This article summarizes salient points one must know about seismic airgun arrays to discuss seriously how they might affect marine life. It is by no means exhaustive but tries to be thorough enough without being too involved to deter the general reader.
The surface multiple attenuation algorithm discussed in this paper is a prestack inversion of a surface‐recorded, 2-D wavefield that aims to remove all orders of all surface multiples present within the wavefield. Although the algorithm requires no assumptions or modeling regarding the positions and reflection coefficients of the multiple‐causing reflectors, it does require complete internal physical consistency between primary and multiple events—something that exists only in ideal 2-D data sets. In field data sets the physical consistency between primaries and multiples is disturbed by phenomena such as variations in the acquisition wavelet, cable feathering, cross‐line dip, a finite near offset, and unequal or too coarse spatial sampling in source and receiver coordinates. Careful survey design can minimize the impact of those phenomena on surface multiple attenuation. If it is not too large, trace extrapolation can solve the finite near‐offset problem. Minor adjustments to the algorithm allow processing of data for which the source and receiver intervals differ by an integer multiple, although for those and other acquisition geometries, trace interpolation may be preferred. In the f-x domain, surface multiple attenuation can be formulated as an equation whose straightforward solution involves the inversion of a large matrix that is a function of the acquisition wavelet. Since that wavelet is generally unknown, solving this matrix equation becomes an optimization problem. Many matrix inversions are needed to estimate the acquisition wavelet that leads to the best multiple suppression, rendering the straightforward solution to the surface multiple attenuation equation quite costly. We offer two alternative approaches. In our first approach we compute an eigenvalue decomposition of the large matrix, allowing the equation to be recast so that the wavelet dependency appears in a diagonal matrix for which repetitive inversion is trivial. In our second approach we begin by using the surface multiple attenuation algorithm with a fixed, approximately correct wavelet to compute the surface multiple wavefield. We then filter the predicted multiples adaptively to match the actual multiples in the original wavefield and subtract these filtered multiples from the original wavefield. The second approach is relatively inexpensive and to some extent can cope with physical inconsistencies between primaries and multiples caused by field data set imperfections.
Marine seismic data acquired with a moving vibrator suffer phase dispersion caused by Doppler shifting of the source sweep function. The dispersion for a particular reflection event depends upon frequency, the type of sweep function, and the Doppler factor associated with that event. Synthetic vibrator data show that, at typical ship speeds, the Doppler factors for steeply dipping events are big enough to cause phase dispersion as large as several hundred degrees. If unaccounted for, such dispersive effects could make a moving marine vibrator unacceptable for imaging steep dips. In a constant‐offset section, the Doppler factor for a reflection event is the product of ship speed and the event’s time dip. That key, simple relationship allows a two‐dimensional f-k filter to remove the phase dispersion caused by the Doppler effect. Comparisons of both synthetic data and Gulf of Mexico field data, before and after application of the phase‐correcting filter, show that the filter improves steep‐dip imaging in marine vibrator data. For the Gulf of Mexico line, steep dips are imaged just as well in the phase‐corrected vibrator data as in air‐gun data.
Prediction methods for seismic multiples are never ideal in practice and an adaptive subtraction process is needed to account for mismatches between the predicted and the actual multiples. We are interested in the problem of separating primary and multiple seismic signals based on their statistical properties. We link recent advances in the blind-source separation problem to the multiple removal problem, and present a novel adaptive subtraction method based on an information maximization principle. Compared with previous methods, our proposed method uses higher-order statistics of the data and incorporates the filtering nature of the adaptive subtraction problem into our algorithm formulation. We use simulations to show that our proposed adaptive subtraction method outperforms the popular least-squares adaptive subtraction and the independent component analysis methods quantitatively, as measured by the mean-squared error, and qualitatively, as evaluated by the visual quality of the image reconstruction.
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