Introduction

Accurate prediction of time-lapse timeshifts is important for monitoring fluid migration and reservoir compaction (Hatchell and Bourne, 2005). Tradtional time-lapse seismic image registration algorithms perform well in the absense of amplitude changes between baseline and monitor images. This assumption generally fails at the reservoir level where fluid injection and/or production induce changes in the elastic and sonic properties of the interval. These changing amplitudes can produce spurious timeshift anomalies (MacBeth et al., 2016). This effect is most pronounced near the tuning thickness due to interference between reflection events associated with thin beds. Similarly, low frequencies can produce arbitrarily large timeshifts. In this paper, we propose to estimate timeshifts in the presense of these problematic amplitude changes by decomposing time-lapse images into discrete frequencies components and simulataneously inverting for regularized timeshifts and amplitude ratios between baseline and monitor seismic images.

Simple cross-correlation based algorithms are among the most commonly used methods for estimating 4D timeshifts. Rickett and Lumley (2001) propose cross-equalization, which includes spatial and temporal registration to compensate for different acquisition geometries and amplitude balancing to scale the data to the same amplitude. Fomel and Jin (2009) estimate 4D timeshifts by picking a regularized warping path which maximizes the local similarity attribute (Fomel, 2007). Karimi et al. (2016) use the local similarity attribute to estimate 4D timeshifts after flattening the time-lapse seismic images using the stratigraphic coordinates transformation (Karimi and Fomel, 2015). Dynamic time warping (Sakoe and Chiba, 1978) was originally proposed for speech recognition and has been applied to estimating 4D timeshifts and many other data registration problems in geophysics (Hale, 2009). Williamson et al. (2007) explain timeshifts and amplitude changes by integrating classical warping and impedence inversion in the limit of small offset and dip and low frequency. This method is particularly attractive, as it iteratively compensates for amplitude changes associated with velocity variations induced by fluid injection or production. Hoeber et al. (2008) incorporate complex trace analysis (Taner et al., 1979) to match local phase and amplitudes between time-lapse seismic images. Lie (2011) extracts both timeshifts and 4D signal using a constrained inversion scheme. Zhang and Du (2016) borrow the optical flow technique (Horn and Schunck, 1981) to predict multidimensional timeshifts at multiple scales In our previous work, we invert for timeshifts and amplitude changes using amplitude-adjusted plane-wave destruction (APWD) filters (Phillips and Fomel, 2016). This technique iteratively refines timeshift estimates by predicting amplitude changes from the seismic data.

In this paper, we decompose the seismic images into discrete frequency components using the local time-frequency transform (LTFT) (Liu and Fomel, 2013) and simultaneously estimate timeshifts and amplitude weights due to changes in the reservoir conditions during production at each frequency using amplitude-adjusted plane-wave destruction (APWD) filters (Phillips and Fomel, 2016). Spectral decomposition partially alleviates the “spurious timeshift" problem associated with tuning, as described by MacBeth et al. (2016). We evaluate the effectiveness of this workflow using a synthetic dataset and field seismic data the Cranfield CO$_2$ sequestration experiment.