The formulation of the EMD based dip filter was given by Chen and Ma (2014):

where is the number of dip components or the number of EMD decomposed components. denotes index, denotes frequency, and denotes spatial trace index. The decomposition is done in each frequency slice in the frequency-space domain via EMD. The details of EMD can be found in Huang et al. (1998).

Equation 14 is formulated in the frequency domain in its original form. In the time-space domain, the EMD based dip filtering is simply

where is the vectorized seismic data, is the th dip component after using the EMD based dip filter. It is obvious that the EMD based dip filter is a linear transform and the summation of all the dip components is the original seismic image.

2020-02-28