An optimal transport approach for seismic tomography: application to 3D full waveform inversion

By Ludovic Métivier, Romain Brossier, Quentin Mérigot, É. Oudet, Jean Virieux. 2016

150 citations recorded by the source corpus.

The use of optimal transport distance has recently yielded significant progress in image processing for pattern recognition, shape identification, and histograms matching. In this study, the use of this distance is investigated for a seismic tomography problem exploiting the complete waveform; the full waveform inversion. In its conventional formulation, this high resolution seismic imaging method is based on the minimization of the L2 distance between predicted and observed data. Application of this method is generally hampered by the local minima of the associated L2 misfit function, which correspond to velocity models matching the data up to one or several phase shifts. Conversely, the optimal transport distance appears as a more suitable tool to compare the misfit between oscillatory signals, for its ability to detect shifted patterns. However, its application to the full waveform inversion is not straightforward, as the mass conservation between the compared data cannot be guaranteed, a crucial assumption for optimal transport. In this study, the use of a distance based on the Kantorovich–Rubinstein norm is introduced to overcome this difficulty. Its mathematical link with the optimal transport distance is made clear. An efficient numerical strategy for its computation, based on a proximal splitting technique, is introduced. We demonstrate that each iteration of the corresponding algorithm requires solving the Poisson equation, for which fast solvers can be used, relying either on the fast Fourier transform or on multigrid techniques. The development of this numerical method make possible applications to industrial scale data, involving tenths of millions of discrete unknowns. The results we obtain on such large scale synthetic data illustrate the potentialities of the optimal transport for seismic imaging. Starting from crude initial velocity models, optimal transport based inversion yields significantly better velocity reconstructions than those based on the L2 distance, in 2D and 3D contexts.

Subfields: Geophysics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/59bc4f42269154b67441cc394e6a85a853bb53e2

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Citations in the corpus

Inferring spatial and signaling relationships between cells from single cell transcriptomic data (2020, methodology): “Recent advancements in optimal transport method development, including ef ﬁ cient algorithms 19 , accessible library 20 , and ﬂ exible formulations 21,22 , enable its broader application 23 – 25 , such as inference of developmental trajectories 26 and handling batch effects 27 in scRNA-seq data.”
Analysis of optimal transport and related misfit functions in full-waveform inversion (2017, background): “A recently introduced class of misfit functions is optimal transport related (Engquist and Froese, 2014; Engquist et al., 2016; Métivier et al., 2016a, 2016b; Yang et al., 2016).”
Computational Optimal Transport (2018, background): “, 2015], sparse recovery and compressed sensing [Indyk and Price, 2011], and seismic inversion [Métivier et al., 2016].”