The Estimation of Petrophysical Parameters Based on Ensemble Smoother With Correlation Localization.

Joint estimation of elastic and petrophysical properties from seismic data and quantification of their uncertainties are critical aspects of reservoir characterization studies. The ensemble smoother with multiple data assimilation (ES-MDA) is proving to be a valuable tool for generating a reliable set of reservoir properties by matching simulated seismic responses with available observations. However, in standard implementations of ES-MDA, when the ensemble size is small, spurious correlations can arise in the cross-covariances of model parameters and seismic data, leading to erroneous parameter updates in inappropriate regions. To mitigate this problem, this paper introduces ES-MDA in conjunction with covariance localization (CL), termed as ES-MDA_CL, which aims to reduce the impact of spurious covariance resulting from small ensembles and provide inversion results with robust error estimation. In the ES-MDA_CL framework, the model parameters are initially generated perturbatively by geostatistical simulations and subsequently updated while constrained by seismic data. The introduction of CL reduces the size of the initial ensembles, thereby increasing the computational efficiency of the entire inversion process. Through synthetic and field data tests, ES-MDA_CL demonstrates satisfactory inversion results with more reasonable computational times compared to ES-MDA. The proposed methodology enables the generation of inversion results with robust uncertainty estimation and holds promise for application to a wide range of geophysical challenges.