For estimating attenuation, diffraction effects are corrected by transmitting at different frequencies using apertures sized to match the on-axis intensity profile and/or resolution cell size between the transmissions where there is no attenuation. Attenuation causes a variance in return. A rate of change is estimated from a ratio of the magnitude of the signals or displacements responsive to the transmissions. The attenuation is calculated from the rate of change over depth of the ratio.