Let us synthesize a downgoing Snell wave with field data, then imagine how the upcoming wave will look and how it will carry to us information about the subsurface.

Slant stacking will take the survey line data *P*(*s*,*g*,*t*), which is a function
of shot location *s*, geophone location *g*, and travel time *t*,
and sum over the shot dimension, thereby
synthesizing the upcoming wave *U*(*g*,*t*), which should have been
recorded from a downgoing Snell wave.
This should be the case even though
there may be lateral velocity variation and multiple reflections.

The summation process is confusing because three different kinds of time are involved:

t |
= | travel time in the point-source field experiments. |

t' |
= | interpretation time. The shallowest reflectors are seen just after . |

= | time in the Snell pseudoexperiment with a moving source. |

Time in the pseudoexperiment in a horizontally layered earth
has the peculiar characteristic that the further you move out the geophone axis,
the later the echoes will arrive.
Transform directly from the field experiment time *t* to
interpretation time *t*' by

(26) |

Figure 11 depicts a downgoing Snell wave.

Figure 11

Figure 12 shows a hypothetical common-geophone gather,
which could be summed to simulate the Snell wave seen at
location *g _{1}* in Figure 11.
The lateral offset of

Figure 12

Repeating the summation for all geophones synthesizes an upcoming wave from a downgoing Snell wave.

The variable *t*' may be called an interpretation coordinate,
because shallow reflectors are seen just after *t*' = 0,
and horizontal beds give echoes that arrive with no horizontal stepout,
unlike the pseudo-Snell wave.
For horizontal beds, the detection of lateral location
depends upon lateral change in the reflection coefficient.
In Figure 11,
the information about the reflection strength at *B* is
recorded rightward at *g _{1}* instead of being
seen above

Figure 13
shows the same two flat layers as figures 1 and 2,
but there are also anomalous reflection coefficients
at points *A*, *B*, and *C*.

Figure 13

Point *A* is directly above point *B*.
The path of the wave reflected at *B* leads directly to *C* and
thence to *g _{1}*.
Subsequent frames show the diffraction hyperbolas
associated with these three points.
Notice that the pseudo-Snell waves reflecting from the flat layers
step out at a rate

10/31/1997