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An acquisition footprint is noise in 3D seismic data thatshould be removed prior to interpretation. This paper pre-sents an adaptation of the standard truncated singular valuedecomposition (TSVD) algorithm that is not only capableof removing random noise, but is actually a very powerfultool for suppressing acquisition footprint artifacts in seis-mic data.

An acquisition footprint is the result of suboptimal spa-tial sampling. Atypical footprint appears as a linear spatialgrid pattern of noise that can be seen on 3D seismic timeslices or horizon amplitude maps. These patterns, mostoften observed on shallow time slices, tend to mirror theacquisition geometry and correlate with the geometric dis-tribution of sources and receivers on the acquisition surface.Surveys acquired using sparse 3D acquisition geometriesshow these patterns very clearly (Figure 1). This type of noiseintroduces a periodic modulation in amplitude values and

affects the lateral continuity of seismic events. Therefore, itis highly desirable to minimize this contamination prior tointerpretation.

There are three main techniques used to reduce the gen-eration of acquisition footprints: (1) acquisition geometrieswhich produce a minimal variation of the bin-to-bin popu-lation of trace offsets; (2) via prestack processes which min-imize the offset-related amplitude differences among tracesprior to stacking; and (3) using poststack processes such asmixing,f-k, and Kx-Ky filtering.

The truncated SVD procedure. Singular value decomposi-tion (SVD) is a well-known and documented technique usedin digital signal processing for random and coherent noiseattenuation. The basic idea is that a seismic wavefield con-

taining both signal and noise can be represented as a matrixA of N traces with T sample points per trace. This matrixcan then be decomposed using the SVD into eigenimagesthat separate the wavefield into its different components

based on energetic criteria. Any eigenimages representingthe noise can then be excluded in the reconstruction of thewavefield.

The TSVD procedure is a variation using four steps inthe standard rank-reduction algorithm. It uses Hankel matrixtheory combined with SVD and can be summarized as fol-lows:

1. Form a Hankel matrix from the input signal.2. Compute the SVD for this matrix.

3. Obtain a reduced-rank matrix by dropping the insignif-icant singular values.4. Construct the output signal from this matrix after aver-

aging along its antidiagonals.

The following real data examples demonstrate the per-formance of the TSVD algorithm in attenuating randomnoise and acquisition footprint. The application is done inthe time slice domain and in a cascaded multidirectionalmanner. Figure 2 illustrates how the methodology works.The selection of eigenimages for the reconstruction of thewavefield after each TSVD iteration is designed so that bothrandom and acquisition footprint noise are suppressed.

Case studies from Saudi Arabia. The data acquired fromvarious areas in the Saudi Arabian peninsula include dif-ferent types of acquisition geometry. In all time slices shownthe scale in x and y is 1:1. A time slice from a 3D survey withsevere acquisition footprint is shown in Figure 3 before andafter the application of the TSVD algorithm. Note the con-siderable reduction of the footprint while the data charac-ter has been retained. Figure 4 illustrates the ability of theTSVD technique to remove random noise using a crosslinefrom a 3D survey. A considerable improvement in signal to

noise ratio can be observed after the application of the TSVDalgorithm.Figure 5 shows an inline from a survey acquired using

sparse 3D acquisition techniques. These are designed tocover large land areas (thousands of square-kilometers) rel-atively quickly and at a reduced cost to the exploration pro-gram. This acquisition design is characterized by largereceiver and shot line spacing combined with relatively lownominal fold. The tradeoff inherent in this type of surveydesign is a less than optimum bin-to-bin offset distribution,less noise cancellation, and a strong acquisition footprint asis evident in this example. The application of the TSVD-

based approach has clearly attenuated the acquisition foot-print and random noise and significantly improved the

Acquisition footprint suppression via the truncated SVD technique:Case studies from Saudi Arabia

MUHAMMADS. AL-BANNAGI, KENFANG, PANOSG. KELAMIS, and GREGS. DOUGLASS, Saudi Aramco, Dhahran, Saudi Arabia

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Figure 1. Time slice exhibiting a strong acquisition footprint and its Kx-Kytransform.

Figure 2. Schematic flow of the cascaded, multidirectional application ofTSVD on time slices.

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event continuity.Figure 6 depicts a zoom of the shallow part of the 3D

inline shown in Figure 5. The curve in the upper part of bothimages is the seismic amplitude of the picked horizon. Theperiodic, high-frequency modulation in amplitude seen onthe top image is a common characteristic of the acquisitionfootprint. The bottom image shows that application of theTSVD technique greatly reduces this amplitude modulationwhile preserving the relative spatial character.

Application of the TSVD algorithm using the new

methodology results in cleaner, more continuous data andis expected to have a positive impact on other attributes suchas coherency, spectral decomposition, and lithology classi-fication. Figure 7 shows three different shallow time slicesof coherency volumes. The original data are shown on theleft and the new TSVD-filtered data are shown on the right.The TSVD method removes much of the acquisition foot-

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Figure 4. Input 3D crossline (top) and after the application of the TSVDalgorithm (bottom).

Figure 5. Input 3D inline (top) and after the application of the TSVDalgorithm (bottom).

Figure 6. Zoom of Figure 5. The horizon amplitude plot above the seismicdata shows the high-frequency amplitude modulation commonly seen indata with a strong acquisition footprint (top). The TSVD (bottom) hassignificantly suppressed this modulation while preserving the relativespatial amplitude.

Figure 3. Input time slice at 320 ms (top) and after the application of theTSVD algorithm (bottom).

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print/noise and thus results in much cleaner time sliceswhich reveal karst and channel edges.

Conclusions. The TSVD algorithm, applied in a cascadedmultidirectional manner in the time slice domain, attenu-ates both acquisition footprint and random noise in 3D seis-mic data while maintaining the data character. Applicationresults of the new technique using different 3D datasets arevery promising and can significantly impact structural andstratigraphic interpretation.

Suggested reading. Acquisition footprintits detection andremoval by Chopra and Larsen (CSEG Recorder, 2000). FIRfilter representations of reduced-rank noise reduction by

Hansen and Jensen (IEEE Signal Processing, 1998). Acquisitionfootprint and fold-of-stack plots by Hill et al. (TLE, 1999).Signal-to-noise ratio enhancement in multichannel seismicdata via the Karhunen-Loeve transform by Jones and Levy(Geophysical Prospecting, 1987). Attenuation of acquisition foot-print for non-orthogonal 3D geometries by Soubaras (EAGE2002, Expanded Abstracts). F-XYeigenimage noise suppression

by Trickett (GEOPHYSICS, 2003). TLE

Acknowledgments: The authors wish to thank the Saudi Arabian OilCompany for encouraging this work and for granting permission to pub-lish this paper.

Corresponding author: Panos Kelamis, panos.kelamis@aramco.com

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Figure 7. Time slices ofcoherency at 332, 400 and524 ms before (left) andafter (right) the applica-tion of the TSVD algo-rithm.