On the estimation of the ratio of ULF wave electric fields in space and the magnetic fields at the ground.

Abstract Three new methods for estimating a ratio of the ultra-low frequency (ULF; 1–100 mHz) wave equatorial electric field amplitude in the Earth’s magnetosphere to ground magnetic field amplitudes for field line resonances are described. These methods use ratios of the time series extrema, ratios of the envelope waveform and the ratio of the spectral amplitude at the field line resonance frequency. These methods were applied to four ULF resonance intervals; three detected by the Van Allen Probe A spacecraft and one detected by the POLAR spacecraft. The intervals were conjoined with the CARISMA and IMAGE ground magnetometer arrays. The spectral ratio results for the Van Allen Probe intervals were approximately twice to three times the ratios estimated from the two time series based methods. The POLAR interval showed similar values across all three methods. The differences are attributed to broad-band frequency signals that modify the time series amplitudes, while the spectral method avoids these off-resonant frequencies. Based on the results of this study, a spectral based method for calculating the ratio at the field line resonance frequency is best.