Methods and apparatus are described for estimating parameters, such as slowness and attenuation, of composite acoustic waves obtained in the course of sonic logging of formations traversed by a borehole. Sonic energy is sensed arriving at a plurality of points spaced vertically along the borehole after refraction, reflection and direct transmission through and along the formations. A window is established of predetermined length and moveout and the composite waves are multiplied by the window. A Fourier transform is obtained of the windowed data and the data are simultaneously analyzed to obtain an estimate of the parameters. The procedure is repeated for different window moveouts and index positions along the composite waves. The analysis is performed at each window position and moveout to obtain the best estimate of the parameters.