Seismic Waveform Inversion Using The Ensemble Kalman Smoother

A framework for probabilistic full waveform inversion is considered, to enable the assessment of uncertainty related to the estimated parameters. Inspired by the success of applying ensemble based methods in the area of reservoir characterisation, we consider the seismic inversion problem as a sequential filtering problem and uses the Ensemble Kalman Filter (EnKF) framework to sequentially condition on observations.

The EnKF has beneficial properties for high-dimensional parameters spaces compared to other sampling based methods. It is however also known to suffer from problems of ensemble collapse and spurious updates, due high-dimensional data space - the full waveform data - and its linear update form. Here is presented some techniques to alleviate these issues namely dimension reduction and Kalman gain localisation. An example using a simple layered model is provided to illustrate the proposed method of sequentially processing of seismic data and inverting for unknown parameters.