Conventional marine acquisition uses a streamer towed at a constant depth. The resulting receiver ghost notch gives the maximum recoverable frequency. To push this limit, the streamer must be towed at a quite shallow depth, but this compromises the low frequencies. Variable-depth streamer (VDS) acquisition is an acquisition technique aimed at achieving the best possible signal-to-noise ratio at low frequencies by towing the streamer very deeply, but by using a depth profile varying with offset in order not to limit the high-frequency bandwidth by notches as in conventional constant-depth streamer acquisition. The idea is to use notch diversity, each receiver having a different notch, so that the final result, combining different receivers, will have no notches. The key step to process VDS acquisitions is the receiver deghosting. We found that the optimal receiver deghosting, instead of being a preprocessing step, should be done postimaging, by using a dual-input, migration and mirror migration, and a new joint deconvolution algorithm that produces a 3D real amplitude deghosted output. This method can be applied poststack, the inputs being the migration and mirror migration images and the output being the deghosted image. Using a multichannel joint deconvolution, the inputs are the migrated and mirror migrated image gathers and the outputs are the prestack deghosted image gathers. This method preserves the amplitude-versus-offset behavior, as the deghosted output can be seen on synthetic examples to be equal to a reference computed by migrating the data modeled without any reflecting water surface. A real data set was used to illustrate this method, and another one was used to check the possibility of performing prestack elastic inversion on the deghosted gathers.

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