novel methodology for estimating Ce within an ensemble-based 4D seismic data assimilation framework. The approach involves projecting observed seismic data onto the subspace defined by predicted data from the prior ensemble and estimating Ce based on the residuals–the difference between observed and projected 4D seismic data. The proposed methodology is tested through application with actual data from three real-world reservoir cases.