1. A differential method of 3D Quantitative-Imaging Ultrasonic Tomography for inspecting a layered system comprised of a heterogeneous object embedded in a volume of space that comprises layers having an acoustic impedance gradient between said layers, wherein said acoustic impedance gradient causes non-linear elastic wave propagation of ultrasonic oscillations through said volume of space, said method comprising: a) providing two or more transducers arranged in a line or as a two-dimensional array on one side of the layered system and in acoustic contact with the upper layer of said layered system, said transducers capable of being activated to either transmit or to receive said ultrasonic oscillations; b) sequentially activating one of said transducers as a transmitter and others of said transducers as receivers of said ultrasonic oscillations to measure the fastest travel times for sequential transmitter/receiver pairs with sequentially changing distances between transmitter and receiver; c) virtually dividing said volume of space into elementary volumes; d) using a differential approach to determine values of the longitudinal wave velocity for each of said elementary volume; and e) applying an ultrasonic computer tomography approach to construct two-dimensional and three-dimensional maps of the distributions of said longitudinal wave velocity values in said volume of space.