where is the prediction operator, is the updating operator. denotes the difference between true odd trace and predicted odd trace (from even trace), denotes a coarse approximation of the data. At the start of the forward transform, e and o correspond to the even and odd traces of the data domain. At the start of the inverse transform, and will have just one trace of the coarsest scale of the seislet domain. The seislet transform differs from the wavelet transform in that the prediction and updating operators utilize the local slope of seismic profiles to predict and update the even and odd traces. The above prediction and update operators can be defined as follows:

where and are operators that predict a trace from its left and right neighbors, correspondingly, by shifting seismic events according to their local slopes. The local slope can be calculated using a robust algorithm as introduced in Fomel (2002).

2020-02-21