Investigating the pilot point ensemble Kalman filter for geostatistical inversion and data assimilation

Parameter estimation has a high importance in the geosciences. The ensemble Kalman filter (EnKF) allows param-eter estimation for large, time-dependent systems. For large systems, the EnKF is applied using small ensembles, which may lead to spurious correlations and, ultimately, to filter divergence. We present a thorough evalua-tion of the pilot point ensemble Kalman filter (PP-EnKF), a variant of the ensemble Kalman filter for parameter estimation. In this evaluation, we explicitly state the update equations of the PP-EnKF, discuss the differences of this update equation compared to the update equations of similar EnKF methods, and perform an extensive performance comparison. The performance of the PP-EnKF is tested and compared to the performance of seven other EnKF methods in two model setups, a tracer setup and a well setup. In both setups, the PP-EnKF performs well, ranking better than the classical EnKF. For the tracer setup, the PP-EnKF ranks third out of eight methods. At the same time, the PP-EnKF yields estimates of the ensemble variance that are close to EnKF results from a very large-ensemble reference, suggesting that it is not affected by underestimation of the ensemble variance. In a comparison of the ensemble variances, the PP-EnKF ranks first and third out of eight methods. Additionally, for the well model and ensemble size 50, the PP-EnKF yields correlation structures significantly closer to a reference than the classical EnKF, an indication of the method's skill to suppress spurious correlations for small ensemble sizes.

Automated summary

Parameter estimation is crucial in geosciences, and the evaluation of the pilot point ensemble Kalman filter (PP-EnKF) shows that it performs well for parameter estimation in different settings, ranking higher than traditional EnKF methods.