In seismology wavelengths are so long that we tend to forget it is physically possible to have a directional wave source and a directional receiver. Suppose we had, or were somehow able to simulate, a source that radiated only down and a receiver that received only waves coming up. Then suppose that we were somehow able to downward continue this source and receiver beneath the sea floor. This would eliminate a wide class of multiple reflections. Sea-floor multiples and peglegs would be gone. That would be a major achievement. One minor problem would remain, however. The data might now lie along a line that would not be flat, but would follow the sea floor. So there would be a final step, an easy one, which would be to upward continue through a replacement medium that did not have the strong disruptive sea-floor reflection coefficient. The process just described would be called impedance replacement. It is analogous to using a replacement medium in gravity data reduction. It is also analogous to time shifting seismograms for some replacement velocity.
The migration operation downward continues an upcoming wave. This is like downward continuing a geophone line in which the geophones can receive only upcoming waves. In reality, buried geophones see both upcoming and downgoing waves. The directionality of the source or receiver is built into the sign chosen for the square-root equation that is used to extrapolate the wavefield. With the reciprocal theorem, the shots could also be downward continued. Likewise shots physically radiate both up and down, but we can imagine shots that radiate either up or down, and mathematically the choice is a sign. So the results of four possible experiments at the sea floor, all possibilities of upward and downward directed shots and receivers, can be deduced.
Extrapolating all this information across the sea-floor boundary requires an estimate of the sea-floor reflection coefficient. This coefficient enters the calculation as a scaling factor in forming linear combinations of the waves above the sea floor. The idea behind the reflection-coefficient estimation can be expressed in two ways that are mathematically equivalent:
After the geophones are below, you must start to think about getting the shots below. To invoke reciprocity, it is necessary to invert the directionality of the shots and receivers. This is why it was necessary to include the auxiliary experiment of upward-directed shots and receivers.