# Multiple attenuation

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

## Basic data processing sequence

Multiple reflections and reverberations are attenuated using techniques based on their periodicity or differences in moveout velocity between multiples and primaries. These techniques are applied to data in various domains, including the CMP domain, to best exploit the periodicity and velocity discrimination criteria (noise and multiple attenuation).

Deconvolution is one method of multiple attenuation that exploits the periodicity criterion. Often, however, the power of conventional deconvolution in attenuating multiples is underestimated. As for the Caspian data example in this section, despite theoretical limitations, deconvolution can remove a significant portion of the energy associated with short-period multiples and reverberations. It also can attenuate long-period multiples if it is applied in data domains in which periodicity is preserved (noise and multiple attenuation).

## Predictive deconvolution in practice

We have learned that a prediction filter predicts periodic events, like multiples, in the seismogram. The prediction error filter yields the unpredictable component of the seismogram — the reflectivity series. For example, consider the simple case of water-bottom multiples. If the reflection coefficient of the water bottom is cw and if water depth is equivalent to a two-way time tw, then the time series is

$\left(1,\ 0,\ \ldots ,\ 0,\ -{{c}_{w}},\ 0,\ \ldots ,\ 0,\ c_{w}^{2},\ 0,\ \ldots ,\ 0,\ -c_{w}^{3},\ 0,\ \ldots\right)$

as represented by trace (b) in Figure 2.4-34. The separation between the spikes is tw in trace (b). Note that the periodicity in the time series (trace (b) or (c)) manifests itself in the amplitude spectrum as periodic peaks (or notches). The greater the spike separation in time, the closer the peaks (or notches) in the amplitude spectrum.

The noise-free convolutional model for the seismogram that contains the water-bottom multiples can be written as

 $x(t)=w(t)\ast m(t)\ast e(t),$ (40)

where m(t) represents the water-layer reverberation spike series as in trace (b) of Figure 2.4-34, and e(t) now represents the earth’s impulse response excluding multiples associated with the water bottom. Predictive deconvolution can suppress the periodic component m(t) in the seismogram as demonstrated by trace (d) in Figure 2.4-3.

Note the two distinct goals for predictive deconvolution: (a) spiking the seismic wavelet w(t), and (b) predicting and attenuating multiples m(t). The first goal is achieved using an operator with unit prediction lag, while the second is achieved using an operator with a prediction lag greater than unity.

The autocorrelation of the input trace can be used to determine the appropriate prediction lag for multiple suppression. Periodicity associated with multiples is evident in the autocorrelogram of trace (c) in Figure 2.4-34, as an isolated series of energy lobes in the neighborhood of 0.2 and 0.4 s. Prediction lag should be chosen to bypass the first part of the autocorrelogram that represents the seismic wavelet. Operator length should be chosen to include the first isolated energy packet in the autocorrelogram. After applying predictive deconvolution, we are left with only the water-bottom primary reflection. Isolated bursts in the autocorrelogram have been suppressed, while periodic peaks in the amplitude spectrum have been eliminated as shown in trace (d). If desired, the basic wavelet can be compressed into a spike as shown in trace (e) by applying spiking deconvolution to the output of predictive deconvolution as shown in trace (d). The sequence can be interchanged by first applying spiking deconvolution as shown in trace (f) followed by predictive deconvolution as shown in trace (g).

Figure 2.4-36  (a) A common-shot gather, (b) after t2–scaling and (c) after muting first arrivals which are largely guided waves, and (d) after spiking deconvolution. The amplitude spectra averaged over the shot record are shown at the top and the autocorrelograms are shown at the bottom.

By using a sufficiently long spiking deconvolution operator, two goals are achieved in one step as seen in trace (h). However, this approach can be dangerous if primary reflections are unintentionally suppressed. This is the case in Figure 2.4-35. Here, the water-bottom reflection is followed by a deeper event at about 0.28 s as seen in trace (a). The impulse response contains water-bottom multiples and the peg-leg multiples that are associated with the deeper reflector as seen in trace (b). The amplitude spectrum has peaks that come in pairs, indicating the presence of two different periodic components in the seismogram. Careful choice of predictive deconvolution parameters yields an output with only the wavelets associated with the water bottom and the deeper reflector as seen in trace (d). This is followed by a spiking deconvolution that yields two spikes representative of the water bottom and the deep primary as seen in trace (e). Spiking deconvolution alone produces the reflection coefficient series and the spikes that represent the multiples as seen in trace (f). If a longer spiking deconvolution operator is used, then the primary reflection easily can be eliminated as in trace (g). If a predictive deconvolution operator is used with an improper parameter choice, then again, the primary reflection can be eliminated easily as in trace (h).

How can we ensure that no primaries are destroyed by deconvolution? Examine the autocorrelogram of trace (c) in Figure 2.4-35. The first 50-ms portion represents the seismic wavelet. This is followed by a burst between 50 to 170 ms that represents the correlation of the water bottom and primary. The isolated burst between 170 to 340 ms represents the actual multiple series (both the peg-legs and water-bottom multiples). The prediction lag must be chosen to bypass the first part of the autocorrelogram, which represents the seismic wavelet and possible correlation between the primaries. The operator length must be chosen to include the first isolated burst, in this case between 170 to 340 ms.

It is only with vertical incidence and zero-offset recording that periodicity of the multiples is preserved. Therefore, predictive deconvolution aimed at multiple suppression may not be entirely effective when applied to nonzero-offset data, such as common-shot or common-midpoint data. Figure 2.4-36a shows a common-shot gather with its autocorrelogram and average amplitude spectrum. The field record is prepared for deconvolution by first applying t2–scaling (Figure 2.4-36b) and muting the first arrivals associated with largely guided waves (Figure 2.4-36c). The autocorrelogram in Figure 2.4-36c indicates the presence of multiples. Note on the shot record the water-bottom reflection is at 0.4 s at near offset. Additionally, there are two strong primary reflectors at 0.6 and 1.4 s at near offset; these primaries give rise to a first-order and peg-leg multiples. Despite the flatness of the spectrum and the attenuation of nonzero lags of the autocorrelogram after deconvolution, the first-order multiples associated with the water-bottom reflection and the peg-leg multiples associated with the primary reflection at 0.6 s still persist in the record (Figures 2.4-36d). This occurs because these events have large moveout which causes significant departure from periodicity at nonzero offsets. On the other hand, note that the peg-leg multiples associated with the primary reflection at 1.4 s have been attenuated significantly by deconvolution. This event has a very small moveout; thus, its perodicity is much preserved.

Predictive deconvolution sometimes is applied to CMP stacked data in an effort to suppress multiples. The performance of such an approach can be unsatisfactory, because the amplitude relationships between multiples often are grossly altered by the stacking process, primarily because of velocity differences between primaries and multiples. Also, geometric spreading compensation by using primary velocity function adversely affects the amplitudes of multiples on nonzero-offset data.

There is one domain in which the periodicity and amplitudes of multiples are preserved — the slant-stack domain. In The slant-stack transform, the application of predictive deconvolution to data in the slant-stack domain for multiple suppression is discussed.