Quantifying the intensity of crystallographic preferred orientation (CPO): some practical considerations and recommended practices

Andrew J. Cross 

Crystallographic preferred orientations (CPOs) commonly develop during the crystal-plastic deformation of rocks and minerals, and are widely used to infer strain intensity and geometry, reconstruct deformation conditions, and estimate material anisotropy. Although CPO intensity is often quantified using scalar metrics that reduce the full orientation distribution to a single value, these measures can be highly sensitive to their calculation parameters and input data quality. Here, we examine the performance of two widely used metrics—the J-index and the M-index—using orientation data from a diverse suite of simulated, natural, and experimental specimens. We show that ODF-based measures of CPO intensity such as the J-index (and the ODF-derived variant of the M-index) can vary markedly with kernel halfwidth and ODF construction method. However, when the ODF is constructed using an automatically selected optimal halfwidth, the ODF-derived M-index closely reproduces the M-index calculated in its original form using random-pair misorientation angle histograms. Nevertheless, this original formulation requires no kernel or ODF construction step, and is largely insensitive to its single free parameter—the histogram bin width—leaving far fewer opportunities for user choice to bias the result. Monte Carlo resampling shows that the M-index can be accurately estimated using ~1,000 independent orientation measurements for moderate-to-strong CPOs (M ≥ 0.3), whereas weak CPOs (M ≈ 0.1) may require up to ~3,900 measurements. We further examine several other controls on measured CPO intensity, including the number of measurements taken per grain, as well as the quality and construction parameters of the orientation map. Because the maximum attainable value of the M-index depends on CPO type, we also propose a normalisation scheme that, within a defined set of end-member textures, allows for more direct comparison among specimens of differing type. Together, these results highlight the inherent limitations of reducing complex orientation distributions to one-dimensional metrics, and underscore the importance of consistent methodology, adequate sampling, and transparent reporting. We therefore set out a series of practical guidelines intended to improve the robustness and comparability of CPO intensity estimates among studies.