In conventional seismic surveys, there is a waiting time between sequentially fired shots. This time is determined such that the deepest reflection of interest is recorded before the following source is fired. In a survey with simultaneous or blended sources, the waiting time between the firing of shots is not dependent on the deepest reflection of interest, it is usually much shorter and/or can have random time delays. Thus, the wavefields due to independent sources are overlapped in the records.

The blended data exhibit strong discontinuities in the source direction, in contrast to the coherency expected from seismic measurements. A strategy for deblending could then be to suppress these discontinuities. In this paper, we propose to do this by designing an energy functional that uses a combination of individual functionals that penalize deviations from local plane waves in the reconstructed (deblended) data, as well as a least squares term that penalizes discrepancies between the deblended and the measured data. In this way, we derive a set of coupled nonlinear partial differential equations that we use for the deblending procedure.