Page 265 - Acquisition and Processing of Marine Seismic Data

256 5. PREPROCESSING

FIG. 5.14 An example mean amplitude spectrum of a marine shot gather showing the signal frequency band as well as low-
and high-frequency noise zones.

domain (Fig. 5.13C). When applied to seismic this noise is completely removed by a
data, a band-pass filter will cut out the ampli- 10–90 Hz band-pass filter (Fig. 5.15B).
tude components with frequencies lower and
higher than cut-off frequency values, f 1 and f 2 , 5.5.1 Filter Operator
respectively. The output data then becomes
band-limited. In practice, band-limited wavelets are used to
Raw seismic data have amplitudes with the filter the seismic data, which are known as filter
entire frequency band between 0 and Nyquist operators in the time domain, and amplitude
frequency, f N . While some of these amplitudes samples of this operator are termed filter coeffi-
correspond to reflection signals, the others con- cients. The most practical filter operator to be
stitute noise components. The frequencies of the used for frequency filtering is determined by
desired amplitude components of the reflected the Fourier transform theory. The main purpose
signals are generally limited to the frequency in band-pass filter operator design is that the fil-
bandwidth of the input data, depending on the ter operator must pass the amplitudes within the
seismic source type and source/streamer depth pass-band without any amplitude distortion,
(Section 2.5.1.2). For instance, if the effective while suppressing the amplitudes outside of this
bandwidth of the data is between 10 and frequency band. The amplitude spectrum of the
140 Hz, and if the sampling rate is 1 ms most suitable filter operator to implement this
(f N ¼ 500 Hz), this means that the amplitude purpose could be defined as a box-car shaped
components between 140 and 500 Hz consist of spectrum
high-frequency noise. Using suitable digital fil-
1 f 1 < f < f 2
ters, undesired frequency components of the AfðÞ ¼ (5.1)
0 other
seismic data can be filtered out while the desired
frequency components are preserved. A high- where f represents the frequency, and f 1 and f 2
frequency random noise interference (with fre- are the cut-off frequencies. Indeed, this is an
quencies higher than approximately 90 Hz) on ideal spectrum that we could use to filter our
a land shot record is shown in Fig. 5.15A, and seismic data when we simply multiply it by