EAGE 68th Conference & Exhibition — Vienna, Austria, 12 - 15 June 2006

B0443D Methodology for OBCPre-ProcessingM.T.A. Soudani* (TOTAL), J.L. Boelle (TOTAL), P. Hugonnet (CGG) & A. Grandi(University of Milan)

SUMMARYIt is more and more observed that OBC PZ images show better quality than thestreamer. This is due to better multiple attenuation, multi-azimuth and high foldcoverage. This leads to a wider bandwidth and a better signal to noise ratio. However,while 3D OBC designs are considered as multi-2D acquisitions, the pre-processing willremain far from the ideals. In the following paper, a fully 3D OBC pre-processingmethodology is presented. This methodology is based on the 3D(τ,p) transform. Due tothe fact that a spatial transform is used, aliasing becomes a real issue. Theinterpolation solution to overcome such a problem is briefly described. Then, thegeneralization of the PZ summation to 3D is discussed and compared to the standard1D approach. Finally, a method for linear noise attenuation is described and itsapplication on a real dataset shown.

Introduction: OBC technology allows the recording of multi-azimuth data thanks to a 3D shot and receiver grid. Generally, the receiver gather domain is well-suited for OBC pre-processing. This is mainly due to the inconsistency from one receiver to another in terms of vector fidelity, coupling and noise coherency. In 3D acquisitions, each receiver is related to a set of shots. This set can be polarized along one direction or regularly sampled in the inline and crossline directions. In the second case, it is possible to apply 3D transforms such as (f,kx,ky) or the 3D(τ,p) transform as far as the Shannon sampling condition is respected. The standard pre-processing algorithms are generally 2D and are applied sail-line by sail-line. Thus, the influence of the crossline offset is neglected. This may lead to errors especially on multiple attenuation algorithms. The use of 3D transforms allows processing with respect to the three dimensions (t,x,y) or (t,r,ψ) where r is the offset and ψ the azimuth. The data shown in this paper are a 3D receiver gather from a wide-azimuth survey acquired with a regular shot grid of (50m x 50m). In the following paragraphs, we will describe the main steps of a 3D pre-processing methodology applied on this gather. Interpolation: According to Shannon’s sampling theory, and in the case of marine data, the spatial grid of (50m x 50m) leads to an aliasing frequency of 15Hz. Thus, it is necessary to interpolate the shots in order to have a finer grid and to shift the aliasing frequency outside the bandwidth of interest. Several interpolation algorithms have been tested. Although the problem is 3D, the best results were provided by the 2D Spitz’ algorithm (Spitz 1991) applied in a 3D context.

Figure 1: Time slice calculated on a 3D receiver gather (a) Before interpolation (b) After

interpolation.

Prediction filters are calculated in the (f,x) and (f,y) domains in order to insert new shots in the inline and crossline directions respectively. After interpolation, the shot grid becomes (12.5m x 12.5m). However, after this step, the direct arrival is still aliased due to its low velocity and its high frequency components and is hence muted for further processing. Figure 1 shows a time slice calculated on the receiver gather at 2s. We see that the interpolation provides good results in terms of event kinematics and amplitude. 3D (τ,p) transform: The 3D linear (τ,p) transform is the 3D extension of the well-known 2D slant stack. It is a plane wave decomposition of the 3D seismic data. This decomposition is obtained by summing the data along axes defined in 3D by the intercept τ and the two slopes px and py. Thus, the data is transformed from the (t,x,y) domain to the (τ, px ,py) thanks to the equation:

( ) ( )∫ ∫+∞

∞−

+∞

∞−−−= dxdyy,x,p.yp.xfp,p,u yxyx ττ (1)

The transformation can also be seen in the cylindrical coordinates (τ, pr ,ψ) where ψ is the azimuth and pr is the radial slope:

( )( )ψψ

sinppcospp

ry

rx

=

= (2)

In the case of 2D propagation in a 1D horizontally stratified medium, the gathers recorded are composed of hyperbolae and transformed to ellipses thanks to the 2D(τ, p) transform. In our 3D case, each reflection on a layer generates a hyperboloid of revolution which is transformed to an ellipsoid thanks to the 3D slant stack. Two of the most important properties of the linear Radon transform concern the periodicity of the multiples and the velocity separation. Indeed, the linear Radon transform is a plane wave decomposition. For each trace in the 3D slant stack domain, the periodicity is preserved, especially for water layer multiples. This period can be estimated from the water depth H, the water velocity Vw and the radial slope pr so that:

( ) rpVV

T22

ww

rtaup 1Hp −= (3)

