Abstract: Methods and apparatuses are provided for detecting and characterizing heterogeneities within a bulk material that exhibit scale-dependent uniformity represented by locally representative volume elements (LRVEs). The invention is particularly useful in the characterization of local variations of crystallographic texture of metals and alloys, including metallurgical Ti alloys. The invention consists of generating ultrasonic waves through different paths in the object, and detecting differences in time, amplitude and/or phase of the detected frequency components traveling the different paths to characterize a statistical mean dimensions of the LRVEs, for example, by autocorrelation. Mean sizes of the LRVEs in the scan directions can be computed by autocorrelation, and mean sizes in the direction of the propagation can also be approximated.