Full waveform inversion (FWI) is a notable technique that provides high-resolution physical parameters of subsurface media. Although FWI is frequently employed to recover velocity models for relatively weak parameter perturbations, its effectiveness is limited by the lack of low-frequency information in the presence of strong parameter perturbations. To address this limitation, we propose to utilize direct envelope inversion (DEI), which highlights the low-frequency information contained within the seismic envelope data to successfully construct velocity models for strong parameter perturbations. However, conventional DEI requires envelope computation for the source wavefield, which limits the application of memory cost-reduction methods and significantly increases the computational time needed for the envelope. To mitigate these computational challenges, we introduce excitation amplitude (ExA) as a means to reduce the computational cost associated with DEI. By utilizing only the most energetic amplitude and its arrival time at each grid point of the direct envelope virtual source field, this method can reduce the computational time and memory requirement while maintaining the accuracy of the DEI. In the numerical examples, we demonstrate that the proposed method overcomes the computational cost limitations of conventional DEI. Additionally, applying our method to field data acquired in the Arctic helped reconstruct strong scattering models for the subsea permafrost.