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.