Dynamic time warping — An improved method for 4D and tomography time shift estimation?

Abstract

Time shift estimation is a key issue in many areas of seismic exploration such as time-lapse studies and traveltime tomography. Automated estimation is useful because it enables applications such as time strain analysis and automated velocity model building. A commonly used automated estimation algorithm is the windowed crosscorrelation. Unfortunately, this method can be inaccurate in areas where time shifts vary significantly over short intervals. Algorithms based on mismatch minimization have been proposed to remedy this problem. All the mentioned methods suffer from cycle skipping in the face of large time shifts. I, therefore, used the dynamic time warping (DTW) algorithm as an alternative method to estimate time shifts. I claimed the time shift estimates produced by DTW are of higher quality than those produced by the previous methods, especially with regard to the cycle-skipping problem. I found that DTW always is able to perfectly restore time shifts applied to traces when the changes are purely temporal. I investigated its accuracy when amplitude changes are present, and found that the algorithm is well suited for time-lapse analysis. Finally, we determined that DTW is resilient against cycle-skipping errors, in the presence of large time shifts and with significant changes in the data, and thus a candidate for use in automated velocity model-building methods, such as waveform tomography or full-waveform inversion.

Review Paper: Methods of measurement for 4D seismic post‐stack time shifts

“…Other applications in the seismic literature include use for non‐stretching normal moveout, P‐S matching and statics corrections (Chen et al ., 2017). In the context of 4D time‐shift estimation, Venstad (2014) compares DTW with WFI and NLI (see above for details of these algorithms). The approach is claimed to be more accurate than methods based on the cross‐correlation of windowed images as the shifts from XCR vary significantly in quality with window size.…”

“…The vertical estimates also need to be smoothed prior to this procedure. In practice, the addition of a regularization term such as that introduced by Venstad (2014) is required to ensure robustness against noise. The power of the DTW algorithm comes from the dynamic programming but this requires a discrete lag value.…”

“…In the examples we use a down‐sampling factor of four, and a Gaussian window. There is thus a trade‐off between resolution of the time‐shift estimates and computational efficiency (Venstad 2014). DTW is suited to parallelization and thus speed can be improved.…”

Structure-adapted Multichannel Matching Pursuit for Seismic Trace Decomposition

“…The dynamic time warping (DTW) algorithm allows us to find the best match between two seismic series without explicitly estimating the local dip information (Hale, 2013;Venstad, 2014;Chen et al, 2018). The DTW between two seismic series can be expressed as follows:…”

“…The dynamic time-warping (DTW) algorithm can be applied to estimate the similarity between two time series and is widely used in geophysics (Hale, 2013;Venstad, 2014;Chen et al, 2018;Yao & Wang, 2022). However, the conventional DTW only uses the Euclidean distance between two seismic traces and ignores the trend.…”