Iterative Deblending With Multiple Constraints Based on Shaping Regularization

It has been previously shown that blended simultaneous-source data can be successfully separated using an iterative seislet thresholding algorithm. In this letter, I combine iterative seislet thresholding with a local orthogonalization technique via a shaping regularization framework. During the iterations, the deblended data and its blending noise section are not orthogonal to each other, indicating that the noise section contains significant coherent useful energy. Although the leakage of useful energy can be retrieved by updating the deblended data from the data misfit during many iterations, I propose to accelerate the retrieval of the leakage energy using iterative orthogonalization. It is the first time that multiple constraints are applied in an underdetermined deblending problem, and the new proposed framework can overcome the drawback of a low-dimensionality constraint in a traditional 2-D deblending problem. Simulated synthetic and field data examples show the superior performance of the proposed approach.