One obvious difference between the two cases is that in the field geometry waves must first go down and then return upward along the same path, whereas in the hypothetical experiment they just go up. Travel time in field experiments could be divided by two. Figure 4 Left is a superposition of many hyperbolas. The top of each hyperbola lies along a straight line. That line is like a reflector, but instead of using a continuous line, it is a sequence of points.
Constructive interference gives an apparent reflection off to the side.
Right shows a superposition of semicircles. The bottom of each semicircle lies along a line that could be the line of an observed plane wave. Instead the plane wave is broken into point arrivals, each being interpreted as coming from a semicircular mirror. Adding the mirrors yields a more steeply dipping reflector.