Data alignment with non-stationary shaping filters

Cross-correlation provides a method of calculating a static shift between two datasets. By cross-correlating patches of data, I can calculate a “warp function” that dynamically aligns the two datasets. By exploiting the link between cross-correlation and shaping filters, I calculate warp functions in a more general way, leveraging the full machinery of geophysical estimation. I compare warp functions, derived by the two methods, for simple one and two-dimensional applications. For the one-dimensional well-tie example, shaping filters gave significantly improved results; however, for the two dimensional residual migration example, the cross-correlation technique gave the better results. I also explain how the helical transform allows the problem of finding a shaping filter to be formulated as an auto-regression.