Seismic method - Geophysics for the Mineral Exploration Geoscientist - page 379

Location ( X ) Location ( X )

f)

Actual structure

Reflector

Location ( X ) Location ( X )

g)

Reflector

Actual structure

Figure 6.22 (cont.)

interference ever more destructive as the spacing between
the diffractors decreases. When the spacing is suf ciently
small the seismic response takes the form of a horizontally
continuous feature coincident with the apices of the indi-
vidual diffraction hyperbolae. This is the appearance of a
horizontal reflector in zero-offset data ( Fig. 6.22a ).
Figure 6.23b shows the result when the closely spaced
diffractors form a dipping line. The interfering hyperbolae
produce a continuous

of the subsurface, which in this case is known. The ampli-
tudes of the adjacent traces where they are intersected by
the travel time curve are summed, and the result is the
amplitude of the sample in a new version of the central
trace, the migrated trace ( Fig. 6.24b ) . The migrated dataset
is formed by repeating this process for every sample in
every trace in the unmigrated dataset. In this idealised
example, the diffraction is perfectly collapsed so that all
of its amplitude (energy) is concentrated at its apex. The
migrated data resemble the actual form of the subsurface,
in this case a single point diffractor, so the purpose of
migration has been achieved.
When the process is applied to real data, where the
hypothetical diffraction coincides with an actual diffraction
the summation process will encounter samples of the same
polarity on adjacent traces. The resultant absolute ampli-
tude on the migrated trace will be large and so an arrival
will

whose dip,
length and down-dip displacement is displaced from the
line of diffractors. This corresponds with the geometrical
distortions illustrated for the dipping re ectors in
Fig. 6.22e . Figure 6.23b shows that one way to correct the
distortions in stacked data, i.e. to migrate the data, is to
treat the subsurface as comprising a series of hypothetical
diffractors, and therefore the data as consisting of a series
of interfering hypothetical diffractions. Each diffraction
hyperbola is transformed, or collapsed, to a

' apparent reector '

' '

located
at its apex. Ideally, the data would then correspond with
the actual structure of the subsurface.
Figure 6.24a illustrates the migration of a simple zero-
offset dataset containing only a single diffraction. The
seismic velocity in the subsurface is constant. The process
is only shown for the central trace at location X. Recall that
each seismic trace is a digital times series. For each sample
in the central trace, the form of a hypothetical diffraction
travel time curve (hyperbola) having its apex at the sample
is calculated. This requires information about the velocity

' point ' . Where a hypothetical diffraction is not

coincident with an actual diffraction, the sample values
along the hyperbola will be random and will tend to sum
to zero. This part of the migrated trace will not contain an
arrival.
The process described above is known as diffraction-
summation migration and, although mathematically
simple, can be very effective. A more sophisticated form
of this type of migration, known as Kirchhoff summation,
accounts for changes in both phase and amplitude along
the diffraction hyperbolae. The same processes can be

be created