  Fractured surfaces carry unique details that can provide an accurate
quantitative comparison to support comparative forensic analysis of those
fractured surfaces. In this study, a statistical analysis comparison protocol
was applied to a set of 3D topological images of fractured surface pairs and
their replicas to provide confidence in the quantitative statistical comparison
between fractured items and their replicas. A set of 10 fractured stainless
steel samples was fractured from the same metal rod under controlled conditions
and were cast using a standard forensic casting technique. Six 3D topological
maps with 50% overlap were acquired for each fractured pair. Spectral analysis
was utilized to identify the correlation between topological surface features
at different length scales of the surface topology. We selected two frequency
bands over the critical wavelength (which is greater than two-grain diameters)
for statistical comparison. Our statistical model utilized a matrix-variate-$t$
distribution that accounts for the image-overlap to model the match and
non-match population densities. A decision rule was developed to identify the
probability of matched and unmatched pairs of surfaces. The proposed
methodology correctly classified the fractured steel surfaces and their
replicas with a posterior probability of match exceeding 99.96%. Moreover, the
replication technique shows the potential to accurately replicate fracture
surface topological details with a wavelength greater than 20$\mu$m, which far
exceeds the range for comparison of most metallic alloys of 50-200$\mu$m. The
developed framework establishes the basis of forensic comparison of fractured
articles and their replicas while providing a reliable quantitative statistical
forensic comparison, utilizing fracture mechanics-based analysis of the
fracture surface topology.
