To improve our ability to suppress multiples, we try to better characterize them. The trouble is that a realistic model has many ingredients. Few of the theories that abound in the literature have had much influence on routine industrial practice. I would put these unsuccessful theories into two categories:

- Those that try to achieve everything with statistics, oversimplifying the complexity of the spatial relations
- Those that try to achieve everything with mathematical physics, oversimplifying the noisy and incomplete nature of the data

Multiple reflection is a good subject for nuclear physicists, astrophysicists, and mathematicians who enter our field. Those who are willing to take up the challenge of trying to carry theory through to industrial practice are rewarded by learning some humility. I'll caution you now that I haven't pulled it all together in this section either!

Here two approaches will be proposed, both of which
attend to geometry
*and*
statistics.
Both approaches are new and little tested.
Regardless of how well they may work,
I think you will find that they
illuminate the task.

The first approach, called
*
CMP slant stack,
*
is a simple one.
It transforms data into a form in which
all offsets mimic the simple, one-dimensional, zero-offset model.
The literature about that model
in both statistics and mathematical physics is extensive.

The second approach is based on a
*
replacement impedance
*
concept.
It is designed to accommodate rapid lateral variations in the near surface.
It is easiest to explain for a hypothetical marine environment where the
sole difficulty arises from lateral variation in the sea-floor reflectivity.
The basic idea is downward continuation of directional
shots and directional geophones to just beneath the sea floor, but no further.
This is followed by upward continuation through
a replacement medium that has a zero sea-floor reflection coefficient.
This process won't eliminate all the multiple reflections,
but it should eliminate the most troublesome ones.

- Transformation to one dimension by slant stack
- Near-surface inhomogeneity
- Modeling regimes
- Subtractive removal of multiple reflections
- Slanted deconvolution and inversion
- The split Backus filter
- Sea-floor consistent multiple suppression
- Replacement-medium concept of multiple suppression

10/31/1997