Recent papers show that imaging with the retrieved Green’s function constructed by the Marchenko equations, called Marchenko imaging, reduces artifacts from internal and free-surface multiples compared with standard imaging techniques. Even though artifacts are reduced, they can still be present in the image, depending on the imaging condition used. We have found that when imaging with the up- and downgoing Green’s functions, the multidimensional deconvolution (MDD) imaging condition yields better images than correlation and deconvolution. “Better” in this case means improved resolution, fewer artifacts, and a closer match with the true reflection coefficient of the model. We have determined that the MDD imaging condition only uses primaries to construct the image, whereas multiples are implicitly subtracted in the imaging step. Consequently, combining the first arrival of the downgoing Green’s function with the complete upgoing Green’s function produces superior (or at least equivalent) images than using the one-way Green’s functions because the first arrival of the downgoing Green’s function excludes all the downgoing multiply reflected waves. We also find that standard imaging algorithms which use the redatumed reflection response, constructed with the one-way Green’s functions, produce images with reduced artifacts from multiples compared with standard imaging conditions, which use surface reflection data. All imaging methods that rely on the Marchenko equations require the same inputs as standard imaging techniques: the reflection response at the surface and a smooth estimate of the subsurface velocities.
Microscopic Calculation of Josephson Current in Tunnel Junctions with Two-Gap Superconductors
