Cycle-skipping mitigation using misfit measurements based on differentiable dynamic time warping

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The dynamic time warping (DTW) misfit function has been employed for full-waveform inversion to mitigate the local minima issue. However, it is not a smooth measurement and can yield strong discontinuities in the adjoint source. Such a weakness hampers the convergence of waveform inversion to informative minima. We introduce a smooth DTW misfit function to remedy this shortcoming. The fundamental idea of the smooth DTW is to replace the {min} operator with its smooth relaxation. This replacement results in differentiable misfit measurements. Moreover, considering that the optimal warping plan indicates the traveltime difference between the observed and synthetic trace, we can construct a penalization term such that the penalized differentiable DTW distance highlights the traveltime difference further. Numerical examples demonstrate the advantage of the penalized differentiable DTW misfit function over the conventional non-differentiable one.
Original languageEnglish (US)
Pages (from-to)1-85
Number of pages85
Issue number4
StatePublished - Mar 19 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-04-27
Acknowledgements: We acknowledge the Supercomputing Laboratory at King Abdullah University of Science& Technology (KAUST) for providing resources that contributed to the research results reported within this manuscript. We thank two anonymous reviewers for their insightful comments to improve our paper. We also thank assistant editor, Professor Yang Liu for his comments. We would like to thank Chevron for making the SEG 2014 Chevron FWIsynthetic available.

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics


Dive into the research topics of 'Cycle-skipping mitigation using misfit measurements based on differentiable dynamic time warping'. Together they form a unique fingerprint.

Cite this