Dynamic Time Warping - An improved method for 4D and tomography time shift estimation?

摘要

Time shift estimation is a key issue in many areas of seismic exploration, like time-lapse studies and travel-time tomography. Automated estimation is useful, as it enables applications like time strain analysis and automated velocity model building. A commonly used automated method is the windowed cross-correlation. Unfortunately, this method can be inaccurate in areas where time shifts vary rapidly. Other methods have been proposed to remedy this problem. All the mentioned methods suffer from cycle-skipping, however, in the face of large time shifts. I therefore propose to use the Dynamic Time Warping (DTW) algorithm as an alternative method to estimate time shifts. DTW was originally designed as an algorithm to measure the amount by which two time series differ, but can also provide an estimate of how, as a combination of amplitude changes and temporal warping. I claim the time shift estimates produced by DTW are of higher quality than those produced by the previous methods, especially with regards to the cycle skipping problem. In this paper, I show that DTW is able to perfectly restore time shifts applied to traces when the changes are purely temporal. I investigate its accuracy when amplitude changes are presents and show that the the algorithm is well suited for time-lapse analysis. Finally, I demonstrate that DTW is resilient against cycle skipping errors, in the presence of large time shifts, and thus a candidate for automated velocity model building, like tomography or full waveform inversion.