Method for reconstructing subsurface Q models (110) from seismic data (10) by performing ray-based (60), centroid frequency shift (50) Q tomography. The seismic source waveform's amplitude spectrum is approximated by a frequency-weighted exponential function of frequency (40), having two parameters to adjust to fit the frequency shift data, thereby providing a better fit to various asymmetric source amplitude spectra. Box constraints may be used in the optimization routine, and a multi-index active-set method used in velocity tomography is a preferred technique for implementing the box constraints (100).