It has been widely observed that deconvolution generally fails in deep water. A possible reason for this is that deep water is not the mathematical limit at which the multiple-reflection problem is equivalent to the shot-waveform problem. But that is not all. Theory predicts that under ordinary circumstances multiples should alternate in polarity. The examples of Figure 1 and Figure 2 confirm it. You will have trouble, however, if you look for alternating polarity on CDP stacks. The reason for the trouble also indicates why deconvolution tends to fail to remove deep multiples from CDP stacks.

Recall the timing relationships for multiples at zero offset.
The
*reverberation*
*period*
is a constant function of time.
Because of moveout, this is not the case at any other offset.
Normal-moveout correction will succeed in restoring zero-offset timing
relationships in a constant-velocity earth,
but when the velocity increases with depth, the multiples
will have a slower RMS velocity than the primaries.
So the question is what velocity to use, and whether,
in typical land and marine survey situations,
the residual time shifts are greater than a half-wavelength.
No equations are needed to answer this question.
All that is needed is the general observation
that conventional common-midpoint stacking suppresses
multiples because they have lower velocities than primaries.
This observation implies that normal moveout
routinely time shifts multiple reflections a half-wavelength
or more out of their natural zero-offset relationships.

To make matters worse, the amplitude relationships that we expect at zero offset are messed up. Reflection coefficient is a function of angle. But on a seismogram from some particular offset, each multiple reflection will have reflected at a different angle.

Vertical incidence timing relationships are
*approximately*
displayed on CDP stacks.
The practical difficulty
is that the CDP stack does not mimic the vertical-incidence situation
well enough to enable satisfactory prediction of multiples from primaries.

Before stack, on marine data, moveout could be done with water velocity, but then any peglegs would not fit the normal-incidence timing relationship. Since peglegs are often the worst part of the multiple-reflection problem, moveout should perhaps be done with pegleg velocity. No matter how you look at it, all the timing relationships for deep multiple reflections cannot be properly adjusted by moveout correction.

- On some land data it was noticed that a deep multiple reflection arrived a short time earlier than predicted by theory. What could be the explanation?

10/31/1997