Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 178

Figure 4.2.10. Shape distortion due to elastic boundary.
The two models described in this section do not provide three-dimensional
information about the formation, but they do describe the immediate vicinity of
the bit. MWD - VSP imaging methods, by contrast, are attractive because the use
of multiple surface receivers enables the mapping and imaging of geological
structures ahead and to the side of the drill bit. The implicit assumption in using
incident and reflected waves, in our derivations, is the availability of a clean
environment that allows us to distinguish between the two. This is possible
under controlled conditions. For example, we can excite a static drillstring at
the surface with a narrow pulse, watch it reflect upwards, and measure all
amplitude, phase and shape changes. This is more difficult while drilling .
Earlier, we stressed the “need to provide for (simulated) semi-infinite
conditions, so that simple comparisons between incident and reflected waves
can be made.” Such conditions can be achieved, if it is possible to extract
incident and reflected waves from transient systems through signal processing.
The basic ideas are discussed next.