For shot-encoded seismic waveform tomography, the restarted L-BFGS algorithm is an effective technique to suppress the crosstalk effect among encoded seismic shots. It restarts the L-BFGS calculation at each iteration segment, consisted of a group of iterations, and re-codes the individual shots randomly not only at the beginning but also at the inside of the iteration segment. Here we simplified this scheme using an invariant shot-encoding within each iteration segment and re-coding individual shots only at the beginning of the segment. This simplification did compromise the image quality at the early stage of inversion, as the crosstalk effect appeared on the inversion result of low-frequency data. However, it eventually achieved both the computation efficiency and the good quality for a multi-scale inversion procedure, which inverts seismic data from low-frequency components to high-frequency components in sequence.