Local uncertainty quantification for 3-D time-domain full-waveform inversion with ensemble Kalman filters: application to a North Sea OBC data set

Abstract

SUMMARY Full-waveform inversion (FWI) has emerged as the state-of-the art high resolution seismic imaging technique, both in seismology for global and regional scale imaging and in the industry for exploration purposes. While gaining in popularity, FWI, at an operational level, remains a heavy computational process involving the repeated solution of large-scale 3-D wave propagation problems. For this reason it is a common practice to focus the interpretation of the results on the final estimated model. This is forgetting FWI is an ill-posed inverse problem in a high dimensional space for which the solution is intrinsically non-unique. This is the reason why being able to qualify and quantify the uncertainty attached to a model estimated by FWI is key. To this end, we propose to extend at an operational level the concepts introduced in a previous study related to the coupling between ensemble Kalman filters (EnKFs) and FWI. These concepts had been developed for 2-D frequency-domain FWI. We extend it here to the case of 3-D time-domain FWI, relying on a source subsampling strategy to assimilate progressively the data within the Kalman filter. We apply our strategy to an ocean bottom cable field data set from the North Sea to illustrate its feasibility. We explore the convergence of the filter in terms of number of elements, and extract variance and covariance information showing which part of the model are well constrained and which are not. Analysing the variance helps to gain insight on how well the final estimated model is constrained by the whole FWI workflow. The variance maps appears as the superposition of a smooth trend related to the geometrical spreading and a high resolution trend related to reflectors. Mapping lines of the covariance (or correlation matrix) to the model space helps to gain insight on the local resolution. Through a wave propagation analysis, we are also able to relate variance peaks in the model space to variance peaks in the data space. Compared to other posterior-covariance approximation scheme, our combination between EnKF and FWI is intrinsically scalable, making it a good candidate for exploiting the recent exascale high performance computing machines.