3-D Results

We apply PS-AMO regularization to a portion of a real OBS data set recorded above the Alba oil field. The Alba oil field is located in the UK North Sea and elongates along a NW-SE axis. The oil reservoir is 9 km long, 1.5 km wide, and up to 90 m thick at a depth of 1,900 m subsea Newton and Flanagan (1993).

The 3-D OBS data set has been already preprocessed and separated into a PP and a PS section. This paper focus on the PS section only. The subset of the data set consists of 250 inline CMPs, 50 crossline CMPs, 200 inline half-offset, and 40 crossline half-offset.

Figure  presents the spatial distribution for the shots on the left, and receivers on the right. Observe the gap in the shot distribution due to the platform. Additionally, Figure  shows the distribution of the CMPs on the left, and the offsets on the right. Note that the main goal of this experiment is to collapse the crossline offset into zero crossline offset. Figure  shows the data, for a particular inline offset, at zero crossline offset. Observe the sparsity of the data and the small number of live traces.

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Figure 2 Source (a) and receiver (b) distribution for the fraction of OBS data set in study.

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Figure 3 CMPs (a) and half-offset (b) distribution for the fraction of OBS data set in study.

 

data Figure 4 Real data problem, data for zero crossline offset, the missing data is obvious.

Figure  presents the main result of this paper. It compares the real data at zero crossline offset, the result of pure stacking all the crossline offsets, and the result of partial stacking the crossline offsets with the PS-AMO operator. The sections for all the cubes are taken at the same position. Note that by just stacking there are still holes in the data. This is not the case after running partial stacking with the PS-AMO operator.

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Figure 5 Result of partial stacking with PS-AMO. (a) Real data at zero crossline offset. (b) Result of simple stacking all the crossline offsets into zero crossline offset. (c) Result of running PS-AMO to collide all the crossline offsets into zero crossline offset.

Additionally, Figure  presents the partial stacking with PS-AMO with and without the normalization. Note that by approximating the Hessian of the PS-AMO transformation using equation 12, we are able to balance the energy of the traces after normalization.

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Figure 6 Result of PS-AMO reduction. (a) Unnormalized PS-AMO reduction. (b) Normalized PS-AMO reduction.