Page 434 - Acquisition and Processing of Marine Seismic Data

9.1 TYPES OF SEISMIC VELOCITY 425

are V 1 , V 2 , …,V n , the RMS velocity can be These assumptions can be summarized as
defined as follows (Yılmaz, 2001):

X
2
2 2 2 V t i (i) Single horizontal layer: NMO velocity
V t 1 + V t 2 + ⋯ + V t n
i
V 2 ¼ 1 2 n (9.6) equals the velocity of the upperlying
RMS ¼ X
t 1 + t 2 + ⋯ + t n t i
medium.
where t 1 , t 2 , …, t n are the one-way travel times of (ii) Horizontally stratified earth: RMS velocity
the signal for each individual layer. This is the is used as NMO velocity provided that
velocity obtained during the velocity analysis the length of the seismic spread is small.
of seismic data and is used in NMO correction (iii) Single dipping layer: NMO velocity is the
for the layered subsurface. velocity of the upperlying medium
divided by the cosine of the inclination
angle, according to the Levin equation.
9.1.5 NMO or Stacking Velocity (V NMO ) (iv) Several layers with arbitrary dips: RMS
velocity is used as NMO velocity
For a specific reflection, the time difference
between the recording time of that reflection at provided that the length of the seismic
any offset from the shot and zero-offset time is spread and inclination angles of the
defined as normal moveout (Chapter 10), which reflectors are small.
arises only due to the offset between source and There is a small difference between NMO and
recording channel. NMO velocity is used to re- stacking velocities, which is generally omitted in
move normal moveout times from CDPs before practice: While NMO velocity is obtained from
stacking, and therefore accurate determination the reflections recorded using small spreads,
of NMO velocity is extremely important for the stacking velocity is derived from the best-fit
quality of final stack sections. It is defined as hyperbola for the reflections from full spreads
x 2 (Taner and Koehler, 1969; Al-Chalabi, 1973). This
2
2
t xðÞ ¼ t 0ðÞ + (9.7) difference is known as spread-length bias, and it
V 2
NMO generally arises from the heterogenic velocity
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi structure of the upperlying medium. Although
x 2
V NMO ¼ (9.8) the difference is prominent for large offsets
2 2
txðÞ t 0ðÞ (Fig. 9.2), stacking and NMO velocities are
assumedtobeequalinpractice.Sincethistimedif-
where t(x) is the arrival time of a reflection signal
ference between observed and theoretical arrival
at offset x, and t(0) is the zero-offset time of that
times at increasing offsets causes issues during
specific reflection.
NMO corrections for long offset data, several cor-
NMO velocity varies with the morphology of
rections for long offsets may be required during
the seafloor and structure of the subsurface:
the velocity analysis using one of the proposed
while it equals the velocity of the upperlying
correction approaches to Eq. (9.7), such as
medium for the horizontal single reflector case,
Al-Chalabi’s third term approach (Al-Chalabi,
it is proportional to the cosine of the inclination
1973), or Castle’s shifted hyperbola (Castle, 1994).
angle in the case of a dipping interface. For short
offsets at a horizontally layered media, NMO
and RMS velocities are identical. The same 9.1.6 Dix Interval Velocity (V DIX )
approach may also be valid for the cable lengths
shorter than the reflector depths in the case of Using the empirical Dix equation, it is possi-
layers with arbitrary dips, providing that the ble to calculate interval velocities from RMS
inclination angles are small enough. velocity distribution of the subsurface. It is used