The invention is a differential 3D Quantitative-Imaging Ultrasonic Tomography method for inspecting a layered system that is comprised of a heterogeneous object embedded in a volume of space that comprises layers having an acoustic impedance gradient between the layers providing non-linear beams travels. A transducer grid is attached to the surface of the layered system in a unilateral manner. By sequentially changing the distance between transmitter and receiver the fastest travel times of the ultrasonic oscillations are measured. A differential approach provides from the data the longitudinal wave velocities values for each elementary volume that make up an inspected volume. These values are used to construct two and three-dimensional maps of the longitudinal wave velocity values distribution in the inspected volume and the porosity values distribution in the heterogeneous object. By applying statistical treatment to the obtained data the longitudinal wave velocity in the inspected material matrix part is estimated.
