Techniques are described whereby measurements derived from acoustic investigations made from inside a borehole penetraing an earth formation are factorized into components with high depth resolution. In one embodiment travel times of an acoustic wave such as the compressional is factored into mud travel time and interval travel times through the earth formation. In another embodiment amplitude measurements of an acoustic wave are factored into components such as receiver gain, earth formation attenuation, and coupling effectiveness at the boundary between the borehole and the earth formation. In both embodiments an additional component can be factored out that is a function of transmitter to receiver spacings. A modified Gauss-Seidel iteration technique is described whereby iterations can rapidly converge with less sensitivity to large variations in the measurements. Factorization of receiver gains effectively enables calibration of the receivers during well logging.