On the other hand, linear events with low velocities are confined in the high values of p. In the next two paragraphs, we will show how we took advantage of these two properties for water-layer multiple attenuation and linear low-velocity noise removal. 3D PZ summation: Soubaras (1996) developed a 1D three step method to suppress water-layer multiples in OBC data. This method does not require any a priori knowledge of seafloor parameters. Firstly, the vertical geophone is calibrated with a frequency dependent operator by taking the hydrophone as a reference. Then, the summation of the hydrophone and the calibrated geophone is performed in order to separate the upgoing and downgoing wavefields, allowing ghost multiple attenuation. Finally, a reflectivity operator is estimated from the data in order to attenuate remaining peg-leg multiples by performing an adaptive subtraction between upgoing and downgoing wavefields. This three step approach is very effective because it is a data-driven method. However, it assumes a 1D propagation introducing a bias on the amplitudes at far offsets and does not handle the coherent linear noise on the vertical geophone. To overcome these limitations, Soudani et al (2005) generalized the Soubaras method in 2D and developed a new methodology for PZ summation in the (τ,p) domain to take into account the 2D propagation aspects. The generalization of this methodology to 3D is straightforward thanks to equation (3). The new PZ summation version assumes a full 3D propagation of the wavefield and attenuates the water layer multiples with respect to the offset and azimuth. However, the complexity of the algorithm becomes O(N2) and we face here a huge amount of data for each receiver gather in the 3D(τ,p) domain. It is no longer possible to compute the operators for each value of the pair (px,py) separately. One way to overcome this difficulty is to split the 3D(τ,p) gathers into sub-cubes. Each sub-cube is defined by four traces that correspond to four reference operators. Then, operators within the sub-cube are expressed with respect to the four reference operators according to equation (4):

4ref3ref2ref1refop )j,i()j,i()j,i()j,i()j,i( λγβα +++= (4) where i,j are the coordinates of the trace within the sub-cube, α, β, γ and λ are weighting functions and ref1, ref2, ref3 and ref4 are the four reference operators. The complexity of the algorithm becomes O((N/M)*(N/L)) where M and L are the number of traces per sub-cube in each direction.

(a) (b) (c) (d)

Figure 2: Crossline just above the receiver. (a) hydrophone, (b) vertical geophone, (c) PZ processed with the 1D approach, (d) PZ processed with the new 3D approach.

Figure 2 shows the initial hydrophone and vertical geophone both in the crossline direction after incoherent noise removal. The 3D PZ summation shows better results with less remaining multiples in comparison with the classical 1D approach. 3D linear noise attenuation: One of the most important issues in OBC processing is the linear noise that we observe on the receiver gather domain and which is no longer coherent in the shot domain. This linear noise generally affects the vertical geophone. Thus, due to the PZ combination, this noise is introduced in the PZ section after water layer multiple attenuation. This noise can be seen in 3D as a cone with a move out of about 1600-1800m/s. When we observe the data generated from a sail-line just above the receiver, this noise appears linear. However, when we analyze the gather from a displaced sail-line, this noise starts to be hyperbolic. This noise can be modelled as the intersection between a cone and a vertical plane. Up to now, the standard processing methodologies were processing the gathers sail-line by sail-line ignoring the crossline offset. After 3D(τ,p) transform, the linear events with low velocity are moved to the high values of pr . Thus, by applying a mute in the 3D(τ,p) domain, we can get rid of this noise. Figure 3 shows a receiver gather before and after linear noise attenuation as well as the removed noise on a sail-line just above the receiver and on a displaced sail-line. These figures illustrate how the noise moves from linear to hyperbolic with respect to the crossline offset. Conclusions: We have shown in this paper the key points of a new fully 3D pre-processing workflow for OBC data. This work is motivated by the desire to take advantage of the azimuth dimension. We have shown that the 3D(τ,p) domain is well suited for water layer multiple attenuation and linear noise removal. Our 2D approach of PZ summation that attenuates both source side and receiver side multiples has been successfully extended to 3D. Finally, the linear noise has been removed from the receiver gather improving drastically the final result. More comparisons with standard processing methodologies will be shown during the presentation. Acknowledgments The authors thank TOTAL for permission to show this work.

Crossline offset=0m

PZ gather before noise attenuation

(a)

PZ gather after noise attenuation

(b)

Attenuated noise (a)-(b)

(c)

Crossline offset=1700m

PZ gather before noise attenuation

(d)

PZ gather after noise attenuation

(e)

Attenuated noise (d)-(e)

(f)

Figure 3: Linear noise attenuation for two different crossline offsets (0m and 1700m)

References: Barr, F. J. and Sanders, J. I., 1989, Attenuation of water-column reverberations using pressure and velocity detectors in a water-bottom cable, 59th Ann. Internat. Mtg: Soc. of Expl. Geophys. Spitz, S., 1991, Seismic trace interpolation in the F-X domain: GEOPHYSICS, Soc. of Expl. Geophys., 56, 785-794. Soubaras, R., 1996, Ocean bottom hydrophone and geophone processing, 66th Ann. Internat. Mtg: Soc. of Expl. Geophys. Soudani, M.T.A., Boelle, J.L. and Mars, J., 2005, New methodology for water-layer multiple attenuation, , 67th Mtg.: Eur. Assn. Geosci. Eng.