Systems and methods for focused blind deconvolution

A method comprising:

• determining a cross-correlation of each pair of signals of a plurality of signals;
• obtaining a cross-correlation of response functions corresponding to each pair of signals based on the cross-correlations of the pairs of signals and subject to a first constraint that the response functions are maximally white;
• and
• obtaining the response functions based on the cross-correlations of the response functions and subject to a second constraint that the response functions are maximally front-loaded.

At least one non-transitory computer-readable storage medium storing processor executable instructions that, when executed by at least one hardware processor, cause the at least one hardware processor to perform a method comprising:

• determining a cross-correlation of a first signal and a second signal;
• obtaining a cross-correlation of a first response function and a second response function based on the cross-correlation of the first and second signals and subject to a first constraint that the first and second response functions are maximally white;
• and
• obtaining the first and second response functions based on the cross-correlation of the first and second response functions and subject to a second constraint that the first and second response functions are maximally front-loaded.

A drilling system comprising:

• a tool configured to be positioned on a drill string;
• a first sensor positioned along the drill string and configured to detect a first signal;
• a second sensor positioned along the drill string and spaced from the first sensor, the second sensor configured to detect a second signal;
• and
• a controller comprising:
• at least one hardware processor, and
• at least one non-transitory computer-readable storage medium storing processor executable instructions that, when executed by at least one hardware processor, cause the at least one hardware processor to perform a method comprising:
• determining a cross-correlation of a first signal and a second signal,
• obtaining a cross-correlation of a first response function and a second response function based on the cross-correlation of the first and second signals and subject to a first constraint that the first and second response functions are maximally white,
• obtaining the first and second response functions based on the cross-correlation of the first and second response functions and subject to a second constraint that the first and second response functions are maximally front-loaded, and
• controlling the tool based on the first and second response functions.