Seismic data extrapolation based on multi-scale dynamic time warping

Seismic data reconstruction can provide high-density sampling and regular input data for inversion and imaging, playing a crucial role in seismic data processing. In seismic data reconstruction, a common scenario involves a significant distance between the source and the first receiver, which makes it unattainable to acquire near-offset data. A new workflow for seismic data extrapolation is proposed to address this issue, which is based on a multi-scale dynamic time warping (MS-DTW) algorithm. MS-DTW can accurately calculate the time-shift between two time series and is a robust method for predicting time-offset ($t-x$) domain data. Using the time-shift calculated by the MS-DTW as the basic input, predict the two-way traveltime (TWT) of other traces based on the TWT of the reference trace. Perform autoregressive polynomial fitting on TWT and extrapolate TWT based on the fitted polynomial coefficients. Extract amplitude information from the TWT curve, fit the amplitude curve, and extrapolate the amplitude using polynomial coefficients. The proposed workflow does not necessitate data conversion to other domains and does not require prior knowledge of underground geological information. It applies to both isotropic and anisotropic media. The effectiveness of the workflow was verified through synthetic data and field data. The results show that compared with the method of predictive painting based on local slope, this approach can accurately predict missing near-offset seismic signals and demonstrates good robustness to noise.