Discrete representations for Marchenko imaging of imperfectly sampled data

Marchenko imaging is based on integral representations for focusing functions and Green's functions. In practice, the integrals are replaced by finite summations. This works well for regularly sampled data, but the quality of the results degrades in a case of imperfect sampling. We have developed discrete representations that account for imperfect sampling of the sources (or, via reciprocity, of the receivers). These representations contain point-spread functions that explain the blurring of the focusing functions and Green's functions due to imperfect sampling. Deblurring the focusing functions and Green's functions involves multidimensional deconvolution for the point-spread functions. The discrete representations form the basis for modifying Marchenko imaging to account for imperfectly sampled data, which is important for field data applications.