Velocity Estimation in Layered Media Using Ensembled-based Sequential Filtering

A method for sequential seismic displacement data assimilation is presented with the aim of constructing probabilistic earth models. The method utilises the Ensemble Kalman filter (EnKF) framework to estimate the P-wave velocity, enabling model uncertainty through the final solution being a probability density function represented by an ensemble of model estimates. The inversion is performed sequentially on subsets of an seismic record, partitioned into many offset-traveltime data blocks. This approach has a regularizing effect on the inversion. While the EnKF is suitable for high-dimensional problems and relatively straight-forward to implement, it suffers from degrading performance when the forecast ensemble does not represent the observation suitably. Some adaptive measures to alleviate deteriorating EnKF updates are discussed in order to make the inversion process more robust. Statistical score rules are used as indicators for these adaptive measures. We present a synthetic example, based on filtered well logs from a borehole, of inverting for 1D acoustic velocity profile.