Joint imaging with streamer and ocean bottom data

Joint Inversion

A joint inversion is performed in a least-squares sense with the objective goal described in equation 3. Panel (c) of Figure 5 shows the image after joint inversion. Notice that the joint image is better than the streamer inversion image around the platform area (x=3950-4000 m), as shown in (c) and (a) of Figure 6, respectively. Moreover, the joint image is better than the OBN inversion image for the dipping reflectors, as shown in (b) and (c) of Figure 7.

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Figure 5. (a) The inverted streamer image, (b) the inverted OBN image, (c) the jointly inverted image, and (d) the reflectivity model. Notice the joint image coherently combines the information between the individually inverted images.

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Figure 6. A zoomed section from x=3000-5000 m and z=50-750 m among (a) the streamer inversion image and (b) the OBN inversion image, (c) the joint inversion image and (d) the reflectivity model. The platform is located at horizontal position of x=3950-4000 m. In this region, most of the useful information comes from the OBN mirror data. The joint image is able to attenuate but cannot completely remove the spurious artifact caused by residual up-going energy in the OBN mirror signal.

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Figure 7. A zoomed section from x=4500-6500 m and z=1300-2000 m among (a) the streamer inversion image, (b) the OBN inversion image, (c) the joint inversion image and (d) the reflectivity model. Although the streamer image looks noisy, joint inversion can properly include the dipping reflector from the streamer image to produce a better joint image.

In our example, the joint image is able to attenuate, but cannot completely remove the spurious artifact caused by residual up-going energy in the OBN mirror signal. One reason for this is that the streamer data are not well illuminated in that area. Figure 8 compares the energy between the synthetic observed, the forward-modeled, and the residual data for one common-receiver gather in the OBN survey. The forward-modeled data is generated by applying $L_{OBN\downarrow}$ to the final inverted model $m$ after 30 iterations. We can see that most of the energy in the synthetic observed data is explained by the forward-modeled data. Also, notice that the relative amplitude of the residual up-going energy (near 2.3 sec) becomes higher.

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Figure 8. (a) The synthetic observed data, (b) the forward-modeled data, and (c) the data residual for one common receiver gather in the OBN survey. All data are clipped at the same bound. Notice that the relative amplitude of the residual up-going energy becomes higher in the data residual. By incorporating more data to produce a single model, joint inversion can help discrimminate between signal and noise in the data.

Joint imaging with streamer and ocean bottom data