Page 329 - Acquisition and Processing of Marine Seismic Data

320 6. DECONVOLUTION

of them are not realistic and cannot be tolerated due to absorption effects. The time-dependent
due to the nature of the seismic methodology, change in the source waveform is termed non-
the deconvolution algorithms still produce satis- stationarity, and attempts are made at compen-
factory results since they have a robust theoreti- sating for it before the deconvolution process, by
cal and mathematical basis. use of a suitable gain recovery application.

6.2.3 Assumption 3: Noise Component
6.2.1 Assumption 1: A Simple
Earth Model Since the noise component in Eq. (6.1) is not
known, this assumption supposes that the noise
According to this assumption, the earthis com-
component in the seismogram is zero, or that it
posed of horizontal layers and no lateral velocity
can be reduced to zero during the preprocessing.
variations exist within these constant velocity
However, recorded seismic traces always
layers. This assumption is violated in areas of
include random and several different types of
anisotropy and complex geology with strong lat-
coherent noise amplitudes, and they are added
eral velocity changes. It is also assumed that the
to the data both in the time and frequency
source generates only compressional (P) plane
domains. The random noise components cannot
waves of vertical incidence, which anticipates a
be predicted beforehand and are variable both in
zero-offset data acquisition geometry in which
time and space.
no shear (S) waves are generated at the interface
by phase conversion. Except for some specific
marine seismic surveys, such as shallow sparker 6.2.4 Assumption 4: Source Waveform
seismic acquisition, zero-offset seismic data is not Deconvolution needs the source waveform to
collected. However, if the reflector is too deep be known. Based on this assumption, the w(t)
with respect to the source-receiver separation, term in Eq. (6.1) is supposed to be known. How-
the incidence angle can be regarded as small ever, for explosive sources the source waveform
enough. In addition, the plane wave assumption is normally not known. Although the waveform
is also invalid since the seismic sources generate from air gun arrays can be recorded in marine
spherical waves, not plane waves.
surveys, this gives the waveform at the onset
time, known as the near-field signature. But
6.2.2 Assumption 2: Stationary Wavelet the signal is exposed to different influences dur-
ing its propagation and its shape becomes quite
This assumption suggests that the source different after ghost interference (Section 2.2.4).
waveform is stationary and does not change If the source waveform is known, then the
while it is propagating through the earth. The applied deconvolution is termed deterministic
pressure wave generated by an explosive deconvolution, and if it is unknown (which is
source, such as dynamite or an air gun, is known the common case), then a statistical deconvolu-
as the source signature, and its amplitude tion is used.
decreases and high-frequency components are
absorbed during its propagation. A certain time 6.2.5 Assumption 5: Wavelet Causality
after its onset, the source waveform becomes
quite different from when it was generated. Fur- A wavelet is a transient waveform of finite
thermore, the waveform in the shallow parts of length. Based on the phase specifications or their
the recorded traces is also quite different from maximum energy distributions, there may be
that in the deeper parts of the seismic data, four types of wavelets: minimum, mixed, zero,