Shock profile analysis using wavelet transform

We study the fine structure of the collisionless shock front, paying particular attention to the large gradients and internal structure within the ramp and to quasiperiodic structures in the ramp vicinity. In order to separate random steep gradients with low amplitudes from steep large-amplitude formations, we apply Gaussian wavelet transforms suitable for this task. We analyze several high Mach number shocks and show that ramp substructure is not uncommon and that the typical scales of the steepest gradient features are significantly smaller than the shock transition width (provided they are stationary in the shock frame). We apply the Morlet wavelet transform to the magnetic field data in order to identify quasiperiodic patterns which may last only several periods. It is likely that short quasiperiodic wave trains dominate in the wave activity. Such wave trains are not always associated with the ramp itself.