Ambient noise seismology has revolutionized seismic characterization of the Earth's crust from local to global scales. The estimate of Green's function (GF) between two receivers, representing the impulse response of elastic media, can be reconstructed via cross-correlation of the ambient noise seismograms. A homogenized wave field illuminating the propagation medium in all directions is a prerequisite for obtaining an accurate GF. For seismic data recorded on glaciers, this condition imposes strong limitations on GF convergence because of minimal seismic scattering in homogeneous ice and limitations in network coverage. We address this difficulty by investigating three patterns of seismic wave fields: a favorable distribution of icequakes and noise sources recorded on a dense array of 98 sensors on Glacier d'Argentière (France), a dominant noise source constituted by a moulin within a smaller seismic array on the Greenland Ice Sheet, and crevasse-generated scattering at Gornergletscher (Switzerland). In Glacier d'Argentière, surface melt routing through englacial channels produces turbulent water flow, creating sustained ambient seismic sources and thus favorable conditions for GF estimates. Analysis of the cross-correlation functions reveals non-equally distributed noise sources outside and within the recording network. The dense sampling of sensors allows for spatial averaging and accurate GF estimates when stacked on lines of receivers. The averaged GFs contain high-frequency (>30 Hz) direct and refracted P waves in addition to the fundamental mode of dispersive Rayleigh waves above 1 Hz. From seismic velocity measurements, we invert bed properties and depth profiles and map seismic anisotropy, which is likely introduced by crevassing. In Greenland, we employ an advanced preprocessing scheme which includes match-field processing and eigenspectral equalization of the cross spectra to remove the moulin source signature and reduce the effect of inhomogeneous wave fields on the GFs. At Gornergletscher, cross-correlations of icequake coda waves show evidence for homogenized incident directions of the scattered wave field. Optimization of coda correlation windows via a Bayesian inversion based on the GF cross coherency and symmetry further promotes the GF estimate convergence. This study presents new processing schemes on suitable array geometries for passive seismic imaging and monitoring of glaciers and ice sheets.