The Earth's geology changes with location.
Most areas of oil exploration are dominated by
sedimentary rocks, which despite their original
flat deposition, are often faulted, folded, and partially eroded.
At most locations, however,
the seismic subsurface image
of such sedimentary rocks
can be locally approximated
by a set of smooth, parallel, planar reflectors.
The local approximation of dipping 2-D sedimentary beds in 3-D
by small *plane reflector volumes*
matches the familiar approximation of a 2-D curve by short straight
line segments.
Occasional discontinuities, such as faults or erosional surfaces,
demarcate these smoothly-varying reflector volumes.
To map these occasional discontinuities,
we
intend
to estimate and remove
the plane reflector contribution at each subsurface location.
The estimation is bound to fail where discontinuities
violate our assumption of a local, parallel, planar model.
The subsequent removal yields a large residual.
The scheme does not detect the discontinuity itself but the
interrupting effect it has on its surrounding neighboring
plane reflector volume.
In other words,
the proposed approach looks at three scales of the subsurface
image. It breaks down the overall image (first scale), to small
mostly homogeneous subcubes (second scale). The approach
estimates and removes the plane reflector contribution in these subcubes
and thereby exposes the discontinuities (third scale)
that violate
the model of a single plane reflector volume.

11/12/1997