Method for improved processing of data with time overlapping recordings of energy sources

A method for seismic surveying, comprising:

• actuating at least one seismic energy source;
• recording signals generated by at least one seismic sensor in response to the actuating, the actuating performed such that energy from different actuations of the at least one source is present in the recorded signals;
• (a) entering the recorded signals as input to a computer;
• (b) in the computer, initializing a model of deblended seismic data and initializing a blending matrix, the model comprising a plurality of seismic signals each having energy corresponding to only one of the plurality of actuations, the blending matrix comprising times of each of the plurality of actuations;
• (c) in the computer, initializing a blended output as a product of the blending matrix and the model;
• (d) in the computer, calculating a residual as a difference between the blended output and the input recorded signals;
• (e) in the computer, transforming the model into a thresholding domain and applying a thresholding function only to the transformed model to generate a deblended portion, the deblended portion comprising a plurality of seismic signals each having energy corresponding to only one of the plurality of actuations;
• (f) in the computer, inverse transforming the deblended portion to generate a thresholded model;
• (g) in the computer, applying the blending matrix to the thresholded model to generate an updated blended output;
• (h) determining whether a difference between the updated blended output and the recorded signals falls below a selected limit, wherein the selected limit is related to a scaled objective function, a scale factor for the scaled objective function related to a number of the plurality of actuations;
• and
• when the difference exceeds the selected limit, in the computer, adding the thresholded model to a back-projected residual comprising a product of the residual and a complex conjugate transpose of the blending matrix to generated an updated model, in the computer, replacing the model at (b) with the updated model and repeating (d) through (h);
• and
• when the selected difference is below the limit, in the computer, at least one of storing and displaying the updated model as a final output, the final output comprising for at least one of the plurality of actuations a plurality of seismic signal sets each having energy corresponding to only one of the plurality of actuations.