Marchenko imaging by unidimensional deconvolution

Obtaining an accurate image of the subsurface still remains a great challenge for the seismic method. Migration algorithms aim mainly on positioning seismic events in complex geological contexts. Multiple reflections are typically not accounted for in this process, which can lead to the emergence of artefacts. In Marchenko imaging, we retrieve the complete up- and downgoing wavefields in the subsurface to construct an image without such artefacts. The quality of this image depends on the type of imaging condition that is applied. In this paper, we propose an imaging condition that is based on stabilized unidimensional deconvolution. This condition is computationally much cheaper than multidimensional deconvolution, which has been proposed for Marchenko imaging earlier. Two specific approaches are considered. In the first approach, we use the full up- and downgoing wavefields for deconvolution. Although this leads to balanced and relatively accurate amplitudes, the crosstalk is not completely removed. The second approach is to incorporate the initial focussing function in the deconvolution process, in such a way that the retrieval of crosstalk is avoided. We compare images with the results of the classical cross-correlation imaging condition, which we apply to reverse-time migrated wavefields and to the up- and downgoing wavefields that are retrieved by the Marchenko method.