Crosscorrelation-based dynamic time warping and its application in wave equation reflection traveltime inversion

Crosscorrelation and dynamic time warping (DTW) are ubiquitous in time-shift estimation. However, the small-shift limitation of crosscorrelation and the instability and high sensitivity to noise of DTW seriously hinder their applications in complex situations. In this study, we develop a method called crosscorrelation-based DTW (CDTW) to address these issues. Our method constructs error matrices by local crosscorrelation instead of Euclidean distance to minimize the sensitivity to noise. The new error matrices are calculated in local windows and contain local structure similarity information of the two input signals. It improves the stability of the algorithm and makes the CDTW method less sensitive to noise and amplitude modulation. Our method estimates the time-varying shift using dynamic programming as the conventional DTW after the new error matrix is formulated. Numerical tests on pairs of signals and seismic images prove that our method can accurately estimate time shifts in cases of time-varying amplitude modulation and strong random noise contamination. Finally, we apply the CDTW method to wave equation reflection traveltime inversion (WRTI) and develop a CDTW-based WRTI method. Synthetic and field applications prove that this method can construct good background velocity models with the reliable reflection traveltime shifts produced by the CDTW method.