Seismic envelope inversion (EI) uses low-frequency envelope data to recover long-wavelength components of the subsurface media. Conventional EI uses the same waveform Fréchet derivative as conventional full-waveform inversion. Due to linearization of the sensitivity operator (Born approximation), neither of these methods can yield good inversion results for media with strong preturbations, such as salt domes, when the source lacks low-frequency information. Because seismic envelope data contain large amount of ultra-low-frequency information and the direct envelope Fréchet derivative maps envelope data perturbation directly to velocity perturbation, the direct envelope inversion (DEI) method (based on the direct envelope Fréchet derivative) can handle such strong nonlinear inversion problems. However, this method is sensitive to source wavelet errors. We developed a source-independent DEI method. To achieve the source-independent objective function, we derive a convolution expression for the envelope data. We derive the gradient of the new objective function by using the direct envelope Fréchet derivative. Numerical tests conducted on a 2D salt model indicate that our method can achieve good reconstruction of salt bodies (strong velocity perturbations) and recover low-velocity background structures (weak velocity perturbations), despite using an inaccurate source wavelet.