Misfit functions based on differentiable dynamic time warping (DTW) have demonstrated an excellent performance in various sequence-related tasks. We introduce this concept in the context of waveform inversion and discuss a fast algorithm to calculate the first and second derivatives of such misfits. The DTW distance is originally calculated by solving a series of min sorting problems, thus it is not differentiable. The fundamental idea of differentiable DTW is replacing the min operator with its smooth relaxation. It is then straightforward to solve the derivatives following the differentiation rules, which results in both the differentiable misfit measurements and warping path. This path weights the traveltime mismatch more than its amplitude counterpart. We can construct a penalization term based on this warping path. The penalized misfit function is adaptable to measure traveltime and amplitude separately. Numerical examples show the flexibility and the performance of the proposed misfit function in mitigating local minima issues and retrieving the long-wavelength model features
|Original language||English (US)|
|Title of host publication||First International Meeting for Applied Geoscience & Energy Expanded Abstracts|
|Publisher||Society of Exploration Geophysicists|
|State||Published - Sep 1 2021|
Bibliographical noteKAUST Repository Item: Exported on 2021-09-07
Acknowledgements: The authors would like to thank Chevron for making the synthetic data available. For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.