Page 243 - Acquisition and Processing of Marine Seismic Data

234 4. FUNDAMENTALS OF DATA PROCESSING

however, can be summed along the hyperbolas on τ-p gathers are also incomplete and do not
or parabolas instead of the lines, which are appear as perfect semielliptical events. Their
termed the hyperbolic and parabolic τ-p trans- amplitudes close to the higher p values on the
form, respectively. τ-p gathers are always lacking.
A linear event on the CDP or shot gather (e.g., Fig. 4.21 shows the τ-p transform of a real shot
refractions, guided waves or direct waves) gather, which consists of a number of reflection
appears as a single point on the τ-p gather at hyperbolas as well as refracted and direct
its corresponding p trace determined by its incli- waves. While linear events like refracted and
nation in the time domain (Fig. 4.20A). Similarly, direct waves appear as single points on a τ-p
a linear event on a τ-p gather becomes a single gather, reflection hyperbolas can be observed
point in the CDP or shot gathers. Hyperbolic as semielliptical events approaching the p value
events such as reflections on CDP or shot gathers of 1/1500 s/m (e.g., the inverse of P wave veloc-
are transformed into semielliptical events on τ-p ity in seawater).
gathers with a specific appearance, determined After carrying out a processing application
by their curvature and zero offset time t(0) on (generally muting or filtering) in the τ-p domain,
the shot gathers (Fig. 4.20B). for instance zeroing out the amplitudes of mul-
In theory, far offset flanks of reflection and tiple reflections, it is possible to reconstruct a
diffraction hyperbolas extend to infinite offsets time signal in the time-offset domain via the
along the distance axis. This means that, in prac- inverse τ-p transform. The point here is that
tice, all of the reflection hyperbolas on shot the total trace number after the inverse trans-
gathers are incomplete because the seismic form is not necessarily the same as the number
streamers are of finite length. Therefore, ampli- of traces in the input shot gather. That is, we
tudes of reflection hyperbolas at long offsets on can obtain extra traces during the inverse trans-
shot records are lacking, and their counterparts form, which means that it is possible to perform

FIG. 4.20 (A) Schematic display of linear events on the shot and τ-p gathers, (B) schematic τ-p domain representation of
different events on a shot gather. (A and D) subcritical reflections (reflected with an angle smaller than critical angle), (B) head
wave, (E) direct wave, (C) supercritical reflection (reflected with an angle higher than critical angle).