Quantifying and correcting residual azimuthal anisotropic moveout in image gathers using dynamic time warping

Discussion

The workflow proposed in this paper simultaneously generates enhanced seismic images and anisotropic attributes, thus leading to two different directions for further studies depending on if one is interested primarily in correcting for residual elliptical HTI anisotropy with dynamic warping or gaining additional information from the attributes generated.

The process of dynamic warping is simply an integer shift data matching problem, which makes its application computationally efficient. For our purposes it aligns one one-dimensional signal to another, seeking to make their values match as closely as possible given the constraints on rate of change and maximum shift provided. This may lead to several issues. First, moveout in the input gathers must already be ``almost'' correct. Even if the nearest peak or trough in the initial gather stack to one in the trace being matched does not actually correspond to the peak in that trace, it will still be matched to that feature. Hence, as much moveout correction as possible should be done prior to implementing this workflow.

Second, the method as described would not function well in the presence of a polarity reversal caused by an amplitude variation with offset (AVO) anomaly. Rather than matching a polarity reversed trough to a peak, it would simply match trough to trough. This issue could be overcome by first correcting for an AVO anomaly in the gathers, determining the shifts in those corrected gathers that would correct for elliptical HTI anisotropy, and then applying those shifts to gathers that have not had their AVO anomaly corrected. Different types of stack could also be used as the matching trace for gather flattening, or different portions of the gather could be matched to different stacks which are seen as most representative of traces within the interval to create a superior flattening result.

Finally, it is possible for seismic events to become distorted due to shifts applied by the warping algorithm. We did not observe this phenomenon in the field data experiment, but appropriately limiting the maximum strain and shift size parameters in the dynamic time warping algoritm is important for avoiding such distortions.

Although the method proposed in this paper focuses on applications to correct residual moveout related to elliptical HTI anisotropy, the data matching process could also shift traces to perform static correction. Residual moveout related to elliptical HTI anisotropy may be distinguished from that caused by static correction, which would appear as a constant shift applied to an entire trace. Note that because the DTW workflow treats each gather independently, static corrections computed by taking the average shift value over a trace would not necessarily be surface-consistent. If only a few traces within a gather feature residual moveout related to static correction, those constant shifts are unlikely to have a large affect on the HTI anisotropy attributes, as they would have to be periodic over $180^\circ$ throughout the gather. If many traces feature moveout related to static correction, it would be beneficial to apply surface consistent correction to the seismic data, as this method for determining anisotropic axis and orientation assumes that the residual moveout is caused by HTI anisotropy.

Seismic images resulting from the stacking of flattened gathers contain more coherent and focused reflection events as shown in the constant crossline slices of Figures 9a and 9b, their zoomed sections of Figures 10a and 10b, and the depth slices of Figures 12a and 12b. Flattening the gathers also overcomes the effective low-pass filter created by stacking gathers with residual elliptical HTI moveout. This is illustrated in the spectra of Figures 10c and 11c, where the flattened stack spectra contain more energy at higher wavenumbers and greater bandwidth than the input stack spectra. Furthermore, this method does not create new structure or shape within the data, which is particularly obvious in Figures 15a and 15b. These more coherent events would likely be easier for an automatic interpretation or computer vision algorithm to follow. Therefore, the gather flattening and image enhancement process outlined here could fit well as part of an automatic interpretation workflow.

Another interesting direction for further study is investigation of the anisotropic azimuth and intensity parameters. These are functions of shifts which correct residual elliptical HTI moveout, and as such may be thought of as an average anisotropy measure over the entirety of a ray path, similar to how root-mean-square (RMS) velocity used in time migration is a measure of the average velocity over a ray path. The method assumes that anisotropy varies slowly in the subsurface, and measures the accumulated anisotropy along a ray path reflecting at a position in the subsurface. It approximates the subsurface elliptical HTI anisotropy field by highlighting areas where anisotropy is present, but may fail in regions where anisotropy values change rapidly. A useful extension could involve developing a transformation from the average anisotropy measures along a raypath which this method provides to a local or interval anisotropy. This local anisotropy could enable more accurate subsurface characterization, allowing for representations of local features rather than tendencies throughout the volume. A simple implementation of this could involve taking the derivative with respect to depth of a vector whose orientation and magnitude are defined by the anisotropic azimuth and intensity. A more complex version could involve a HTI ray tracing step and solving for the attributes throughout the volume based on the anisotropic attributes tied to those ray paths.

We have defined this paper's workflow so that each gather is independent, and thus the processing may be ran in parallel, enabling a relatively simple implementation for large data sets. For the field data experiment in this paper, each gather has 500 traces and there are approximately 300,000 gathers within the volume. Running the process on 200 threads, the flattening of gathers and determination of principal axes was completed in under six hours, much faster than the time required for a processing workflow that took elliptical HTI anisotropy into account. We are not proposing a complete method for residual moveout correction, but rather a way of determining the orientation of the moveout whose correcting shifts may be modeled by an ellipse and a measure of how strong that elliptic component is. The method described in this paper is an inexpensive approximation to more costly anisotropic processing methods, but is not intended to replace them.

Quantifying and correcting residual azimuthal anisotropic moveout in image gathers using dynamic time warping