The estimation of time-lapse time shifts between two, or several, repeated seismic surveys has become increasingly popular over the past eighteen years. These time shifts are a reliable and informative seismic attribute that can relate to reservoir production. Correction for these time shifts or the underlying velocity perturbations and/or subsurface displacement in an imaging sense also permits accurate evaluation of time-lapse amplitudes by attempting to decouple the kinematic component. To date, there are approximately thirty methods for time-shift estimation described in the literature. We can group these methods into three main families of mathematical development, together with several miscellaneous techniques. Here we detail the underlying bases for these methods, and the acknowledged benefits and weaknesses of each class of method highlighted. We illustrate this review with a number of time-lapse seismic examples from producing fields. No method is necessarily superior to the others, as its selection depends on ease of implementation, noise characteristics of the field data, and whether the inherent assumptions suit the case in question. However, cross-correlation stands out as the algorithm of choice based on the Pareto principle and waveform inversion the algorithm delivering best resolution. This is a companion study to the previous review of time-shift magnitudes and a discussion of their rock physics basis.

An absorbing boundary condition is necessary in seismic wave simulation for eliminating the unwanted artificial reflections from model boundaries. Existing boundary condition methods often have a trade-off between numerical accuracy and computational efficiency. We proposed a local absorbing boundary condition for frequency-domain finite-difference modelling. The proposed method benefits from exact local plane-wave solution of the acoustic wave equation along predefined directions that effectively reduces the dispersion in other directions. This method has three features: simplicity, accuracy and efficiency. Numerical simulation demonstrated that the proposed method has higher efficiency than the conventional methods such as the second-order absorbing boundary condition and the perfectly matched layer (PML) method. Meanwhile, the proposed method shared the same low-cost feature as the first-order absorbing boundary condition method.

This study complements two earlier papers on the interpretation and estimation of post‐stack time‐shifts that detail the most popular measurement methods to date. In this current work, the focus is on describing the magnitude and identifying the origin of the uncertainty present in these time‐shift values. We also consider how the underlying assumptions behind conventional time‐shift estimation methods can contribute to the inadequate resolution of the subsurface time‐lapse changes. The various errors fall into three broad categories: (1) those related to intrinsic data limits that cannot be avoided; (2) those associated with seismic measurement methods that can be corrected with some effort; and finally (3) those that arise due to approximations to the wave physics made during the design or implementation of the methods. In the first category are limitations due to sampling rate and signal‐to‐noise ratio, and wavelet interferences resulting from the narrow band nature of the seismic data and the heterogeneous nature of the geology itself. The effects produce errors of typically a fraction of a millisecond, but exceptionally in 4D data with poor repeatability up to 1 ms. In the second category are acquisition and processing errors. These are usually of the order of a few milliseconds but can reach up to 10s of milliseconds and are, therefore, essential to correct. It is possible to correct the effects of tides and seawater variations in marine acquisition if these changes are monitored and measured. Navigation and timing are identified as issues to consider carefully. For land data, daily and seasonal near‐surface variations are still problematic, and source and sensors must be buried to deliver interpretable time‐shifts. The impact of choices made during processing can be significant but is specific to the workflow and dataset and thus cannot be generically assessed. However, the effects from residual multiples can be identified and treated. Of moderate importance is the third category of errors, which consists of four items. Of these, the effect of lateral image shifts and amplitude effects are judged to play a minor role. Deviation from the assumption of vertical ray‐paths during post‐stack analysis appears to be of concern only for reservoirs with noticeably dipping structures and strong contrasts. The effect of pre‐stack variations on the post‐stack measurements remains a topic to be more thoroughly examined, and the conclusion is unclear. Finally, it is apparent that uncertainties in all categories are strongly dependent on the field setting and geographical location.

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