DC component in Hilbert transform concept for seismic data
The 'DC Component' is a standard term used to describe the mean energy of a signal ( https://en.wikipedia.org/wiki/DC_bias ), which in the frequency domain corresponds to the component of 0 frequency. The DC component does not depend on the time -- while the other frequencies 'wiggle' around it. In seismic signals I think we don't generally have a DC components: the signal moves around a point of 0 pressure/displacement.

The authors then make their statement in a bit of an awkward way in my opinion. What they mean, is that the Hilbert transform applied to any 'DC component' is 0: thrown away!