  Electromagnetic ion cyclotron (EMIC) waves lead to rapid scattering of
relativistic electrons in Earth's radiation belts, due to their large
amplitudes relative to other waves that interact with electrons of this energy
range. A central feature of electron precipitation driven by EMIC waves is
deeply elusive. That is, moderate precipitating fluxes at energies below the
minimum resonance energy of EMIC waves occur concurrently with strong
precipitating fluxes at resonance energies in low-altitude spacecraft
observations. This paper expands on a previously reported solution to this
problem: nonresonant scattering due to wave packets. The quasi-linear diffusion
model is generalized to incorporate nonresonant scattering by a generic wave
shape. The diffusion rate decays exponentially away from the resonance, where
shorter packets lower decay rates and thus widen the energy range of
significant scattering. Using realistic EMIC wave packets from $\delta f$
particle-in-cell simulations, test particle simulations are performed to
demonstrate that intense, short packets extend the energy of significant
scattering well below the minimum resonance energy, consistent with our
theoretical prediction. Finally, the calculated precipitating-to-trapped flux
ratio of relativistic electrons is compared to ELFIN observations, and the wave
power spectra is inferred based on the measured flux ratio. We demonstrate that
even with a narrow wave spectrum, short EMIC wave packets can provide
moderately intense precipitating fluxes well below the minimum resonance
energy.
