Ensemble-based uncertainty estimation in full waveform inversion

Uncertainty estimation and quality control are critically missing in most geophysical tomographic applications. The few solutions to cope with that issue are often left out in practical applications when these ones grow in scale and involve complex modelling. We present a joint full waveform inversion and ensemble data assimilation scheme, allowing local Bayesian estimation of the solution that brings uncertainty estimation to the tomographic problem. This original methodology relies on a deterministic square root ensemble Kalman filter commonly used in the data assimilation community: the ensemble transform Kalman filter (ETKF). Combined with a 2-D visco-acoustic frequency domain full waveform inversion scheme, the resulting method allows to access a low-rank approximation of the posterior covariance matrix of the solution. It yields uncertainty information through an ensemble-representation, that can conveniently be mapped across the physical domain for visualization and interpretation. The combination of ETKF with full waveform inversion is discussed along with the scheme design and algorithmic details that lead to our mixed application. Both synthetic and field-data results are presented, along with the biases that are associated with the limited rank ensemble representation. Finally, we review the open questions and developments perspectives linked with data assimilation applications to the tomographic problem.