General Treatment of Reflection of Spherical Electromagnetic Waves from Spherical, Uneven Antarctic Surface and Its Implications for the Mystery Events Detected by ANITA

We develop a general formalism to study the reflection of radio waves, generated by ultra high energy cosmic ray events, from the Antarctic ice surface. Our formalism is based on plane wave decomposition of spherical waves and is applicable to the observations made by the ANITA detector. We find that our numerical result shows good agreement with the calibration data obtained by the High-Altitude Calibration (HiCal) experiment. ce features such as the local sastrugi. We incorporate these roughness models to investigate whether the non-uniform surface roughness of Antarctica can explain these anomalous events.