High-melt areas of glaciers and ice sheets foster a rich spectrum of ambient seismicity. These signals not only shed light on source mechanisms (e.g. englacial fracturing, water flow, iceberg detachment, basal motion) but also carry information about seismic wave propagation within glacier ice. Here, we present two approaches to measure and potentially monitor phase velocities of high-frequency seismic waves (≥1 Hz) using naturally occurring glacier seismicity. These two approaches were developed for data recorded by on-ice seasonal seismic networks on the Greenland Ice Sheet and a Swiss Alpine glacier. The Greenland data set consists of continuous seismograms, dominated by long-term tremor-like signals of englacial water flow, whereas the Alpine data were collected in triggered mode producing 1-2 s long records that include fracture events within the ice (‘icequakes'). We use a matched-field processing technique to retrieve frequency-dependent phase velocity measurements for the Greenland data. In principle, this phase dispersion relationship can be inverted for ice sheet thickness and bed properties. For these Greenland data, inversion of the dispersion curve yields a bedrock depth of 541 m, which may be too small by as much as 35 per cent. We suggest that the discrepancy is due to lateral changes in ice sheet depth and bed properties beneath the network, which may cause unaccounted mixing of surface wave modes in the dispersion curve. The Swiss Alpine icequake records, on the other hand, allow for reconstruction of the impulse response between two seismometers. The direct and scattered wave fields from the vast numbers of icequake records (tens of thousands per month) can be used to measure small changes in englacial velocities and thus monitor structural changes within the ice
