Page 441 - Acquisition and Processing of Marine Seismic Data

432 9. VELOCITY ANALYSIS

where V is the velocity of the upperlying to the RMS velocity of the reflection hyperbola
medium and t(0) is the zero offset time of the at its dedicated zero-offset time t(0).
reflection. According to Eq. (9.10), we can com- The specific value used to calculate a contour
pute the velocity of a given reflection if x, t(0), plot of velocity versus t(0) time so far is the
and t(x) are known. Since we do not know stacking amplitude. The most suitable represen-
whether an amplitude at time t(x) resides to a tation quantity, however, may not be the reflec-
specific reflection hyperbola with a zero-offset tion amplitude, depending on the S/N ratio of
time t(0), we must compute a number of theoret- the input CDP. In practice, the semblance value
ical hyperbolas with a range of velocity values calculated from the reflection amplitudes coin-
using Eq. (9.10), and determine the best-fit curve ciding with the theoretical hyperbolas is calcu-
with the observed hyperbola in an automatic lated and used to prepare the contour plots.
way. To achieve this, a minimum and a maxi- Hence, velocity spectrum plots are also known
mum velocity, with an increment value, are as semblance plots. Semblance is a statistical
selected. Using Eq. (9.10), a number of theoreti- parameter varying from 0 to 1, and can be calcu-
cal arrival time hyperbolas are computed for lated as
each zero-offset time on a specified CDP, each
" # 2
M
calculated by using different velocities between X X
the minimum and maximum velocity values. f i jj
1 t i¼1
That is, several hyperbolas are computed for S ¼ M (9.11)
each velocity increment from minimum to max- M X 2
f i
imum velocity for t(0) ¼ 0 ms; then t(0) is
i¼1
increased a few milliseconds (e.g., 20 ms), and
all the hyperbolas are computed again for the where f i represents the amplitude at two-way
same velocity range, and the computations go time t (i) of the ith trace in the input CDP, and
on for all zero-offset times along the time axis M is the number of traces in the CDP gather.
until a maximum trace time is achieved. These All these processes are schematically illus-
theoretical hyperbolas are then matched with trated in Fig. 9.7. A synthetic input CDP gather
the real hyperbolas on the recorded CDP, and with two reflection hyperbolas of 2500 and
the amplitudes concurring with the arrival times 3500 m/s RMS velocity is shown in the upper
of theoretical hyperbolas on the recorded CDP panel. For t(0) ¼ 0 ms zero offset time, six theo-
are summed up. Unless one of the theoretical retical reflection hyperbolas are computed (red
hyperbolas completely coincides with a real curves) by Eq. (9.10) for 1500, 2000, 2500, 3000,
observed one on the recorded CDP, the summa- 3500, and 4000 m/s velocities, and are num-
tion will produce a small value. When the theo- bered from 1 to 6 (panel A). The recorded ampli-
retical and observed hyperbolas match, a large tudes on the CDP gather coinciding with these
sum is obtained. A maximum can only be theoretical hyperbolas are used to calculate a
obtained in case of the summation along the semblance value for each hyperbola by
theoretical hyperbola calculated with the veloc- Eq. (9.11). The calculated semblance values are
ity of that specific reflection. Thus, we can pre- placed in their relevant places in a time-velocity
pare a specific contour plot consisting of these panel in the bottom left of Fig. 9.7, whose hori-
summed amplitudes, horizontal and vertical zontal and vertical axes are velocity and t(0)
axes, which represent the velocity used to calcu- time, respectively. For instance, the semblance
late the theoretical reflection hyperbolas and value for t(0) ¼ 0 ms calculated using the ampli-
zero-offset times, respectively. Each enclosure tudes along the theoretical hyperbola for
of a maximum value on this plot corresponds 1500 m/s velocity (red hyperbola of number 1