A method and system for evaluating the cement behind casing and fully inverting acoustic properties of the material, including density and the speed of sound. A density map of the cement sheath is determined using a nuclear logging technique. An acoustic impedance value of the cement sheath is provided, either by measurement using an ultrasonic logging technique or simulated using an acoustic model. The acoustic model may assume a vertical incident plane wave and flat plates for casing and the cement sheath. From the density map and the acoustic impedance value, a map of the speed of sound in the cement sheath, or a gap therein, may be determined.