“…We also thank S. Kaplan, C. Li, J. Cheng, J. Shragge, E. Slob, and one anonymous reviewer for their constructive suggestions, which helped to improve this paper. Fomel (2006) and Fomel and Liu (2010) propose a digital wavelet like transform, which is defined with the help of the wavelet-lifting scheme (Sweldens, 1995) combined with local PWD. The wavelet lifting uses predictability of even traces from odd traces of 2D seismic data and finds a difference r between them, which can be expressed as r ¼ o − P½e;…”