Cross-correlation based time warping of one-dimensional seismic signals

The computation of a dynamic displacement field between pairs of seismic traces has numerous geophysical applications including the estimation of displacement vectors in time lapse seismic, Pto S-wave image registration and residual moveout correction. In this paper, I present a cross-correlation based methodology for the estimation of small time displacements between signals followed by stretching to match the signals. The utility of the algorithm was demonstrated through a synthetic time lapse example illustrating production effects and the associated time shifts between baseline and monitor surveys. The differencing of the baseline and monitor traces prior to warping results in apparent amplitude changes below the reservoir interval. Upon application of the warping algorithm, the undesirable amplitude changes below the reservoir interval are reduced. INTRODUCTION The need to compute a dynamic displacement field and the subsequent warping or matching between pairs of signals is often required in the field of signal processing. The use of these techniques spans various disciplines ranging from speech recognition (Sakoe and Chiba, 1978) to numerous geophysical applications. For example, Hale (2009) estimated apparent displacement vectors from time lapse seismic (4D) images and Herrera and van der Baan (2012) used dynamic time warping for seismic to well-ties. Other geophysical applications include Pto S-wave image registration and residual moveout correction. Various methodologies have been proposed in the literature to achieve the goal of matching two signals with time variant shifts. These include crosscorrelation based techniques (e.g., Hale, 2009) as well as optimization techniques where a cost function is minimized to obtain a solution (e.g., Herrera and van der Baan, 2012; Hale, 2013). The applicability of these two different approaches are then related to the rate at which the shifts vary, where rapidly varying shifts are better handled by optimization techniques and smaller shifts can be handled by cross-correlation (Hale, 2013). In this paper, I present a cross-correlation based methodology for estimating small time shifts in one-dimensional seismic signals related to (1) 4D effects due to changes in reservoir conditions over time or (2) residual moveout in common midpoint (CMP) gathers. The motivation for (1) is that warping of 4D seismic signals allows for a direct comparison of changes in reflection amplitudes due to production effects without the accompanying time shifts below the reservoir interval, and (2) is that warping of offset traces in a CMP gather could improve AVO analysis by correcting residual moveout. In the following, I discuss the steps involved in estimating the dynamic displacement field followed by stretching to match the signals. Subsequently, I demonstrate the applicability of the algorithm with a synthetic 4D example.