Spectral Parameterization of 3D Gaussian Geomodels for Fast-Ensemble History Matching: Application in Tight and Faulted Reservoirs

Summary

History matching of continuous 3D geological models is limited by the dimensionality of the parameter field, which drives both the computational cost of the inversion and its ill-posedness. This paper develops an efficient data assimilation framework in which the geomodel is represented through an orthogonal spectral decomposition and updated with the ensemble smoother with multiple data assimilation (ES-MDA). The heterogeneous 3D property field is transformed into the frequency domain, where the macroscopic geological trend and the spatial continuity are carried by a very small fraction of low-frequency coefficients of the order of 1% of the spectrum. Because the transform basis is analytically predefined rather than inferred from the ensemble, the parameterization is constructed once, at negligible cost, and remains fixed throughout assimilation. A Pearson correlation screening is then applied to the retained coefficients to isolate the subspace to which the dynamic response is most sensitive, which limits overparameterization and the associated noise-induced ensemble collapse. The framework is evaluated on two contrasting real-field models: a tight sandstone gas reservoir matched on bottomhole pressure (BHP), and a faulted oil reservoir in which three fault transmissibility multipliers are inverted jointly with the property field. In both cases, an effective subspace of only five to seven degrees of freedom is sufficient to reproduce the observed production history. A hold-out experiment on the first case, in which the final quarter of the record is withheld from assimilation and predicted by the matched ensemble, reduces the mean relative pressure error over the unobserved period from 69.0% for prior to 20.8% for the posterior, confirming that the calibrated models retain predictive skill; the same experiment shows that the posterior ensemble spread is narrower than the residual forecast error warrants. Benchmarking against the higher-order singular value decomposition (HOSVD), an ensemble-derived tensor basis, yields comparable energy compaction and inversion accuracy while avoiding the tensor decomposition itself, giving a 13.6-fold speedup in parameterization and a 6.4-fold speedup in single-model reconstruction. The resulting workflow provides a practical, scalable, and physically interpretable route to efficient 3D reservoir characterization.