2021/09/30 by Fuqiang Chen, Daniel Peter, Matteo Ravasi · 14 citations
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Classification of discontinuities #Computer science #Differentiable function #Dynamic time warping #Geology #Geophysical Methods and Applications #Image warping #Inversion (geology) #Mathematical analysis #Mathematics #Maxima and minima #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #Structural basin #physics.geo-ph
paper · pdf · open access · doi:10.1190/geo2021-0598.1
published in Geophysics 87(4), R325-R335 (Society of Exploration Geophysicists)
openalex created_date 2021/09/13 · arxiv created 2021/12/08 · openalex publication_date 2022/03/19 · arxiv updated 2022/03/22 · openalex updated_date 2026/08/05
The dynamic time warping (DTW) distance has been used as a misfit function for wave-equation inversion to mitigate the local minima issue. However, the original DTW distance is not smooth; therefore it can yield a strong discontinuity in the adjoint source. Such a weakness does not help nonlinear inverse problems converge to a plausible minimum by any means. We therefore introduce for the first time in geophysics the smooth DTW distance, which has demonstrated its performance in time series classification, clustering, and prediction as the loss function. The fundamental idea of such a distance is to replace the min operator with its smooth relaxation. Then it becomes possible to define the analytic derivative of DTW distance. The new misfit function is entitled to the differentiable DTW distance. Moreover, considering that the warping path is an indicator of the traveltime difference between the observed and synthetic trace, a penalization term is constructed based on the warping path such that the misfit accumulation by the penalized differentiable DTW distance is weighted in favor of the traveltime difference. Numerical examples demonstrate the advantage of the penalized differentiable DTW misfit function over the conventional non-differentiable one.