Page 433 - Acquisition and Processing of Marine Seismic Data

424 9. VELOCITY ANALYSIS

for the same reason. Under pressure, velocity h 2 h 1
V int ¼ (9.2)
changes with the saturation in such a way that, t 2 t 1
under low pressures, saturated rocks have Interval velocity is an intrinsic characteristic of
higher velocities as compared to dry rocks. In the subsurface rocks. Some of the migration
addition, dry rocks are more sensitive to algorithms require interval velocities to be
pressure increase because the pore fluids in
known, and they can be obtained from RMS
the matrix of the saturated rocks cannot be
velocities using the Dix equation in the seismic
compressed.
processing stage.
Signal frequency also affects the velocity
obtained at sonic and ultrasonic frequencies.
Frequency dependence of medium velocity is 9.1.2 Average Velocity (V ave )
known as dispersion. If the velocity decreases Average velocity is the average of the seismic
with the signal frequency, then it is termed nor- velocity between sea surface and a specific
mal dispersion. In marine seismics, guided reflector, and is used for the conversion of seis-
waves show dispersive behavior (Section 3.8).
mic data from time to depth. If there are n num-
ber of layers down to the target reflector, the
total thickness of these layers is divided by the
9.1 TYPES OF SEISMIC VELOCITY
summation of one-way travel time of the signal
for each layer, that is
Seismic wave velocity can be directly
obtained from sonic log measurements in the X
h 1 + h 2 + ⋯ + h n h i
wells as a function of depth. Velocity in two V ave ¼ ¼ X (9.3)
t 1 + t 2 + ⋯ + t n t i
and three dimensions can also be obtained indi-
rectly from multichannel seismic data. Based on
the area of application, there are different veloc-
ity definitions in seismic exploration, such as 9.1.3 Instantaneous Velocity (V ins )
interval, NMO, or root-mean-square (RMS) If the wave velocity varies continuously with
velocities, etc. However, the most convenient depth, then the h 2 h 1 difference becomes ∂h
velocity type extracted from analyzing the seis- while the t 2 t 1 difference turns into ∂t. Instanta-
mic data is the one that provides the best stack neous velocity is the differentiation of the depth
section, which is directly related to the NMO with respect to time, and its time integral gives
and RMS velocities. Using velocity analysis the average velocity between source and reflec-
tools, the only velocity that we can obtain from
tor. Instantaneous velocity can be defined as
seismic data is the RMS velocity, yet it is possible
to compute interval velocities from RMS veloci- ∂h
V ins ¼ (9.4)
ties via empirical relationships. ∂t
Z T
9.1.1 Interval Velocity (V int ) V ave ¼ V ins tðÞdt (9.5)
0
Interval velocity is the average velocity
between two reflective interfaces. If two reflec-
tors located at depths h 2 and h 1 give one-way 9.1.4 Root-Mean-Square Velocity (V RMS )
travel times t 2 and t 1 , respectively, then the inter-
If the subsurface consists of n number of layers,
val velocity of the layer between the depths h 2
and h 1 is given by and if their corresponding interval velocities