We have to choose .Inserting a smoother signifies the assertion that the dips in
seismic data should change in a gradual way.
Choosing an isotropic smoother means we expect the dips to vary
similarly in all directions.
However, we know that the dip spectrum of the data probably changes more
quickly in some directions than in others.
We want to smooth most heavily along directions
where the dip is nearly constant.
In a constant-velocity, flat-layered earth, events fall along hyperbolas like
We want a smoother with an impulse response which is highly elongated
in the radial direction.
To get a big impulse response cheaply,
I apply the inverse of a directional derivative,
pointed in the radial direction.
To directly apply the inverse,
the roughener has to be causal, which means
that the inverse will only smooth in one direction Claerbout (1998).
We want to have an impulse response which is smoothed both
in towards zero radius and out towards large radius, so we
make it the cascade of the
causal smoother and its anticausal adjoint.