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I applied Tieman's method on two different examples of synthetic
data. The goal here is to compare the effects of sampling on the quality of
the Tieman shot gather slant stacks with quality of standard slant stacks
applied to shot gathers. The data sets were generated by an algorithm
that generates a given number of regularly spaced constant fold cmp
gathers with given offset spacing over a set of seventy five dipping
reflectors. The reflectors are chosen to be randomly dipping in ranges from
at randomly chosen depths measured from the
center of the midpoint array. I chose a large number of random reflectors
to maximize the aliasing effects that occur on the shot gathers in hopes
that the limits of either method, the Tieman or the standard slant stack,
in distinguishing dips would be tested. Figure 1 is a constant
offset section of the first example data set which depicts the geometry of
this reflector model.
earth
Figure 1 Reflector model in time and
midpoint for a constant offset of two km

 
The sampling of the time axis and midpoint axis for both test data sets are
512 an 256 respectively while the sampling of the offset axis in the first
test is 80 and 20 for the second test. In the following
Figure 2 are examples of a cmp gather and a shot gather
of this data set.
gatheraniso
Figure 2 Simulated gathers:
(left) cmp gather, (right) shot gather
The shots were modeled as being shot offend, a situation commonly
encountered in marine surveys, thus the gathers only have positive offsets.
The disparity in symmetry between the hyperbolic events in the cmp
gather vs. the asymmetric events in the shot gather is clearly evident.
Next: 80 SAMPLE TEST
Up: Holden: Tieman & synthetic
Previous: TIEMANS'S TRANSFORM
Stanford Exploration Project
11/12/1997