RTM generates seismic images of high quality. However, it requires solving for forward and backward wavefields and then the stacking of the cross-correlated images over the shots. This results in a very expensive computational cost. Shot encoding schemes were introduced as an attempt to reduce that cost: they combine different shot records and process them together instead of individually. Even if the cost reduction can be up to 10 folds, the final stacked image with an encoding scheme has inevitable crosstalk noise when compared to the conventional RTM. In this work, we propose a new wavefield reconstruction method by using the encoded wavefields as a measurement and recovering the non-encoded wavefields resulting from individual shots. The problem is formulated as either a sparse recovery problem or a L2 norm minimization problem. For the sparse recovery problem, the curvelet transform or the discrete cosine transform were employed to project wavefields to corresponding basis and the resulting undetermined linear problem was solved with the SPGL1 algorithm. In the case of the l2 minimization problem, a limited-memory BFGS algorithm was employed to solve the recovery problem in the original domain. Preliminary results indicate our method is able to reduce then cross-talk noise significantly.


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