Page 406 - Acquisition and Processing of Marine Seismic Data

7.7 SURFACE-RELATED MULTIPLE ELIMINATION 397

operator. Multiple free seismic data at the sea primaries, and higher-order multiples from
surface z 0 in the frequency domain can be lower-order multiples. Based on the geometry
expressed as (Verschuur et al., 1992) in Fig. 7.32A, a primary reflection originated
from shot location S L arrives at location M L ,
2 2 3
½
ðÞ
ðÞ
S 0 z 0 ¼ S z 0 A ωðÞ S z 0 ½ ðފ ⋯ and a surface-related multiple is recorded at
ðފ + A ωðÞ S z 0
(7.4) location R L . We can consider this multiple as
two successive primary events: one is originated
where S(z 0 ) is the matrix consisting of all input
from the shot at S L and recorded at M L , and the
seismic shots with multiples, S 0 (z 0 ) is the matrix
of all shots without multiples, and A(ω) is the other is originated from the shot at M L and
surface operator. The summation of second, recorded at R L . If the location of M L is known,
third, etc. terms in the righthand side of then we can predict the multiple by autoconvol-
Eq. (7.4) constitute surface-related multiples, ving the already recorded events. For each shot
which are subtracted from recorded seismic and receiver in the input data, a shot gather at
data. In the SRME technique, these multiples location S L and a common receiver gather at loca-
tion R L are selected from the input data. Traces
are predicted by the convolution of source and
from both gathers are combined, providing that
receiver gathers: When we consider that the
the receiver location of the former trace coincides
increasing order of multiples consists of primary
with the source location of the later trace. Convo-
events as shown in Fig. 7.32A, a surface-related
lution of two sets of traces and summing up the
multiple can be predicted by convolving these
results give the predicted multiple trace for that
primary events and multiplying the result by
source-receiver pair. That is, the common shot
the sea surface reflection coefficient. This is
gather from location S L is convolved with the
accomplished by convolving the input seismic
data with itself both in time and space domains. common receiver gather at location R L in
While convolution in the time domain provides Fig. 7.32B, and the results are summed. In fact,
the arrival time of multiples, convolution in the the autoconvolution of the input data corre-
space domain gives their offsets. This procedure sponds to doubling of arrivals in the time and
enables us to obtain the multiples directly from space directions (Fig. 7.33), which is simply used

FIG. 7.32 (A) Increasing order of surface-related multiples can be regarded as successive primary events. (B) Common shot
gather from location S L is convolved with the common receiver gather at location R L , and the results are summed to predict the
multiples.