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We present and evaluate the prospects for detecting coherent radio counterparts to gravitational wave (GW) events using Murchison Widefield Array (MWA) triggered observations. The MWA rapid-response system, combined with its buffering mode (
$\sim$4 min negative latency), enables us to catch any radio signals produced from seconds prior to hours after a binary neutron star (BNS) merger. The large field of view of the MWA (
$\sim$
$1\,000\,\textrm{deg}^2$ at 120 MHz) and its location under the high sensitivity sky region of the LIGO-Virgo-KAGRA (LVK) detector network, forecast a high chance of being on-target for a GW event. We consider three observing configurations for the MWA to follow up GW BNS merger events, including a single dipole per tile, the full array, and four sub-arrays. We then perform a population synthesis of BNS systems to predict the radio detectable fraction of GW events using these configurations. We find that the configuration with four sub-arrays is the best compromise between sky coverage and sensitivity as it is capable of placing meaningful constraints on the radio emission from 12.6% of GW BNS detections. Based on the timescales of four BNS merger coherent radio emission models, we propose an observing strategy that involves triggering the buffering mode to target coherent signals emitted prior to, during or shortly following the merger, which is then followed by continued recording for up to three hours to target later time post-merger emission. We expect MWA to trigger on 
$\sim$
$5-22$ BNS merger events during the LVK O4 observing run, which could potentially result in two detections of predicted coherent emission.
We recently reported on the radio-frequency attenuation length of cold polar ice at Summit Station, Greenland, based on bi-static radar measurements of radio-frequency bedrock echo strengths taken during the summer of 2021. Those data also allow studies of (a) the relative contributions of coherent (such as discrete internal conducting layers with sub-centimeter transverse scale) vs incoherent (e.g. bulk volumetric) scattering, (b) the magnitude of internal layer reflection coefficients, (c) limits on signal propagation velocity asymmetries (‘birefringence’) and (d) limits on signal dispersion in-ice over a bandwidth of ~100 MHz. We find that (1) attenuation lengths approach 1 km in our band, (2) after averaging 10 000 echo triggers, reflected signals observable over the thermal floor (to depths of ~1500 m) are consistent with being entirely coherent, (3) internal layer reflectivities are ≈–60$\to$
–70 dB, (4) birefringent effects for vertically propagating signals are smaller by an order of magnitude relative to South Pole and (5) within our experimental limits, glacial ice is non-dispersive over the frequency band relevant for neutrino detection experiments.
